Data Compression Algorithms

All of us are familiar with zip/unzip or gzip/gunzip programs for compressing and uncompressing large genomic files. How do various program compress and decompress large files? Today we shall broadly review data compression schemes and explain how Burrows Wheeler transform can help in compressing data. This topic may seem unrelated to search programs, but it is indeed one of the necessary technical blocks in understanding FM-index.

We earlier discussed about transforms and reversible transforms. Please note that all compression schemes are reversible transforms on input files. They are transforms, because they turn the input into something else. They have to be reversible, or otherwise you cannot recover your input file from its compressed form.

Intuitively you can see that some files beg to be compressed. For example, if a sequence has very long chain of 10000 As, you can save space by writing ‘10000A’ instead of keeping a long chain of ‘AAAAAAAAAAAA….’. The compression algorithm will go through the genome file, look for long repetitive chains and replace them with a number followed by a letter. The decompression algorithm will go through a compressed file and replace each instance of number followed by letter with long chain of letters. Neat? A more sophisticated program may even replace ‘TATATATATATATATA’ by ‘8TA’ and so on.

Unfortunately, such easy cases are rare. Most genomic files provide very few opportunities for compressing long chains of simple repetitive sequences. However, you can transform the genome file into something else with long repetitive sequences and then use the above compression scheme. How can you do that? As we explained earlier in ‘Finding us in’, Burrows Wheeler transform changes a text in such a way that identical characters tend to come together. So, you can design a compression scheme that first performs BWT on the genome sequence and then replaces long chain of letters by numbers+letters. The reverse compression executes the opposites of above steps in reverse order. The above method will give back the original genome sequence from its compressed form, because BWT is reversible.

Popular programs like zip or gzip do not use BWT. To learn how they save space, you need to understand how computers store data.

A computer does not read English characters, or Chinese characters for that matter. It only knows two numbers - ‘0’ and ‘1’. To store English text in a computer, all English characters has to be assigned some number with combination of 0s and 1s. For example, English character ‘A’ can be given a number ‘001000001’, ‘B’ can be given a number ‘001000010’ and so on. This is called binary representation. Why do we need so many 0s and 1s to represent one character? Because we need to have enough room for 26 small letter, 26 capital letters, numbers 0-9, brackets, asterix, semi-colon and everything else you see on the keyboard. All those characters are assigned binary form of fixed width.

That is quite a luxury, if all you have are As, Cs, Gs and Ts. You can pick binary forms of all As as ‘00’, all Cs as ‘01’, all Ts as ‘10’ and Gs as ‘11’ and save quite a bit of space. Popular file compression programs do exactly that. They find out which characters are present in the file, and create a new binary representation removing all the clutter.

In fact they go one step further, and adjust lengths of binary representations of various characters according to their frequencies in the text. For example, if you have a GC-rich genome, you may assign ‘G’ and ‘C’ with smaller binary representations than ‘A’ and ‘T’, and save even more space. The letter ‘e’ has much higher abundance than the letter ‘z’ in regular English text. So, assigning ‘e’ with smaller binary representation than ‘z’ results in significant space reduction. All these are taken care of by the popular compression algorithms. Various coding schemes such as Huffman coding, arithmetic coding, etc. are used to perform this task.

An understanding of how compression works can sometimes help you get better compression by reformatting the data. We had a huge file of K-mers that we wanted to move from one machine to another. When we applied gzip to the original file, the 13G file reduced in size to 3G. So, we decided to sort the file and then apply gzip. The sorting step brought down the size of the compressed file to only 250 Mb. Sorting is an expensive step, but it resulted in 52 fold reduction in size instead of 4 fold reduction for the unsorted file. Sorting brought identical words together and helped the compressing program to replace them by number+word, as we explained earlier.

Written by M. //

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