Lossless Compression of Audio


This page comparing various lossless audio compression algorithms and programs hasn't changed much since January 2003.  I am no longer maintaining it and I suggest that the best place to maintain an up-to-date account of this subject is in the Wikipedia at:
http://en.wikipedia.org/wiki/Audio_data_compression#Lossless_compression

Some short updates


If you want the test samples . . .

Update 2010-04-16:
I apologise for the test files not being available for some time.  I have not been able to find my December 2000 CDRs of these files.  This was the basis of what I used to have in a separate directory, which I described in this way:

I have a set of audio samples which I think give a good range of material to try compression algorithms on.  I can send this to you on two CD-Rs if you like, or if you have broadband Internet and are happy to download a bunch of stuff (674 Megabytes) you can get Zipped (ordinary Zip format) compressed versions of the 11 music tracks I used for these tests.  Please see ../../0-big/ and give the username lossless and the password audio.  There is also a bunch of compression programs there and the batch files etc. I used for testing.  The files on these CD-Rs, and in the above-mentioned directory, are from December 2000. 

I have found most of the test files - 00 HI to 10SI - and these are avialable: Please see ../../0-big/ and give the username lossless and the password audio.  The test files are stereo 44.1kHz 16 bit .WAV files, compressed with PKZIP - so they can be decompressed by WinZip and many other programs.  The Unix/Linux "unzip" program can also decompress them.

Why I am no longer pursuing this field

The question of compressing audio without any loss of quality (including especially without having to even think about how lossy a lossy algorithm is, because the binary bits are fully restored) is obviously important.  I partially developed my own algorithm and found it was not as good, at least initially, as existing approaches.

I have a very strong sense - and I think it is shared by many people with experience in this field - that existing algorithms come within a few percent of theoretical limits in terms of compression efficiency.  No-one knows exactly the maximum compression which could be achieved on a given file, but the way the various algorithms all approach a particular percentage for a particular piece of music, and how those percentages vary widely according to the nature of the music, seems to indicate the best of the algorithms is getting close to some unknown theoretical limit.

Therefore, in my view, straight-out improvements in compression ratio are likely to be limited to a few percent.   Since the cost of storage is falling precipitously (RAM, hard disks, FLASH memory, writeable DVDs etc.) and since the costs of transmission (Internet in general and broadband access to the Net in particular) are falling while transmission speeds are generally improving, I don't feel like doing a lot of work to achieve minor improvements in file size. However, I salute those who are pursuing this!

There are improvements to be made beyond compression ratio:
Before I sign off, here is a mini rant about sampling rate and bit-depth for audio recording.

When recording raw audio, I think its good to use a 20 bit converter and run at a higher than normal (44.1kHz) sampling rate if possible.  This makes it easier to avoid clipping with unexpected high peaks.

With the following exceptions, I think that for mixed, finished, music, there is no point in going beyond 44.1kHz 16 bit stereo:

When thinking about edited, ready-to-listen-to, audio, as far as I know, in any realistic listening situation, with proper care and the best techniques, there is no audible degradation in using 16 bit 44.1kHz stereo.  By this I mean that if the physical sound level is such that the highest peaks won't cause serious discomfort, then you won't be able to hear the noise and distortion which is inherent in properly done 16 bit audio.  There should be no distortion - because the dither should linearise it and the result becomes part of the 1 step noise floor.  With care, it is not hard to get the frequency response flat from 30 Hz to 18 kHz, and for there to be no "phase distortion" - no shifting of signals according to their frequency.  So all that is left is the dither and the way the dither interacts with the signals to linearise them, perceptibly several bits below the limits of a 16 bit system without dither.

Many people attest that they can hear the difference between 16 bit 44.1kHz audio and some higher sampling rate and/or bit depth.  My response to this is that they are not necessarily listening to 16 bit 44.1kHz done properly - or alternatively that the difference they hear is actually that the other format does change the sound.

The only real test is to switch between a live (analogue microphone) signal and its digitised and regenerated version. 

Most physical audio situations (rooms, outdoors etc. with a microphone) have a signal-to-noise ratio well below the ~96db inherent in a properly engineered 16 bit system.  Good Delta-Sigma ADCs, as far as I know, are capable of remarkably good conversion of any waveform (apart perhaps from rail-to-rail square-waves and the like), and properly constructed oversampling DACs can work fine too.  These can both work without any significant distortion, noise or phase problems.

Audio recorded at 96kHz with a 24 bit sample rate will be very hard to compress losslessly.  Firstly, the sampling rate is over twice what I think it really needs to be.  Secondly, of the 24 bits, only 14 to 16 are going to be of a musical signal and the rest will be random noise from:

Below this, apart from a few fixes to typos and other things (which were important - thanks!) the page is basically as it was in January 2003.



My particular interest is in delivery of music via the Net - with compression which does not affect the sound quality at all.  I am primarily interested in compression ratios, not speed of the programs.  This is the first web site devoted to listing all known lossless audio compression algorithms and software - please email your suggestions and I will try to keep it up-to-date.

Copyright Robin Whittle 1998 - 2000 rw@firstpr.com.au  Originally written 8 December 1998. Complete new test series and update 24 November to 11 December 2000.

Latest update 13 January 2003.  The update history is at the bottom of this page.

Back to the First Principles main page -  for material on telecommunications, music marketing via Internet delivery, the Devil Fish TB-303 modification, the world's longest Sliiiiiiinky and many and other show-and-tell items.

To the /audiocomp/ directory, which leads to material on lossy audio compression, in particular, comparing AAC, MP3 and TwinVQ.
 
This new series of tests was performed as a project paid for by the Centre for Signal Processing, Nanyang Technological University, Singapore.  Dr Lin Xiao, of the Centre, whose program AudioZip is one of the ten programs I tested, was keen that my tests be independent.  To this end, I used exactly the same test tracks I used in 1998, adding only two pink noise tracks which do not count towards the averages for file-size and compression ratio .  Thanks to Lin Xiao and his colleagues for enabling me to do a proper job of this!

Let me know if you would like me to send you a dual CD-R set with all the test files so you can reproduce these tests yourself.


Tests: what can be achieved with lossless compression?

Short answer: 60 to 70% of original file-size with pop, rock,  techno and other loud, noisy music; 35% to 60% for quieter choral and orchestral pieces.

My primary interest is in compression of 16 bit 44.1 kHz stereo audio files - as used in CDs.  There are lossless compression systems for 24 bit and surround-sound systems.  While I have a few links to these, they are not tested here.   My tests are for programs which run on a Windows machine, though I have Linux machines as well, and some of these programs run under Linux too.   I only found one Mac-only lossless compressor (ZAP) and have not tested it.

In my 1998  tests I was not interested in speed, but in November 2000, in view of the fact that the compression ratios of the leading programs were fairly similar, I decided to test their speed as well, since this varies enormously.

Five programs distinguished themselves with high compression ratios:

Since each program performed differently on different types of music, and since the choice of music in these tests is arbitrary, I cannot say with confidence that any of these programs will produce generally higher rates of compression than the others.  With my particular test material, all five produce significantly higher rates of compression than the other programs I tested.

Since the difference between the best three programs and the next best three is only a few percent, many other factors are likely to influence your choice of which program is most useful to you.

A full description of the test tracks follows the test results themselves.  All tracks were 44.1 kHz 16 bit stereo .WAV files read directly from audio CD and are either electronic productions or microphone based recordings - except for my Spare Luxury piece which was generated entirely with software.    The music constituted 775 Megabytes of data - 73 minutes of music.   The tabulation of these figures was done by MS-DOS directory listings and pasting the file-sizes as a block into a spreadsheet.  (See notes below on exactly how I did it.)  Those files are here:  sizes9.txtand  lossless-analysis.xls .  I am pretty confident there are no clerical or other errors, but these intermediate documents enable you to check.

