Adaptive Huffman coding

Adaptive Huffman coding (also called Dynamic Huffman coding) is an adaptive coding technique based on Huffman coding. It permits building the code as the symbols are being transmitted, having no initial knowledge of source distribution, that allows one-pass encoding and adaptation to changing conditions in data.

The benefit of one-pass procedure is that the source can be encoded in real time, though it becomes more sensitive to transmission errors, since just a single loss ruins the whole code.

There are a number of implementations of this method, the most notable are FGK (Faller-Gallager-Knuth) and Vitter algorithm.

It is an online coding technique based on Huffman coding. Having no initial knowledge of occurrence frequencies, it permits dynamically adjusting the Huffman's tree as data are being transmitted. In a FGK Huffman tree, a special external node, called 0-node, is used to identify a newly-coming character. That is, whenever new data are encountered, output the path to the 0-node followed by the data. For a past-coming character, just output the path of the data in the current Huffman's tree. Most importantly, we have to adjust the FGK Huffman tree if necessary, and finally update the frequency of related nodes. As the frequency of a datum is increased, the sibling property of the Huffman's tree may be broken. The adjustment is triggered for this reason. It is accomplished by consecutive swappings of nodes, subtrees, or both. The data node is swapped with the highest-ordered node of the same frequency in the Huffman's tree, (or the subtree rooted at the highest-ordered node). All ancestor nodes of the node should also be processed in the same manner.

Since the FGK Algorithm has some drawbacks about the node-or-subtree swapping, Vitter proposed another algorithm to improve it.

Some important terminologies & constraints :-

Blocks are interlinked by increasing order of their weights.

A leaf block always precedes internal block of same weight, thus maintaining the invariant.

'NYT(Not Yet Transferred) is special node and used to represents symbols which are 'not yet transferred.

Encoder and decoder start with only the root node, which has the maximum number. In the beginning it is our initial NYT node.

When we transmit an NYT symbol, we have to transmit code for the NYT node, then for its generic code.

For every symbol that is already in the tree, we only have to transmit code for its leaf node.

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