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Thread: Advice in data compression

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    Advice in data compression

    Hello to all,

    I am having problems trying to compress data from this file (gv2.txt in .rar in attachment).
    It contains only numbers and the best compression that I got was with paq8o8z and the output file was 954 bytes (6184 bytes original).
    I was wondering can I compress that file even further, i.e. to go less than 900 bytes and with what compression method/algorithm.
    What would you, experts of the compression world, suggest me, a novice in all of this!

    Thank you for your time and effort in advance!

    Sincerely yours,
    Caslav
    Attached Files Attached Files

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    Member Fu Siyuan's Avatar
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    I've learnt that there is no universal good compression model. So it's not a surprise that even if the current 'best algorithm' can't compress it to your satisfied size. I looked into the original file. It contains only thousands of bytes (0x0-0xff) but writes in text. And the difference between successive numbers isn't much. So I believe a simple transform would make it less than 900 bytes.

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    I tried all sort of compression algorithms and paq was the best, and yes the numbers contained in .txt go from 0-255.
    I also tried delta coding and I couldn't pass the 900 bytes barrier.

    Could you suggest me some simple transforms?
    Thank you!

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    Maybe you could start transforming source file from text to bytes,
    this would make the source file 4x smaller.
    Note however that final compressed result is likely to be just a little bit better, and yes, there is a limit to what compressors can do.

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    When I transformed text to bytes I get a file around 1675 bytes...

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    When I transformed text to bytes I get a file around 1675 bytes...
    you mean, before compression ?

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    Programmer osmanturan's Avatar
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    I've analyzed the file with MATLAB. The source almost random. Delta filter does not help. Because, the range is increased and standard deviation is still high. Here's some stats:

    Text-to-Byte conversion (without whitespaces which is easy to model in our case): 1674 bytes
    Max. Sample Value: 244
    Min. Sample Value: 44
    Max. Range: 200
    Mean: 133.1756
    Std. Dev.: 46.3860

    After Delta Transform:
    Max. Sample Value: +168
    Min. Sample Value: -168
    Max. Range: 336
    Mean: 0.1219
    Std. Dev: 47.8287

    If you can give some more descriptive information about the source model, we can offer something.
    BIT Archiver homepage: www.osmanturan.com

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    Member Fu Siyuan's Avatar
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    Maybe you could start transforming source file from text to bytes,
    I meant this. Unfortunately, I tried and get far from less than 900 bytes.

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    Member biject.bwts's Avatar
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    Red face

    Quote Originally Posted by Chuckie View Post
    When I transformed text to bytes I get a file around 1675 bytes...
    Quote Originally Posted by Fu Siyuan View Post
    I meant this. Unfortunately, I tried and get far from less than 900 bytes.
    I don't have the converted file. Assuming you converted bijectively then
    you have all the information of the original file.

    At this point a farther bijective compression is needed such as ARB255
    or BICOM. If this doesn't work you could transform the file more buy
    creating a new file from the byte file doing, a BWTS once or twice,
    or, a UNBWTS once or twice.

    At this point using ARB255 after a series of BWTS's or UNBWTS's
    would gain nothing but what ever method you tried on the original
    1675 byte file might work or even BICOM which is a bijective
    ppm compressor.

    Hope this helps small file compression is fun

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    Programmer osmanturan's Avatar
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    I have tried LPC model fitting via genetic algorithm with MATLAB. The result is same. The source almost random. By assuming that it's an analog signal, I've plotted it's frequency spectrum. Seems, the source itself consists all frequency components This shortly means, it's hard to compress. I really wonder what kind of source are generated this output
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    Administrator Shelwien's Avatar
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    bwtmix wins
    http://www.ctxmodel.net/files/gv2_0.rar
    Code:
    Results
    899 - gv2.ari
    1674 - gv2.bin
    6184 - gv2.txt
    1674 - gv2unp.bin
    6184 - gv2unp.txt

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    The input looks like a sound wav sample.
    If that is the case, then even very moderately lossy compression would provide much stronger compression and remain acceptable...

    [Edit] nice record Shelwien !