Audio files contain a certain amount of information - "entropy" - so they cannot be compressed losslessly to any size smaller than that.  So it is not realistic to expect an ever-increasing improvement in lossless compression algorithm performance.  The performance can only approach more closely whatever the basic entropy of the file is.  No-one quite knows what that entropy is of course . . . I think that would require understanding the datastream in a way which is exactly in tune with it's true nature.  For instance a .jpg image of handwriting would appear to contain a lot of data, unless you could see and recognise the handwriting and record its characters in a suitably compressed format.  The true nature of sound varies with its source, physical environment and recording method, and a lossless compression program cannot adapt itself entirely to the "true" nature of the sound in each piece of music.  Therefore it is not surprising that different algorithms work best on different kinds of music.

Here are the test results, with the figures in the main body of the table showing the compressed file size as a  function of the original size.  Those instances which are the smallest are in bold-face, larger characters and with a green background.  The average file sizes are the average of the file sizes of the test  tracks 00 to 10.  The average compression ratio is simply 100 divided by the average file size percentage. Except where noted (WaveArc -4 and with RKAU -l2 and -l3) I have selected the highest compression option for all programs tested.

The two test files 11PS and 12PM are pink-noise files with a -12dB signal level.  11PS is independent stereo channels and 12PM is the same signal on both channels -  the left channel of 11PS.  These are not realistic tests of compression of music, but they show something about the internal functioning of the programs.  The compression ratios for these pink noise files do not contribute to the averages at the bottom of the table.  It is unavoidably wide, so scroll sideways and print in landscape.   The table alone, for those who want to print it, is available as an HTML file here: table.html.

  Shorten
Tony
Robinson
Wave
Zip
Gadget
labs
MUSI-
Compress
Wav-
Arc -4
Dennis Lee
Wav-
Arc -5
Dennis Lee
Pegasus
SPS
jpg.com
Sonarc
2.1i 
Richard
P. 
Sprague
LPAC
Tilman 
Liebchen
Wav-
Pack 
3.6B 
David
Bryant
Audio
Zip
Lin Xiao
Monkey
3.81B
Matthew
T. 
Ashland
RKAU
1.07
Malcolm
Taylor
00HIChoral 37.23 44.81 36.49 34.73 36.69 40.91 39.57 41.77 40.28 38.98 33.28
01CESolo Cello 42.01 44.71 41.98 40.44 41.14 41.53 40.33 41.38 40.52 39.61 39.18
02BEOrchestra 55.68 57.99 42.00 40.72 42.43 53.15 40.55 43.89 43.48 39.86 39.01
03CCBallet 58.28 60.29 57.32 54.58 56.52 55.97 54.31 56.51 55.20 53.82 52.80
04SLSoftw. Synth. 42.54 45.23 42.02 39.64 40.70 40.99 39.61 41.88 40.65 38.32 33.06
05BMClub Techno 74.07 75.43 69.51 68.45 70.70 72.91 68.45 69.75 69.34 66.81 66.60
06EBRampant Techno 68.50 69.56 66.95 66.23 67.67 68.97 67.02 66.48 65.80 66.30 65.88
07BIRock 65.04 66.54 62.07 58.79 62.48 59.50 57.59 61.78 58.36 57.15 56.95
08KYPop 74.36 75.28 71.39 70.41 72.08 71.13 69.55 71.76 69.47 68.09 68.07
09SRIndian Classical 1 53.54 56.11 46.70 44.63 52.39 51.99 44.45 46.58 47.76 43.41 43.89
10SIIndian Classical 2 58.60 61.50 56.12 50.99 53.46 50.99 49.73 54.34 50.70 49.24 49.23
11PSPink noise 86.70 89.06 86.25 86.21 86.42 87.13 86.15 86.54 85.87 86.45 85.49
12PMPink noise   mono 86.71 89.06 43.15 43.14 43.27 87.14 43.09 46.29 78.32 46.24 42.75
Average size
Tracks 00 - 10
57.26 59.77 53.87 51.78 54.20 55.28 51.92 54.19 52.87 51.05 49.81
Average ratio
Tracks 00 - 10
1.746 1.673 1.856 1.931 1.845  1.809 1.926 1.845 1.891 1.959 2.008
  Shorten WaveZip WaveArc
-4
WaveArc
-5 
Pegasus
SPS
Sonarc LPAC Wave
Pack 
Audio
Zip
Monkey RKAU
Time to compress 3min 
20sec Kylie pop track 
(500 MHz Celeron)
0:17
0:22
0:30
 4:37
1:42
 66:00
1:18
0:21
6:26
0:28
3:14

 
The compress time tests were performed with a 500MHz Celeron with 128MB of RAM and a 13Gig IDE hard disc.  It took 7 seconds to copy the test file (00ky.wav 35.9 MB) from and to the disc.  These figures should be regarded as accurate to only +/- 20%.

The test files are described below.  6 second 1 Megabyte sample waveforms are provided. The .wav files are stored in a directory which is not linked to exactly here, to stop search engines downloading them. The directory is /audiocomp/lossless/wav/  .  Type this into your browser if you wish to download .wav files.   Compression of these 6 second samples will no-doubt produce different ratios then compressing the entire file, due to variations in the sound signal from moment to moment.

After I did these tests, I discovered some non-ideal aspects of two files:

I have not changed them, since they are the same files as I used in 1998.
Description of audio track 
(Size Megabytes)
Average 
level dB
Smallest 
file size 
as ratio 
of original
Length
min:sec
Comments Source
Choral - Gothic Voices: Hildegard von Bingen: Columbia aspexit (00HI.wav 55.9MB) -29.5 34.7% 5:17   A Feather on the Breath of God Hyperion CDA66039 
Solo cello - Janos Starker J.S. Bach: Suite 1 in G Major (01CE.wav 173.2MB) -20.4 40.3% 16.45   Sefel SE-CD 300A (Out of print in 2005.)
Orchestra - Beethoven 3rd Symphony (02BE.wav 43.6MB) -21.1 40.6% 4.07 Mono Berlin Philharmonic Music and Arts CD520, from a Classic CD magazine issue 54 cover disc.
Ballet - Offenbach, Can Can (03CC.wav 24.4MB) -14.6 54.3% 2.18 12 sec 
silence
Unknown orchestra, Tek (Innovatek S.A. Bruxelles) 93-006-2
Software synthesis: my "Spare Luxury" Csound binaural piece (04SL.wav 85.0MB) -20.5 39.6% 8.02   I made this in 1996.  It has not been released on CD.
Club techno - Bubbleman (Andy Van): Theme from Bubbleman (05BM.wav 59.1MB) -11.7 68.5% 5.35   Vicious Vinyl Vol 3 VVLP004CD
Rampant trance techno - ElBeano (Greg Bean): Ventilator(06EB.wav 44.0MB) -14.3 65.8% 4.09   Earthcore EARTH 001
Rock - Billy Idol, White Wedding (07BI.wav 88.9MB) -17.3 57.6% 8.23   Chrysalis CD 53254
Pop - Kylie Minogue, I Should be so Lucky (08KY.wav 35.9MB) -14.9 69.5% 3.23   Mushroom TVD93366
Indian classical (mandolin and mridangam) - U. Srinivas:Sri Ganapathi (09SR.wav 71.7MB) -12.1 44.4% 6.45   Academy of Indian Music (Sandstock) Aust.SSM054 CD
Indian classical (sitar and tabla) PT. Kartick Kumar & Niladri Kumar,: Misra Piloo (10SI.wav 89.4MB) -19.4 49.7% 8.27   OMI music D4HI0627
Pink noise stereo (11PS.wav) -12.2 85.8% 1.00    
Pink noise mono (12PM.wav) -12.2 43.1% 1.00    

The 10 programs I tested

Shorten  Tony Robinson

WaveZip  Gadget labs (MUSI-Compress)

WavArc Dennis Lee

Pegasus SPS jpg.com

Sonarc 2.1i  Richard P. Sprague

LPAC  Tilman Liebchen

WavPack 3.1 David Bryant

AudioZip  Lin Xiao Centre for Signal Processing, Nanyang Technological University, Singapore

Monkeys Audio 3.7 Matthew T. Ashland

RKAU Malcolm Taylor

FLAC Josh Coalson (Not tested yet.) 


