Nor is there a general test to determine whether the compression of astring can be improvedany further, because that would be equivalent to testing whether the compressedstring is random.Because determining the length of the shortest descriptions of strings is not computable,neither is optimal compression. It is not hard to find difficult cases. For example,consider the short description "a string of a million zero bytes compressed withAES in CBC mode with key 'foo'". To any program that does not know the key, thedata looks completely random and incompressible.
Archivers sometimes add a checksum to detect transmission errors. The checksum iscomputed and stored before compression and verified after decompression. The needfor a checksum is questionable because networks and storage media typically useerror correction so that errors are very unlikely. Decompression errors are morelikely to result from software bugs or deliberate manipulation. A single bit changein an archive can produce a completely different file. A checksum increases thearchive size slightly (usually by 4 bytes) and also increases compression and decompressiontime by the time it takes to compute it. Some common checksum functions:
Ian Sutton The Complete Guide to Compression TUTORiAL
PAQ7 (Dec. 2005) was a complete rewrite. It uses logistic mixing rather than linearmixing, as described in section 4.3.2. It has models for color BMP, TIFF, and JPEGimages. The BMP and TIFF models use adjacent pixels as context. JPEG is alreadycompressed. The model partially undoes the compression back to the DCT (discretecosine transform) coefficients and uses these as context to predict the Huffmancodes.
Lossless compressors ignore meaningless data in selecting contexts. Meaninglessor random data has no predictive value and is itself not compressible. A lossy compressornot only ignores the meaningless data, but also discards it completely. Decidingwhich data is meaningful is a hard AI problem that applies to both lossless andlossy compression. Both require a deep understanding of human cognitive psychology. 2ff7e9595c
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