Arithmetic Coding

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.

Represent 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]; ```

Create and Decode an Arithmetic Code

Encode and decode a sequence from a source having three symbols.

Create a sequence vector containing symbols from the set of {1,2,3}.

`seq = [3 3 1 3 3 3 3 3 2 3];`

Set the `counts` vector to define an encoder that produces 10 ones, 20 twos, and 70 threes from a typical 100-symbol set of test data.

`counts = [10 20 70];`

Apply the arithmetic encoder and decoder functions.

```code = arithenco(seq,counts); dseq = arithdeco(code,counts,length(seq));```

Verify that the decoder output matches the original input sequence.

`isequal(seq,dseq)`
```ans = logical 1 ```