Arithmetic Coding
Section Overview
Arithmetic coding offers a way to compress data and can be useful
for data sources having a small alphabet. The length of an arithmetic
code, instead of being fixed relative to the number of symbols being
encoded, depends on the statistical frequency with which the source
produces each symbol from its alphabet. For long sequences from sources
having skewed distributions and small alphabets, arithmetic coding
compresses better than Huffman coding.
The arithenco and arithdeco functions
support arithmetic coding and decoding.
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Representing Arithmetic Coding Parameters
Arithmetic coding requires statistical information about the
source of the data being encoded. In particular, the counts input
argument in the arithenco and arithdeco functions
lists the frequency with which the source produces each symbol in
its alphabet. You can determine the frequencies by studying a set
of test data from the source. The set of test data can have any size
you choose, as long as each symbol in the alphabet has a nonzero frequency.
For example, before encoding data from a source that produces
10 x's, 10 y's, and 80 z's in a typical 100-symbol set of test data,
define
counts = [10 10 80];
Alternatively, if a larger set of test data from the source
contains 22 x's, 23 y's, and 185 z's, then define
counts = [22 23 185];
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Example: Creating and Decoding an Arithmetic Code
The example below performs arithmetic encoding and decoding,
using a source whose alphabet has three symbols.
seq = repmat([3 3 1 3 3 3 3 3 2 3],1,50);
counts = [10 10 80];
code = arithenco(seq,counts);
dseq = arithdeco(code,counts,length(seq));
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