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    Administrator Shelwien's Avatar
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    Sound? this? Its more easy to see some 2D correlations there,
    but I couldn't see any specific row size actually.
    Code:
    000:  09 09 0B 10 0F 10 0E 0F │ 10 11 10 11 12 10 10 10
    010:  11 0D 0C 10 0D 0A 0A 0D │ 10 0F 11 10 10 11 11 10
    020:  0E 0B 0C 0D 0F 11 12 10 │ 12 12 12 12 12 13 13 12
    030:  10 0D 0D 10 12 12 12 11 │ 12 11 11 12 12 12 11 0C
    040:  0B 0B 0D 0F 12 12 11 10 │ 0E 05 0A 0C 0D 0D 0E 0D
    050:  0E 10 11 11 12 11 12 12 │ 0E 0D 0F 04 03 10 0A 04
    060:  05 06 09 11 0F 12 11 11 │ 12 11 0D 02 03 03 04 04
    070:  07 10 12 0A 04 07 06 03 │ 05 08 10 0F 11 11 0A 03
    080:  09 0B 09 07 0B 0F 0A 0E │ 0D 0E 05 0B 0B 0D 11 12
    090:  12 11 08 03 09 09 07 09 │ 0C 12 14 10 0D 08 0C 0E
    0A0:  07 05 03 0F 10 11 0D 0E │ 03 06 07 0A 07 0E 07 09
    0B0:  06 08 07 0F 0B 0B 12 11 │ 11 11 02 03 06 06 05 05
    0C0:  04 03 07 08 10 13 16 10 │ 07 08 0D 05 05 05 07 0A
    0D0:  0A 07 03 03 10 10 10 07 │ 08 06 08 0C 04 10 0B 03
    0E0:  05 0E 05 0C 02 0D 07 0A │ 0C 0B 0C 08 0E 03 13 05
    0F0:  0F 06 09 02 0F 04 09 09 │ 13 0B 11 12 11 02 03 08
    100:  07 0C 03 05 10 08 08 0F │ 14 16 14 0C 0C 05 03 0D
    110:  10 07 0D 0B 04 02 05 11 │ 10 11 0E 0C 12 10 0E 02
    120:  0C 05 0A 08 09 09 0B 0D │ 0F 0B 0B 0D 10 0A 11 0C
    130:  13 11 0E 02 02 09 0C 09 │ 0C 0C 0B 0F 16 14 0E 0F
    140:  0D 10 14 12 0F 03 02 0E │ 10 11 03 0C 0D 13 0F 03
    150:  03 02 0F 0F 0D 15 16 13 │ 15 11 02 03 02 0C 0F 10
    160:  10 0E 0D 0E 13 11 04 02 │ 03 0F 10 17 15 16 14 0D
    170:  02 02 02 0E 0F 0A 0B 0F │ 0D 13 0E 0B 02 02 09 10
    180:  10 0F 10 15 16 16 16 16 │ 13 05 03 03 02 07 11 0F
    190:  0F 04 10 17 17 17 02 0A │ 0F 10 03 02 0F 0E 0F 08
    1A0:  0E 13 16 0D 11 16 14 15 │ 0E 02 03 03 04 04 0E 0E
    1B0:  10 0A 03 0A 08 10 12 14 │ 10 02 0B 0E 12 0D 03 02
    1C0:  03 04 10 0E 0F 13 16 17 │ 16 15 13 05 04 03 02 02
    1D0:  09 0F 10 10 05 13 07 02 │ 12 08 0A 0F 10 00 04 06
    1E0:  09 06 04 03 0E 10 11 11 │ 16 16 10 03 03 02 0C 0F
    1F0:  05 10 03 0D 06 05 05 0F │ 10 02 02 07 05 02 02 03
    200:  0E 0F 0F 10 11 12 16 16 │ 14 10 02 02 02 02 0E 0E
    Also, this is the freq table (starting from 0 aka 44):
    Code:
    { 1, 1, 55, 71, 
    124, 160, 99, 67, 75, 83, 65, 58, 73, 75, 91, 
    103, 122, 80, 95, 59, 34, 23, 28, 21,  8,  3 }
    Last edited by Shelwien; 24th March 2010 at 18:39.