Any program listed as running under Windows 95 or 98 will presumably run under Windows ME, NT, 2000, XP etc. 

Shorten Tony Robinson
 
Homepage http://www.softsound.com/Shorten.html
email info@softsound.com
Operating systems MS-DOS, Win9x.
Versions and price Win9x and demos free. More functional MS-DOS and Win9x version available for USD$29.95.
Source code available? (In the past.)
GUI / command line GUI & Command line.
Notable features High speed.
Real-time decoder In paid-for version.
Other features
  • Near-lossless compression available. 
  • Shorten "supports compression of Microsoft Wave format files (PCM, ALaw and mu-Law variants) as well as many raw binary formats".
  • Paid-for version includes:
    • Batch encoding and decoding.
    • Creation of self-extracting encoded files.
    • MS-DOS Command line encoder/decoder.
Theory of operation A 1994 paper by Tony Robinson is available at from this Cambridge University site.
Options used for tests GUI program: "lossless".

Technical background to the program is at:  http://svr-www.eng.cam.ac.uk/reports/abstracts/robinson_tr156.html .  I tested version "2.3a1 (32 bit)" as reported in the GUI executable.  This was from the shortn23a32e.exe installation file.

Seek information in Shorten files, and other programs which compress to the Shorten file format

There is another version of Shorten, "shortn32.exe" V3.1 at: http://etree.org/shncom.html.  etree.org is concerned with lossless compression for swapping DAT recordings of bands who permit such recordings.  This is an MS-DOS executable which reports itself (with the -h option) as:

    shorten: version 3.1: (c) 1992-1997 Tony Robinson and SoftSound Ltd
  Seek extensions by Wayne Stielau - 9-25-2000
 

This adds extra data to the file, or as a separate file, to enable quick seeking within a file for real-time playback.  It compresses and decompresses.   I was unable to get it to compress without including the seek data, so I did not test it.   I assume its performance is the same as the program I obtained from Tony Robinson's site.

Another program based on  Tony Robinson's Shorten is by  Michael K. Weise - a Win98/NT/2000 GUI program called "mkw Audio Compression Tool - mkwACThttp://etree.org/mkw.html .  This generates compressed Shorten files with seek information. It can also compress to MP3 using the Blade codec.  I tried installing the "version 0.97 beta 1" of this program, but there was an error.

Real-time players for Shorten files

In addition to the real-time player included in the full (paid-for) version of Shorten, there is a free plugin for the ubiquitous Windows MP3 (etc. & etc.) audio player Winamp http://www.winamp.com .  The plug-in - ShnAmp v2.0 - http://etree.org/shnamp.html.  This uses the special files with seek information produced by the programs mentioned above.

There is a functionally similar real-time player program for Xmms the X MultiMedia System (Linux: and other Unix-compatible operating systems):xmms-shnwhich is freely available, with source code, from: http://freeshell.org/~jason/shn-utils/xmms-shn/ .
 


WaveZip Gadget labs (MUSICompress)

 
Homepage WaveZip http://www.gadgetlabs.com but see note below on availability.
MUSICompress http://hometown.aol.com/sndspace
email None.
Operating systems Win9x.  (MUSICompress command line demo program runs in DOS box under any version of Windows.)  
Versions and price Win9x evaluation version is free.  A paid-for 24 bit upgrade was available, but Gadget Labs has now gone out of business.  (MUSICompress command line demo program is free to use.)
Source code available? No, but see the Al Al Wegener's Soundspace site (below) for information and source code regarding the MUSI-Compress algorithm.
GUI / command line GUI.
Notable features High speed.  Handles 8 and 16 bit .WAV files in stereo and mono.  Also supports ACD (Sonic Foundry's ACID) and BUN (Cakewalk Pro).
Real-time decoder No.
Other features Very handy file selection system
Theory of operation Soundspace Audio's page for their MUSICompress algorithm: http://hometown.aol.com/sndspace   See notes below.
Options used for tests There are no options.  (But see note below on commandline version of MUSICompress.)

On 1 December 2000, Gadget Labs ceased trading and put some of its software in the public domain, with the announcement:

"We regret to announce that Gadget Labs is no longer in business.  We sincerely appreciate the support from customers during the last 3 years, and we regret that we didn't meet with enough success to be able to continue to deliver our products and service.  This web site includes technical information and software drivers that are being placed in the public domain.  Please note that usage of the information and drivers contained here is at the user's sole discretion, responsibility, and risk."
Gadget Labs was primarily known for its digital audio interface cards.  A Yahoo Groups discussion group regarding Gadget Labs is here.  The WaveZip page at their site (wavezip.htm) has disappeared.  There is no mention of WaveZip at their site at present.   For now, I have placed the evaluation  version 2.01 of WaveZip in a directory here:  WaveZip/ . It is 2.7 megabytes.

In October 2001, Al Wegener wrote to me to point out the command line demo version of MUSICompress which is available for free (subject to  non-disclosure and no-dissassembly) at his site.  He wrote:
Even though the console interface is not nearly as nice as WaveZIP was, people can still submit WAV-format files to this PC app and both compress and decompress their files.  This version also supports lossy compression, where users can play with a decrease in quality (one LSB at a time), vs. an increase in compression ratio.

By the way, I've gotten several new customers recently that use MUSICompress specifically because it's fast.  On many of these customers' files, an extra 10% compression ratio just isn't worth a 20x wait.

MUSI-Compress Theory

The information sheet at: http://members.aol.com/sndspace/download/musi_txt.txt indicates that MUSI-Compress is capable of reducing rock recordings to between 60 and 70% of their original size. An informative paper from the developer, Al Wegener, is available in Word 6 format from the Soundspace site.  MUSICompress is written in ANSI C using integer math only.  It has been ported to at least two DSPs and is used in the WaveZIP program (see below).

There is also a Matlab version, and the documentation which comes with this indicates that MUSICompress typically uses:
Compression requires between 35 and 45 instructions per sample.
Expansion requires between 25 and 35 instructions per sample

According to Al Wegener, like other commercial lossless audio compression algorithms, MUSICompress uses a predictor to approximate the audio signal - encoding the prediction data in the output stream - and then computes a set of difference values between the prediction and the actual signal.  These difference values are relatively small integers (in general) and these are compressed using Huffman coding and sent to the output stream.  The compress and decompress functions can apparently be implemented in hardware with 4,700 gates and 20,500 bits of RAM (compress) and 3,800 gates and 1,500 bits of RAM (decompress) - which sounds pretty snappy to me.
 
 
The diagram to the left, from the abovementioned paper, depicts the approach taken by all the compression algorithms reviewed on this page.  The raw signal is approximated by some kind of "prediction" algorithm, the parameters of which are selected to produce a wave quite similar to the input waveform.  Those parameters are different for each frame (say 256 samples) of audio and are packed into a minimum number of bits in the output file (or stream, in a real-time application).  Meanwhile, the difference between the "predicted" waveform and the real signal is packed into as small a number of bits as possible.  Often, the "Rice" coding (AKA Rice packing) algorithm is used, but MUSI-Compress uses Huffman packing instead.  Some of the material mentioned below contains more detailed theoretical descriptions of Rice packing and other algorithms - and I have my own explanation below

This diagram is relevant to all the lossless algorithms I know of. (I worked on my own algorithm which worked on different principles for a while - but it did not work out well.  A good "prediction" system is crucial.)  The predictor is replicated in the decoder - and it must work from prediction parameters and the previously decoded samples.  The predicted value is added to the "error" value to create the final exactly correct value for that sample.  Then the prediction algorithm is run again, based on the newly decoded sample and some previous ones, to predict the next sample.


