Prefix code: Difference between revisions

Revision as of 11:25, 22 November 2014

Revision as of 11:27, 22 November 2014

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A fixed-length code is necessarily a prefix code. It is possible to turn any code into a fixed-length code by padding fixed symbols to the shorter prefixes in order to meet the length of the longest prefixes. Alternately, such padding codes may be employed to introduce redundancy that allows autocorrection and/or synchronisation. However, fixed length encodings are inefficient in situations where some words are much more likely to be transmitted than others.

[[Truncated binary encoding]] is a straightforward generalization of fixed-length codes to deal with cases where the number of symbols ''n'' is not a power of two. Source symbols are assigned codewords of length ''k'' and ''k''+1., where ''k'' is chosen so that ''2<mathsup>2^{k}</sup> < n <≤ 2^{<sup>k+1}</mathsup>''.

[[Huffman coding]] is a more sophisticated technique for constructing variable-length prefix codes. The Huffman coding algorithm takes as input the frequencies that the code words should have, and constructs a prefix code that minimizes the weighted average of the code word lengths. This is a form of [[lossless data compression]] based on [[entropy encoding]].