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    Programmer Jan Ondrus's Avatar
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    Quote Originally Posted by Shelwien View Post
    Sound? this? Its more easy to see some 2D correlations there,
    but I couldn't see any specific row size actually.
    Code:
    000:  09 09 0B 10 0F 10 0E 0F │ 10 11 10 11 12 10 10 10
    010:  11 0D 0C 10 0D 0A 0A 0D │ 10 0F 11 10 10 11 11 10
    020:  0E 0B 0C 0D 0F 11 12 10 │ 12 12 12 12 12 13 13 12
    030:  10 0D 0D 10 12 12 12 11 │ 12 11 11 12 12 12 11 0C
    040:  0B 0B 0D 0F 12 12 11 10 │ 0E 05 0A 0C 0D 0D 0E 0D
    050:  0E 10 11 11 12 11 12 12 │ 0E 0D 0F 04 03 10 0A 04
    060:  05 06 09 11 0F 12 11 11 │ 12 11 0D 02 03 03 04 04
    070:  07 10 12 0A 04 07 06 03 │ 05 08 10 0F 11 11 0A 03
    080:  09 0B 09 07 0B 0F 0A 0E │ 0D 0E 05 0B 0B 0D 11 12
    090:  12 11 08 03 09 09 07 09 │ 0C 12 14 10 0D 08 0C 0E
    0A0:  07 05 03 0F 10 11 0D 0E │ 03 06 07 0A 07 0E 07 09
    0B0:  06 08 07 0F 0B 0B 12 11 │ 11 11 02 03 06 06 05 05
    0C0:  04 03 07 08 10 13 16 10 │ 07 08 0D 05 05 05 07 0A
    0D0:  0A 07 03 03 10 10 10 07 │ 08 06 08 0C 04 10 0B 03
    0E0:  05 0E 05 0C 02 0D 07 0A │ 0C 0B 0C 08 0E 03 13 05
    0F0:  0F 06 09 02 0F 04 09 09 │ 13 0B 11 12 11 02 03 08
    100:  07 0C 03 05 10 08 08 0F │ 14 16 14 0C 0C 05 03 0D
    110:  10 07 0D 0B 04 02 05 11 │ 10 11 0E 0C 12 10 0E 02
    120:  0C 05 0A 08 09 09 0B 0D │ 0F 0B 0B 0D 10 0A 11 0C
    130:  13 11 0E 02 02 09 0C 09 │ 0C 0C 0B 0F 16 14 0E 0F
    140:  0D 10 14 12 0F 03 02 0E │ 10 11 03 0C 0D 13 0F 03
    150:  03 02 0F 0F 0D 15 16 13 │ 15 11 02 03 02 0C 0F 10
    160:  10 0E 0D 0E 13 11 04 02 │ 03 0F 10 17 15 16 14 0D
    170:  02 02 02 0E 0F 0A 0B 0F │ 0D 13 0E 0B 02 02 09 10
    180:  10 0F 10 15 16 16 16 16 │ 13 05 03 03 02 07 11 0F
    190:  0F 04 10 17 17 17 02 0A │ 0F 10 03 02 0F 0E 0F 08
    1A0:  0E 13 16 0D 11 16 14 15 │ 0E 02 03 03 04 04 0E 0E
    1B0:  10 0A 03 0A 08 10 12 14 │ 10 02 0B 0E 12 0D 03 02
    1C0:  03 04 10 0E 0F 13 16 17 │ 16 15 13 05 04 03 02 02
    1D0:  09 0F 10 10 05 13 07 02 │ 12 08 0A 0F 10 00 04 06
    1E0:  09 06 04 03 0E 10 11 11 │ 16 16 10 03 03 02 0C 0F
    1F0:  05 10 03 0D 06 05 05 0F │ 10 02 02 07 05 02 02 03
    200:  0E 0F 0F 10 11 12 16 16 │ 14 10 02 02 02 02 0E 0E
    Also, this is the freq table (starting from 0 aka 44):
    Code:
    { 1, 1, 55, 71, 
    124, 160, 99, 67, 75, 83, 65, 58, 73, 75, 91, 
    103, 122, 80, 95, 59, 34, 23, 28, 21,  8,  3 }
    Attached Images Attached Images     
    Attached Files Attached Files