WavArcDennis Lee

 
Homepage Unknown - but the program is available here: wavarc/..
email Unknown.
Operating systems MS-DOS. (ie, in an MS-DOS window in Win9.x.)
Versions and price Free. 
Source code available? No. 
GUI / command line Command line.
Notable features Potentially very high compression.  Multiple files stored in one archive.
Real-time decoder No.
Other features High compression ratio.  Selectable speed/compression trade-off. Compresses WAV files and stores all other files without compression in the archive.
Theory of operation ?
Options used for tests "a -c4" and "a -c5".

Dennis Lee's Waveform Archiver is a freeware command-line program to run under MS-DOS or in a Windows command line mode.  It can store multiple .WAV files in a single archive.

Dennis Lee's web page:  http://www.ecf.utoronto.ca/~denlee/wavarc.htm disappeared sometime in 1999.  Emails to that site (University of Toronto) enquiring about him have not resulted in any replies.

No source code was available, and there was no mention of what algorithms are used.  This program was made available on a low-key basis - but its performance in "compression level 5" mode significantly exceeds the alternatives that I was aware of when I did my first rounds of tests in late 1998.  When compressing, I found that the report it gives on screen about the percentage file size is sometimes completely wrong.  I tested version 1.1 of 1 August 1997.

Dennis told me by email on 4 December 1998 that he had done a lot of work on version 2.0 of Waveform Archiver - but is not sure when it will be finished:


WavArc began life in 1994, as explained in wavarc/WA.TXT .  I would be very glad to hear of Dennis Lee.  I did an extensive web search in November 2000, but found no leads.


Pegasus SPSjpg.com

 
Homepage http://www.jpg.com/products/sound.html
email sales@jpg.com
Operating systems Win9x.
Versions and price Full version USD$39.95.
Evaluation version limited to 10 compressions.
Source code available? No. 
GUI / command line GUI.
Notable features WAV files, 8 and 16 bit, stereo and mono. 
Real-time decoder No.
Other features Batch compression in paid-for version.
Theory of operation http://www.jpg.com/imagetech_els.htm for generalised ELS algorithm. 
Options used for tests There are no options.

In 1997 Krishna Software Inc.  http://www.krishnasoft.com. wrote a lossless audio compression program for Windows.  The program has some limited audio editing capabilities and several compression modes, but the most significant lossless compression algorithm - ELS - comes from Pegasus Imaging, http://www.jpg.com who seem to have developed it initially for JPG image compression.  The SPS program is available from both companies.

Pegasus-SPS provides four lossless compression modes and has the ability to truncate a specified number of bits for lossy compression.  I used the default and highest performance "ELS-Ultra" algorithm for my tests.  This was reasonably fast and produced results a fraction of a percent better than the next two best performing algorithms. When the compression function is working, this program seems to use virtually all the CPU cycles - at least under Windows 98 - so don't plan on doing much else with your computer!

Some information on ELS - Entropy Logarithmic Scale - encoding is at: http://www.pegasusimaging.com/imagetech_els.htm this leads to a .PDF file which has a scanned version of a 47 page 1996 paper explaining the algorithm: "A Rapid Entropy-Coding Algorithm" by Wm. Douglas Withers.

I tested version 1.00 of Pegasus-SPS.


Sonarc 2.1i  Richard P. Sprague

 
Homepage  None.
email  None.
Operating systems MS-DOS.
Versions and price  Was shareware, but author is uncontactable.
Source code available? No. 
GUI / command line Command line.
Notable features  
Real-time decoder No.
Other features  
Theory of operation
Options used for tests "-x -o0"  = use floating point and for each frame, search for the best order or predictor.

Sonarc, by Richard P. Sprague was developed up until 1994. His email address was "76635.652@compuserve.com" but in December 1998, this address was no longer valid. Sonarc has quite good compression rates, but it is very slow indeed.

There is an entry for it in the speech compression FAQ http://www.speech.cs.cmu.edu/comp.speech/Section3/Software/sonarc.html . Sonarc is also listed in Jeff Gilchrist's magnificent MS-DOS/Windows "Archive Comparison Test" site http://compression.ca/act/act-index.html which gives an FTP site for the program:     ftp://ftp.elf.stuba.sk/pub/pc/pack/snrc21i.zip .  This is the program I tested: version 2.1i. You can get a copy of it here:  sonarc/ . The programs are MS-DOS executables, dated 27 June 1994.  The documentation file, with the shareware arrangements and author's contact details is here: sonarc/sonarc.txt .  (A page of links regarding speech coding and the like: http://www.answerconnect.com/articles/speech-resources .)


LPAC Tilman Liebchen

 
Homepage http://www.nue.tu-berlin.de/wer/liebchen/lpac.html
email
Operating systems Win9x/ME/NT/2000, Linux, Solaris.
Versions and price Free.
Source code available? Tilman Liebchen writes that he is contemplating some form of availability, and that   "the LPAC codec DLL can be used by anyone for their own programs. I do not supply a special documention for the DLL, but any potential user can contact me.".
GUI / command line GUI and command line.  In the future (Dec 2000) the LPAC codec DLL will operate as part of the Exact Audio Copy CD ripper.
Notable features 8, 16, 20 and 24 bit support. 
Real-time decoder Yes, and a WinAmp plug-in.
Other features High compression ratio.  CRC (Cyclic Redundancy Check) for verifying proper decompression.
Theory of operation Tilman Liebchen writes "adaptive prediction followed by entropy coding". 
Options used for tests Extra High Compression, Joint Stereo and no Random Access. 

Tilman Liebchen is continuing to actively develop LPAC, the successor to LTAC which I tested in 1998.
The results shown here are for the "Extra High Compression" option with "Joint Stereo" and no "Random Access".  The Random Access is to aid seeking in a real-time player, and adds around 1% to the file size.  But see the sizes9.txt for the actual file sizes.  In all cases not using the "Joint Stereo" option produced files of the same size or larger.

On 17 January, Tilman wrote:

The new LPAC Codec 3.0 has just been released. It offers significantly
improved compression ("medium" compression is now better than "extra
high" compression was before) together with increased speed (approx.
factor 1.5 - 2). I would be lucky if you could test the new codec and
put the results on your page.
I haven't tested it yet.
 

WavPack 3.1 David Bryant

 
Homepage http://www.wavpack.com
email david@wavpack.com
Operating systems MS-DOS
Versions and price Free.  Version 3.1 and 3.6 Beta.
Source code available? No.
GUI / command line Command line.
Notable features High speed. 
Real-time decoder WinAmp plugin currently being developed.
Other features Compresses non .WAV files, including Adaptec .CIF files for an entire CD. 
Nice small distribution file < 82 kbytes.
Theory of operation http://www.wavpack.com/technical.htm
Options used for tests No options affected the lossless mode.

I tested version 3.6 Beta of WavPack, using the -h option for the high compression mode which Dave Bryant added in 3.6.  WavPack is freely available, without source code but with a good explanation of the compression algorithm.  It is intended as a fast compressor with good compression ratios for .wav files.  Compression and decompression rates of 8 times faster than audio are achieved on a Pentium 300 MHz machine. The algorithm makes use of the typical correlation which exists between left and right channels in a stereo file.  Two additional features are lossless compression of any file, with high compression for those containing audio (such as CD-R image files) and selectably lossy compression.

 

AudioZip  Lin Xiao  Centre for Signal Processing, Nanyang Technological University, Singapore

 
Homepage Was: http://www.csp.ntu.edu.sg:8000/MMS/MMCProjects.htm  This is now defunct.  Lin Xiao will let me know of a new site soon. (17 July 2002)
email Lin Xiao (Dr) Previously at EXLIN@ntu.edu.sg  He is now longer with the University.  Please contact me if you want his email address.
Operating systems Win9x.
Versions and price Free.
Source code available? No. 
GUI / command line GUI.
Notable features High compression ratio. 
Real-time decoder No.
Other features  
Theory of operation "LPC with Rice encoding." 
Options used for tests Maximum.