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    Member biject.bwts's Avatar
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    Quote Originally Posted by Shelwien View Post
    bwtmix wins
    http://www.ctxmodel.net/files/gv2_0.rar
    Code:
    Results
    899 - gv2.ari
    1674 - gv2.bin
    6184 - gv2.txt
    1674 - gv2unp.bin
    6184 - gv2unp.txt
    dropping in the old BWTMIX I used as a starting code I
    get
    903
    replacing that one with BWTS in stead of BWT
    using bmixbwts I get
    898 which is better

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    Guys, thank you, THANK YOU VERY VEEEE...EERY MUCH...

    When I saw 899 bytes I couldn't believe my eyes.
    Shelwien, I appreciate your effort very much, thank you!

    I am satisfied with this result, but my "boss" wants me to use paq8, alas.
    So does anybody know a decent paq8 to reach the result of bwtmix?!

    I tred paq8o8z with gv2.bin and got around 934 bytes.
    Used FrontPAQ (no source code) and got 913 bytes...



    Thx again and I am sorry we ain't close so I can buy you guys a beer or two... (if there is another way I can return the favor...)

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    Often when comparing compressors you include the size of the decompressor too - the footprint if you like.

    Is the footprint of the (de)compressor important?

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    Programmer osmanturan's Avatar
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    AFAIR, ZPAQ has a BWT config file which have a potential to reach that barrier if you really want to stick PAQ series. You may want to look at it.
    BIT Archiver homepage: www.osmanturan.com

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    I can't download from
    http://www.ctxmodel.net/files/gv2_0.rar
    Can somebody attach the file in the post?

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    Administrator Shelwien's Avatar
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    ...
    Attached Files Attached Files

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    Quote Originally Posted by Shelwien View Post
    ...
    thanks!

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    Last edited by Sportman; 25th March 2010 at 21:37.

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    Administrator Shelwien's Avatar
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    > When I saw 899 bytes I couldn't believe my eyes.

    Actually its possible to further improve it, like
    - remove 44 and 52 from "alphabet" and store their offsets instead
    (they occur only once)
    - reorder the values (preferably, separately for BWT and bitwise coding)
    - skip coding of high 3 bits (preferably, also mask out other unused codes)

    > I am satisfied with this result, but my "boss" wants me to use paq8, alas.

    With paq8 all points above apply, and also you can
    - use my binary transform from gv2_0.rar instead of plain ascii to binary
    - remove the paq8 archive header (its like 30 bytes)
    - disable unapplicable models (like text,images)

    But in general paq8 is a bad idea here - similar or better results can
    be reached with a tuned order0 coder, so all the paq8's complexity
    doesn't make any sense.

    > So does anybody know a decent paq8 to reach the result of bwtmix?!

    The file is too small, so redundancy (like headers, rc flush overhead,
    slow learning rate) is very noticeable with paq8.
    And tuning paq8 to specific case is hard and probably unreasonable
    if there're actually more data like that.
    But even then something different, like m1, makes more sense than paq.

    > I tred paq8o8z with gv2.bin and got around 934 bytes.
    > Used FrontPAQ (no source code) and got 913 bytes...

    That's because of headers probably.
    Anyway, you can try all the versions there http://paq8.hys.cz/ http://dhost.info/paq8/
    also older at (since paq1; they might show better results actually)
    http://cs.fit.edu/~mmahoney/compression/#paq or
    http://mattmahoney.net/dc/#paq
    with all compression levels on both binary files (direct and (x-44)/8)
    and find the best result, after cutting out the archive header.

    But actually this approach is really wrong :)
    Last edited by Shelwien; 25th March 2010 at 20:45.