The current version of AudioZip is rather slow - at least at the Maximum compression mode, which I used in these tests. Its user interface is quite primitive, for instance it is necessary to manually enter the name of each compressed file.  However Lin Xiao writes that he and his team are working to make AudioZip faster and more user friendly.  See the note below in the RKAU section on how AudioZip and RKAU achieved the highest compression ratios for the pink noise file.
 


Monkey's Audio 3.7 - 3.81 Matthew T. Ashland

 
Homepage http://www.monkeysaudio.com
email email@monkeysaudio.com
Operating systems Win9x.
Versions and price Free.
Source code available? "Freely available source code, simple SDK and non-restrictive licensing - other developers can easily use Monkey's Audio in their own programs -- and there are no evil restrictive licensing agreements."
GUI / command line GUI and command line.  Encoder can be used by Exact Audio Copy CD ripper.  
Notable features High speed and high compression. 
Real-time decoder Standalone program and plugins for Winampand Media Jukebox.  Also, apparently available as a plugin for Windows Media Player:  http://www.mediaxw.org .
Other features CRC checking. Includes ID3 tags as used in MP3 to convey information about the track.  Can be used as front end for other compressors, including WavPack, Shorten and RKAU.  Compresses WAV files, mono or stereo, 8, 16 or 24 bits.
Theory of operation Adaptive predictor followed by Rice coding.
http://www.monkeysaudio.com/theory.html
Options used for tests Command line version -c4000.

I tested the command line 3.81 Beta 1 commandline-only version of Monkey's Audio, using the -c4000 option for highest compression.  A separate renamer program is handy for changing the extension of file names - it can recurse into sub-directories.  Monkey's Audio is actively being developed - in April 2002, the version was 3.96.

 



RKAU Malcolm Taylor

 
Homepage http://rksoft.virtualave.net/rkau.html
email mtaylor@clear.net.nz
Operating systems Win9x.
Versions and price Free.
Source code available? No. 
GUI / command line Command line. (But Monkeys Audio can be a GUI front end.)
Notable features High compression. 
Real-time decoder Winamp plugin.
Other features Selectable lossy compression modes.
Can include real-time seek information for use with realtime players.
Theory of operation ?
Options used for tests -t- -l2
-t- -l2 -s-
-t- -l3
-t- -l3 -s-

I tested the v1.07 version, with options -t-" to not include real-time tags.  Malcolm told me that the highest compression option "-l3" sometimes produced compression lower than "-l2", so I tried both options.  Likewise the program's default behaviour of assuming there is something in common with both stereo channels does not always lead to the best compression.  I tried RKAU with and without the -s- option, giving me four sets of file sizes.  See ( oops - this file has gone missing: analysis-rkau-107.html ) for these results and the "best-of" set chosen from the four options.  The best-of set is reproduced below.  These are the figures I have used in the main comparison table.
 
 
  With or without -s- 
to disable separate stereo channels
Either -L2 or -L3 Best of RKAU 1.07 -t- with or without -s- and at either -l2 or -l3
%
00HI -s- L2 18,610,940 33.28
01CE     L3 69,471,291 39.18
02BE     L3 17,001,008 39.01
03CC     L3 12,879,953 52.80
04SL -s-   L3 28,109,211 33.06
05BM     L3 39,382,534 66.60
06EB     L2 28,985,245 65.88
07BI     L3 50,598,306 56.95
08KY     L3 24,435,044 68.07
09SR   L2 31,464,353 43.89
10SI -s- L2 44,015,255 49.23
11PS -s-   L3 9,048,056 85.49
12PM   L2 4,524,830 42.75
Average size00 - 09       49.812
Average ratio       2.00755

Note that the average file size and compression ratio is based on the best achievable after compressing each file in four ways and manually choosing the smallest file size - something which is not likely to be practical for everyday use.  It shows that RKAU has potentially better compression ratios than other programs for the files I tested, but that at present, the program is not smart enough to choose the best approach for each file.

The best results with any one option were for "-l2" (with -t- and without -s-).  The average file size was 50.132% and the average compression ratio was 1.99475.

Malcolm suggests that other programs would benefit from correct choice of whether or not to treat the stereo channels separately, or to treat them together (I guess compressing L+R as one channel and L-R as the other, presumably quieter channel).  You can see by the results for the stereo and "mono" (both stereo channels the same) which programs are taking notice of stereo correlations.  RKAU does this by default, but sometimes it would be better if it did not.  Here are the options for each program:
 
 
Program Default - does it recognise correlation between channels? Option to control
Joint Stereo?
Comments
Shorten   No.  
WaveZip (Gadget Labs)   No.  
WaveArc Yes. No.  
PegausSPS Yes. No.  
Sonarc   No.  
LPAC Yes. Joint Stereo is on by 
default.
Best to use Joint Stereo - the results are the same or better then without it.
WavPack   No.  
AudioZip To some extent. No.  
Monkey 3.81 beta Yes. No.  
RKAU Yes. Yes: -s- -s- is sometimes better. -l2 is sometimes better than -l3. 

I have not counted the pink-noise results towards the average compression percentages/ratios, because they do not represent musical signals, it is interesting to see which algorithm achieves the highest compression ratio for the stereo pink noise file.  This signal has no musical pattern in terms of spectrum or sample-to-sample correlation other than pink noise filtering of white noise to give a spectrum of -3dB per octave, compared to white-noise (each sample completely random) which has a flat frequency response.  (For more on pink noise, see: dsp/pink-noise/).  This indicates that the RKAU and AudioZip's algorithms are highly attuned.
 


FLAC Josh Coalson

 
Homepage http://flac.sourceforge.net/
http://sourceforge.net/projects/flac
email jcoalson@users.sourceforge.net
Operating systems Win9x, Linux, Solaris - any Unix.
Versions and price Free.
Source code available? Yes!  GPL and LGPL.  Written in C.
GUI / command line Command line. 
Notable features Open source, patent-free format and source code for codec.
Real-time decoder Winamp and XMMS plugins.
Other features Uses stereo interchannel correlation in several possible ways, including variants such as L, (R-L).  Several predictor algorithms and two approaches to Rice coding of the residuals.  All these can be used optimally per block.  The current version of the codec uses fixed blocksizes, but the format enables them to be varied dynamically.  Provision for metadata, such as ID3 tags.
Theory of operation http://flac.sourceforge.net/format.html
Options used for tests Not tested yet.

FLAC (Free Lossless Audio Coder) was released in an Alpha form on 10 December 2000.    I have not yet tested it.  There are a number of parameters which may affect compression ratios, so I will try a few combinations.



Please provide feedback!

Please let me know your suggestions for improving this page, particularly for correcting any problem with my description of the programs tested.

I can't keep linking to every paper or page regarding lossless audio compression, but I would like to link to he major ones.  Mark Nelson's compression link farm below, is likely to be a more complete set of links.
 

If you like this page, please consider writing to Dr Lin Xiao EXLIN@ntu.edu.sgwho organised the funding for my work on it in November-December 2000.

With about 150 visits a day, this page is one of the most popular on my website.
 


Programs I did not test or report on fully


Links specific to lossless audio compression



My work, an explanation of Rice Coding and an exploration of alternative coding strategies for generally short variable length integers

In November 1997 I spent some time pursuing an old interest - lossless compression of audio signals.  I tried sending, for instance, every 32nd sample, and then sending those in between - sample 16, 48 etc. - as differences from the interpolation of the preceding and following 32nd sample.  Then I would do the 8th samples which were missing, and then the 4th and then all the odd samples on the same basis.

This constitutes using interpolation between already transmitted samples as a predictor - and the results are not particularly promising.

I also experimented using the highest quality MP3 encoding as a predictor, but even using LAME at 256 kbps, the difference between this (once decoded and aligned for shifts in the output waveform's timing) were quite large.  The difference was generally broadband noise, with its volume depending on the volume of the input signal.  This does not look like a promising approach either.

In December I figured out an improvement to traditional "101 => 000001" Rice encoding.  It turned out to be a generally sub-ovariation on the Elias Gamma code.

Here is a quick description of Rice and Elias Gamma - and a link to an excellent paper on these and other funtionally similar codes.
 

Rice Coding, AKA Rice Packing, Elias Gamma codes and other approaches

In a lossless audio compression program, a major task is to store a larege body of signed integers of varying lengths.  These are the "error" values for each sample: they tell the decoder the difference between its predictor value (based on some variable algorithm working on previously decoded samples) and the true value of the sample.

The coding methods here all relate to storing variable length integers, in which the distribution is stronger for low values than for high.
 

I have not read the original paper:

     R. F. Rice, "Some practical universal noiseless coding techniques"  Tech Rep. JPL-79-22, Jet Propulsion Laboratory, Pasadena, CA, March 1979.

I have read various not-so-great explanations of Rice coding.  There seems to be several often-related algorithms which come under this heading.

Initially, there are Golumb codes, as per the paper:

    S.W. Golomb, "Run-Length Encodings", IEEE Trans Info. Theory, Vol 12 pp 399401 1966.

Golumb codes are a generalised approach to dividing a number into two parts, encoding one directly and the other part - the one which varies more in length, in some other way.

Rice codes are a development of Golumb codes.  Here I will deal only with Rice codes of order k = 1, which is the same (I think) as Golomb codes of order m = 1.

The basic principle of Rice coding for k = 1 is very simple:   To code a number N, send N zeros followed by a one.

To send 0 (0 binary) with Rice coding, the output is 1.
To send 1 (1 binary) with Rice coding, the output is 01.
To send 4 (100 binary) with Rice coding, the output is 00001.

There are other Rice codes for k = 2 and higher values, but they are not so straightforward and suffer from the problem of involving three, four or more bits even when sending a simple 0.

Terminology is a bit of a problem, since there is a larger, more complex operation as part of a lossless audio compression algorithm (described below) which is often referred to as "Rice" coding or packing, but technically, the Rice coding (for k = 1) is nothing more than the above.  I will refer to them collectively as Rice - but I think there should or must be a separate term for the more complex algorithm described below.
 

The following discusses how Rice (and later some other algorthms) is used as part of a larger operation on multiple signed binary numbers - the "error" values in a lossless compressor algorithm.  The "error" values are to be stored in the file in as compact form as possible.  They will be used by the decoder to arrive at the final value for each output sample, by adding this "error" value to the output of the predictor algorithm, which is operating from previously decoded samples.

These "error" numbers are generally small, but quite a few of them are large, due to the complex and unpredictable nature of sound.  Huffman coding can also be used, and is used by some of the programs tested here.

These error numbers are typically twos-complement (signed) 16 bit integer, but their values are often small, say in the range of +/- a hundred or so, and so can be shortened to a 9 bit twos-complement integer.  Some may be much larger - say +/- several thousand.  Few are the full 16 bits, but some may be.   How do you compress this ragged assortment of numbers?

For these signed numbers, there is a preliminary step of converting to positive integers with a right-affixed sign bit.   Lets use some examples, which we will consider as a frame of 8 "error words" to be compressed.

   Decimal      16 bit signed    Sign    Integer        Integer with sign
                integer                                 at right

     +20   0000 0000 0001 0100   +           1 0100          101000
     +70   0000 0000 0100 0110   +         100 0110        10001100
      -5   1111 1111 1111 1011   -              101            1011
    +129   0000 0000 1000 0001   +        1000 0001       100000010
    -300   1111 1110 1101 0100   -      1 0010 1100      1001011001
     +12   0000 0000 0000 1100   +             1100           11000
    +510   0000 0001 1111 1110   +      1 1111 1110      1111111100
     -31   1111 1111 1110 0001   -           1 1111          111111
 

The decimal and spaced-out 16 bit signed binary integer representations are to the left.  Following that are the numbers converted into a sign and an unsigned integer, with leading zeroes removed.   Then those integers have there corresponding sign bit tacked on to the right end, with negative being a "1".

This right column of binary numbers is what we want to store in a compact form.  The big problem is that their lengths vary dramatically.

The first part of the Rice algorithm is to decide a "boundary" column, in this set of numbers.  To the right, the bits are generally an impossible-to-compress mixture of 1s and 0s.  To the left, for some samples at least, there are some extra ones and zeros which we need to code as well.  For example, by some algorithm (which can be complex and iterative for Rice coding of these numbers on the left) a decision is made to set the boundary so that, in this example, the right-most 6 bits (including the sign bit which has been attached) is regarded as uncompressible.  These bits will be sent directly to the output file.  Also, by some means, the decoder has to be told, via a number in the output file, to expect this six bit wide stream of bits.  (The decoder already knows the block length, which is typically fixed, so when it receives 48 bits, in this case of an 8 sample frame, in the context of already having been told to expect 6 bits of each sample sent directly, then it knows exactly how to use these 48 bits.  Typically lossless audio programs use longer frames, say several hundred samples.)

So the body of data we are trying to compress is broken into two sections:

            101000
        10  001100
              1011
       100  000010
      1001  011001
             11000
      1111  111100
            111111

or, more pedantically:

            101000
        10  001100
            001011
       100  000010
      1001  011001
            011000
      1111  111100
            111111

Sending the right block is straightforward - but how to efficiently encode the stragglers on the left?  (Note, "straggler" is my term!)  Here they are, expressed as the shortest possible integer.   I have added two columns for their decimal equivalent and for which of the 8 samples they are:

    Binary    Decimal      Straggler of
                           sample number

         0     0           0
        10     2           1
         0     0           2
       100     4           3
      1001     9           4
         0     0           5
      1111    15           6
         0     0           7
 

As mentioned above, the Rice algorithm (for k = 1) has a simple rule for transmitting these numbers.  Send the number or 0s as per the value of the number, and then send a 1 to indicate that this is the end of the number.  (In other descriptions, a variable number of 1s may be sent with a terminating 0.)

So to send straggler number 0, which has a value of 0, the Rice algorithm sends (i.e. writes to the output file) a single "1".

To send straggler number 0 (value 2) the Rice algorithm sends "001".

Similarly, for straggler number 6, the Rice algorithm sends "0000000000000001".

To encode the above 8 stragglers, the Rice algorithm puts out:

     10011000010000000001100000000000000011

Now, seeing strings of 0s in a supposedly compressed data stream does seem a little incongruous.  As the Kingdom of Id's fearless knight, Sir Rodney was heard to say, when during a ship inspection he was shown first the head (lavatory) and then the poopdeck: "Somehow, I sense redundancy here.".

So I "invented" an alternative.  Initially I could find no reference to such an improvement on basic Rice (k = 1), but a more extensive web-search showed that my system was a sub-optimal variation on "Elias Gamma" coding.
 
 

More efficient alternatives to Rice Coding - Elias Gamma and other codes

The code I "invented" is not exactly described in papers I have found, so I will give it a name here: Pod Coding because it reminds me of peas in a pod.

Rice (k = 1) coding has the following relationship between the number to be coded and the encoded result:

Number             Encoded result
Dec   Binary

 0    00000        1
 1    00001        01
 2    00010        001
 3    00011        0001
 4    00100        00001
 5    00101        000001
 6    00110        0000001
 7    00111        00000001
 8    01000        000000001
 9    01001        0000000001
10    01010        00000000001
11    01011        000000000001
12    01100        0000000000001
13    01101        00000000000001
14    01110        000000000000001
15    01111        0000000000000001
16    10000        00000000000000001
17    10001        000000000000000001
18    10010        0000000000000000001

Rice coding makes most sense when most of the numbers to be coded are small.  This suits the "exponential" or "laplacian" distribution of numbers which typically make up the differences of a lossless audio encoding algorithm.
 

(Speaking very loosely here - where is a reference on the various distributions and a graphic of their curves?  Gaussian is a bell-shaped curve.  Britannica has some explanations and diagrams: http://www.britannica.com/bcom/eb/article/2/0,5716,115242+8,00.html . . .