  24. #24
    Administrator Shelwien's Avatar
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    As an example, http://nishi.dreamhosters.com/u/gv2_1.rar
    858 bytes. Its just the postcoder from bwtmix now, without BWT,
    with some tweaks. I'd post the source if anybody wants that,
    but its not really useful imho.
    Details:
    -1 5-bit coding
    -1 extra check for >=26
    -1 redundant rc cache byte removed
    -2 rc flush optimized
    -4 file size field removed (hardcoded 1674)
    -26 tuning of model's parameters

    But anyway, all of this doesn't make sense really.
    Improving compression by 5% at 1k scale doesn't mean
    that there'd be the same improvement at 1M scale
    (in fact, likely the reverse, because tuning for small files
    tends to oversimplify the models).
    I guess, it might be still applicable if there's random access
    to small independently compressed records or something,
    but again, in that case there're some better methods.
    Attached Files Attached Files
    Last edited by Shelwien; 26th March 2010 at 00:38.

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    Programmer Bulat Ziganshin's Avatar
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    just store it inside decoder

  26. #26
    Administrator Shelwien's Avatar
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    Most of modification applied are still generic and would work for any
    samples of that kind.

  27. #27
    Member Skymmer's Avatar
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    Chuckie, if you still want some PAQ8 as final touch for your file then you can use the following chain:
    gv2.txt -> 1.exe -> gv2.bin -> rename to 0 -> paq8kx_v7 -8 0 -> 899 bytes
    Actually you can use any level in this situation.

  28. #28
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    Quote Originally Posted by Shelwien View Post
    As an example, http://nishi.dreamhosters.com/u/gv2_1.rar
    858 bytes. Its just the postcoder from bwtmix now, without BWT,
    with some tweaks. I'd post the source if anybody wants that,
    but its not really useful imho.
    Details:
    -1 5-bit coding
    -1 extra check for >=26
    -1 redundant rc cache byte removed
    -2 rc flush optimized
    -4 file size field removed (hardcoded 1674)
    -26 tuning of model's parameters

    But anyway, all of this doesn't make sense really.
    Improving compression by 5% at 1k scale doesn't mean
    that there'd be the same improvement at 1M scale
    (in fact, likely the reverse, because tuning for small files
    tends to oversimplify the models).
    I guess, it might be still applicable if there's random access
    to small independently compressed records or something,
    but again, in that case there're some better methods.

    I'd like the source code please... If nobody wants it send it to my mail: clivada@gmail.com thx

    Wonderful work!!

    Thank you for your addiotional post for paq8.
    Last edited by Chuckie; 26th March 2010 at 12:18.

  29. #29
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    Quote Originally Posted by Skymmer View Post
    Chuckie, if you still want some PAQ8 as final touch for your file then you can use the following chain:
    gv2.txt -> 1.exe -> gv2.bin -> rename to 0 -> paq8kx_v7 -8 0 -> 899 bytes
    Actually you can use any level in this situation.

    I can't believe just by renaming gv2.bin -> 0 the file is 6 bytes smaller... o_0
    Some would say: "LOL!"

  30. #30
    Administrator Shelwien's Avatar
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    > I'd like the source code please...

    Well, this (still 85: http://nishi.dreamhosters.com/u/gv2_2.rar

    Though original bwtmix postcoders at http://ctxmodel.net/files/mix_test/mix_test_v9.rar
    seem to make 890-891 as is.

    > I can't believe just by renaming gv2.bin -> 0 the file is 6 bytes smaller... o_0

    There's nothing surprising really, and I already mentioned it a few times.
    Most paq archives have a header like this:
    (except for paq8px where its compressed too)

    Code:
    00000000:  70 61 71 38 70 20 2D 36 │ 0D 0A 31 36 37 34 09 67   paq8p -6  1674 g
    00000010:  76 32 2E 62 69 6E 0D 0A │ 1A FB 65 F6 F5 F9 3B C6   v2.bin  √eЎї∙;╞
    00000020:  20 F3 2C 49 0F 22 E9 D7 │ B1 85 D2 F8 2C 41 38 EB    є,I"щ╫▒Е╥?,A8ы
    00000030:  15 E8 54 78 A0 91 AA FD │ DB 9F E8 FC 3B 85 17 E3   шTxаСк?█Яш№;Еу
    And this header can be safely excluded from your counts... (up to 1A)
    or actually removed by hacking the paq8 source.

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