. . . the best reference I can find is from Tony Robinson's paper:

   http://svr-www.eng.cam.ac.uk/reports/ajr/TR156/node6.html

This includes some very helpful graphs.

One page: http://www.bmrc.berkeley.edu/people/smoot/papers/imdsp/node1.html describes laplacian as being double-sided exponential.)

In January 2002, Reg Dunn pointed me to an impressive reference on distibutions by Michael P. McLaughlin:  http://www.causascientia.org/math_stat/Dists/Compendium.pdf 


Here is the "pod" approach.  The example is probably easier to understand than the formal explanation:

Number             Encoded result
Dec   Binary
 0    00000        1
 1    00001        01
 2    00010        0010
 3    00011        0011
 4    00100        000100
 5    00101        000101
 6    00110        000110
 7    00111        000111
 8    01000        00001000
 9    01001        00001001
10    01010        00001010
11    01011        00001011
12    01100        00001100
13    01101        00001101
14    01110        00001110
15    01111        00001111
16    10000        0000010000
17    10001        0000010001
18    10010        0000010010

Here is the formal definition.

For 0, send:                   1

For 1, send                    01

For 2 bit numbers 1Z, send     001Z

For 3 bit numbers 1YZ, send    0001YZ

For 4 bit numbers 1XYZ, send   00001XYZ

For 3 bit numbers 1WXYZ, send  000001WXYZ
 

There's no problem for the decoder knowing how many bits WXYZ etc. to expect - it is one less than the number of 0s which preceded the 1.

In two instances, "pod" coding produces one more bit than the Rice algorithm.  In 4 instance it produces the same number of bits.  In all other case, it produces less bits than the Rice algorithm.

Number            Rice      Pod       Benefit
Dec   Binary      bits      bits
 0    00000        1         1
 1    00001        2         2
 2    00010        3         4        -1
 3    00011        4         4
 4    00100        5         6        -1
 5    00101        6         6
 6    00110        7         6         1
 7    00111        8         6         2
 8    01000        9         8         1
 9    01001       10         8         2
10    01010       11         8         3
11    01011       12         8         4
12    01100       13         8         5
13    01101       14         8         6
14    01110       15         8         7
15    01111       16         8         8
16    10000       17        10         7
17    10001       18        10         8
18    10010       19        10         9
19    10011       20        10        10
20    10100       21        10        11
 

There would be few situations in which the loss of efficiency encoding "2" and "4" would not be compensated by the gains in coding numbers higher than "5".

In the above example, the output of the Rice and "Pod" algorithms respectively would be as follows, first broken with commas and then without:

Rice:    1,001,1,00001,0000000001,1,0000000000000001,1

"Pod":   1,0010,1,000100,00001001,1,000011111,1
 

Rice:    10011000010000000001100000000000000011

"Pod":   1001010001000000100110000111111
 

I imagine that "Pod" coding (the way it encodes each straggler) would be suitable for sending individual signed and unsigned integer values in a compressed datastream, such as changes from one frame to the next in prediction parameters and the number of bits (width of the block to the right of the "boundary") to be send directly without coding,
 

"Pod" packing has the fortuitous property that the number of bits produced is exactly twice the number of bits encoded - except for encoding "0" which produces 1 bit.

This should greatly simplify the algorithm in a Rice-like system for deciding where to set the boundary between bits to be sent unencoded, and those stragglers to the left to be encoded with the "Pod" algorithm.

A practical implementation could determine the bit length for each complete "sample" (including its sign bit on the right) which is being accumulated in the array prior to coding.   By maintaining a counter for each possible sample length, and incrementing the appropriate counter for each sample created, then an array of integers would result showing how many 10 bit numbers there were in the frame, how many 9 bit numbers and so on.

Since "Pod" coding produces precisely 2 bits for every input bit, and one bit if the input is 0, then as we move the boundary (between "stragglers" to the left and "direct send" bits to the right) to the right, we can answer the question of when to stop rather easily:

  1. Samples which are not stragglers require 1 bit to code with "Pod".
  2. No matter how long the straggler, moving the boundary to the right (including the case of a "1" appearing as a straggler in the column immediately to the left of the boundary) will require 2 bits to encode this extra straggler bit.
  3. Moving the boundary to the right saves 8 bits (in this example) by reducing the number of bits to be sent without coding from the block to the right of the boundary.
The result is a simultaneous equation involving a potential cost in the straggler encoding part of N (the number of samples in the frame) and that cost being 2 times the number of stragglers minus 1 times the number of non-stragglers.

Therefore, the break-even point is the boundary position where 1/3 of the samples have stragglers and 2/3 don't.

The optimal position for the boundary is the one to the left of the position which would increase the number of stragglers to more than 1/3 of the number of samples in the frame.

With the Rice algorithm, this process is more complex (I think) because the exact number of bits to be sent depends on the exact values of the stragglers, not just their bit-length.  Some papers give a simple formulae based on the values of all the samples to determine the optimal placement of the boundary.

I have not implemented or tested this "Pod" approach.

This approach would provide the most benefit over the "Rice" approach when the stragglers have relatively high values - which means when most of the samples are small and a few are much larger.  Since "Pod" outperforms the Rice algorithm when the samples peak at around 16 or more times the maximum value which will fit to the right of the "boundary" and since, at a guess, the average of those samples which do not form stragglers would be around a half to a third of that value, this "Pod" approach would only have benefits for relatively "spiky" values.

To what extent this is true of error samples to be encoded in a lossless audio algorithm, I can't say, but I would venture that it is is proportional to the unpredictability of the music.

Now it turns out that my "pod" approach is a variation, and not necessarily the best variation, on "Elias Gamma" coding.

By far the best paper I can find on Golumb, Rice, Elias and some more involved and novel codes is by Peter Fenwick ( http://www.cs.auckland.ac.nz/~peter-f/ )

Punctured Elias Codes for variable-length coding of the integers
Peter Fenwick   peter-f@cs.auckland.ac.nz
Technical Report 137 ISSN 1173-3500    5 December 1996
Department of Computer Science, The University of Auckland peter-f@cs.auckland.ac.nz
This is available as a Postscript file at: ftp://ftp.cs.auckland.ac.nz/out/peter-f/  TechRep137.ps .  I have converted it into a PDF file here: TechRep137.pdf.  (Peter Fenwick wrote to me that this is fine.)
 

Peter Fenwick's purpose co-incides closely with our interest - how to efficiently encode integers of varying lengths, when most of the integers are small.

He refers to a paper:

P. Elias, Universal Codeword Sets and Representations of the Integers, IEEE Trans. Info. Theory, Vol IT 21, No 2, pp 194-203, Mar 1975.
There is an abstract for this at:  http://galaxy.ucsd.edu/welcome.htm but no PDF.

Peter Fenwick's paper describes:

He describes the Elias Gamma (actually the Gamma symbol with a prime - so maybe Elias Gamma Prime) code as:

Number             Encoded result
Dec   Binary       "Codeword"
 1    00001        1
 2    00010        010
 3    00011        011
 4    00100        00100
 5    00101        00101
 6    00110        00110
 7    00111        00111
 8    01000        0001000

Note that this does not include encoding for zero.

My "pod" approach is simply extending the above code with a 0 to the left of all the above codewords, and a "1" for encoding zero.

This is not how Elias Gamma is normally extended to cover 0.  The usual approach is to use the same pattern, but start at 0 rather than 1 for the number range it encodes.  This is known as "biased Elias Gamma".  Here are the two codes alongside each other, with their benefits over standard Rice coding:

Two bugs in my table were pointed out to me in July 2004 by Carlos Mourao and fixed in October 2005.  Carlos noted:

Always when the decimal input is a power of 2 minus one, 
Elias Gamma coding will need two more bits than Pod
coding, then loosing to Pod in these situations.

Number             "Pod"        Biased Elias    "Pod"       Biased Elias Gamma
Dec   Binary                    Gamma           benefit     benefit

 0    00000        1            1
 1    00001        01           010                         -1
 2    00010        0010         011              -1
 3    00011        0011         00100                       -1
 4    00100        000100       00101            -1
 5    00101        000101       00110                        1
 6    00110        000110       00111             1          2
 7    00111        000111       0001000           2          1 (was 3)
 8    01000        00001000     0001001           1          2
 9    01001        00001001     0001010           2          3
10    01010        00001010     0001011           3          4
11    01011        00001011     0001100           4          5
12    01100        00001100     0001101           5          6
13    01101        00001101     0001110           6          7
14    01110        00001110     0001111           7          8
15    01111        00001111     000010000         8          7 (was 9)
16    10000        0000010000   000010001         7          8
17    10001        0000010001   000010010         8          9
18    10010        0000010010   000010011         9         10

Standard Rice coding is clearly the best approach when most of the numbers to be encoded are small.

From the example above, here are the "stragglers" encoded with Rice, my "Pod" extension to Elias Gamma, and the more usual approach: Biased Elias Gamma:

Rice:               10011000010000000001100000000000000011
"Pod":              1001010001000000100110000111111
Biased Elias Gamma: 1011100101000101010000100001

There are many potential Start-Step-Stop codes - please read the paper for a full explanation.  The reference for these is:

 E.R. Fiala, D.H. Greene, Data Compression with Finite Windows, Comm ACM, Vol 32, No 4, pp 490-505 , April 1989.
One such code, with an open-ended arrangment so it can be used for arbitrarily large numbers, rather than stopping at 679 as in the paper's Table 5, is what I would call {3, 2, N} Start-Step-Stop coding, where N is some high number to set a limit to the system.

Number range    Codeword
to be coded

  0 -   7       0xxx           ( 4 bits total, 1 bit prefix + 3 bits data)
  8 -  39       10xxxxx        ( 7 bits total, 2 bit prefix + 5 bits data)
 40 - 167       110xxxxxxx     (10 bits total, 3 bit prefix + 7 bits data)
168 - 679       1110xxxxxxxx   (13 bits total, 4 bit prefix + 9 bits data) etc.

If it was desired to limit the system to 679, (or perhaps limit it to a slightly lower number and use the last few as an escape code for the rare occasion of encoding anything higher) then the last line would be as it is in the paper:

168 - 679       111xxxxxxxx    (12 bits total, 3 bit prefix + 9 bits data)
 

This gives excellent coding efficiency for larger numbers, but at the expense of smaller values.  In lossless coding, our scheme will very often be encoding 0, so the above system does not look promising.

An alternative would be {2, 2, N} Start-Step-Stop:

  0 -   3       0xx            ( 3 bits total, 1 bit prefix + 2 bits data)
  4 -  11       10xxxx         ( 6 bits total, 2 bit prefix + 4 bits data)
 12 -  83       110xxxxxx      ( 9 bits total, 3 bit prefix + 6 bits data)  (Thanks Melchior!)
 84 - 339       1110xxxxxxxx   (12 bits total, 4 bit prefix + 8 bits data) etc.

Or {1, 2, N} Start-Step-Stop has another curve, favouring lower values still:

  0 -   1       0x             ( 2 bits total, 1 bit prefix + 1 bits data)
  2 -   9       10xxx          ( 5 bits total, 2 bit prefix + 3 bits data)
 10 -  41       110xxxxx       ( 8 bits total, 3 bit prefix + 5 bits data)
 42 - 169       1110xxxxxxx    (11 bits total, 4 bit prefix + 7 bits data) etc.

Peter Fenwick describes new codes in which 0's are interspersed after 1's to indicate that the (reversed) number is not finished yet.  These "punctured" codes take a bit of getting used to, but are very efficient at higher values.  The bit length at higher values approximates "1.5 log N bits, in comparison to 2 log N bits for the Elias codes" (logs base 2).

There is a ragged pattern of code-word lengths.

Number             P1           P2
Dec   Binary

 0    00000        0            01
 1    00001        101          001
 2    00010        1001         1011
 3    00011        11011        0001
 4    00100        10001        10101
 5    00101        110101       10011
 6    00110        110011       110111
 7    00111        1110111      00001
 8    01000        1000001      101001
 9    01001        1101001      100101
10    01010        1100101      1101101
11    01011        11101101     100011
12    01100        1100011      1101011
13    01101        11101011     1100111
14    01110        11100111     11101111
15    01111        111101111    000001
16    10000        1000001      1010001
 

The capacity of these various codes to help with coding the "stragglers" in a lossless audio compression algorithm depends on many factors I can't be sure of at present.  Those codes which take more than one bit to code 0 are clearly at a disadvantage, since with the border set optimally for Rice or "Pod"/Biased Elias Gamma, most (2/3 or more) of the numbers will be 0.

However, since these codes are highly efficient at coding larger integers, the "cost" of having longer stragglers is much less.  Standard Rice coding of stragglers of values more than about 3 bits long can clearly be improved upon with Biased Elias Gamma. This uses about 2 bits per bit of straggler to be coded.  But Peter Fenwick's "punctured" codes use only about 1.5 bits for longer values.   This should enable the "boundary" separating the stragglers from the bits to be sent without compression further to the right, so reducing the number of bits to be sent uncompressed.
 
 

Some other links to sites concerning coding techniques for variable length integers:



 

Tabulation details

These are low level details of how I processed the file size results.

I used a batch file or GUI to compress all the WAV files to individual compressed files with a distinctive file name extension.  Then I would use a batch file containing "dir > dir.txt" to list the directory and so the file sizes.  I would edit out all other lines except those of the compressed files and put them in the correct order, and then add those to sizes9.txt.  Then I would use the MS-DOS command "type sizes9.txt" to show the text in an MS-DOS window.  There is a rectangular text select command there and I selected the block of file sizes, complete with commas and by pressing Enter copied them to the clipboard.  In thespreadsheet, I selected the column containing file sizes and pressed Control V.  Voila!  The spreadsheet does the rest.  Then I manually copied the percentages and ratio from the spreadsheet into the HTML table.

The excel spreadsheet and "sizes9.txt" URL is listed near the top of this page.  To add your own pair of columns to the spreadsheet, select the block for an existing program, copy it to the clipboard, place your cursor in the Row 1 cell immediately to the right, and then paste into there.

This page was created with Netscape Communicator 4.7's Composer.  In December 2000, Mozilla's Composer still has a way to go.


Updates in reverse order


  • 2005 October 21.  Added material at front explaining why I am no longer updating this page, with a few final updates, and a link to the relevant Wikpedia page.  Also did a few link updates and fixes for problems reported to me.  Thanks!
  • 2003 January 12.  Added link to WinAce and to Michael P. McLaughlin's compendium of probability distributions.
  • 2002 August 7.  Added link to OptimFROG.
  • 2002 July 17.  Added notes on demise of WaveZip web site.
  • 2002 April 13.  Updated licensing notes for Monkey's Audio and noted there is a Windows Media Player plugin. 
  • 2001 October 31.  Added mention of new MUSICompress web site.
  • 2001 March 22.  Added mention of APT-X Windows DLL.
  • 2001 January 17.  Added mention of LPAC 3.0.
  • 2000 December 19.  Added listing of FLAC, but not tests.
  • 2000 December 18.  Slight change do DAXK notes - that the Mac version performs better than the PC version.
  • 2000 December 14. Added mention of MKT and updated RKAU results, with extra tables showing which of the options worked best for each file. Added a table in the RKAU section on the options available in all programs for using stereo correlations.  Rounded average file size and compression ratios to the nearest number, up or down, so 67.545 becomes 67.55 and  67.544 becomes 67.54.
  • 2000 December 12. Completely revised section on Rice coding etc. adding material on Elias Gamma codes. Added mention of the DAKX Windows version 1.0.
  • 2000 December 11. Added test results for RKAU 1.07.  Mentioned RAR.
  • 2000 December 10. Page completely revised. The old page is here.

  • Robin Whittle  rw@firstpr.com.au
    Return to the main page of the First Principles web site.