Adaptive Huffman coding

Adaptive Huffman coding is an [adaptive coding] technique based on Huffman coding, that allows one-pass encoding of the message by creating the codebook, as the data is being transmitted.

The algorithm

Code is represented as a tree structure in which every node has a corresponding weight and a unique number.
Numbers go down, and from left to right so if A is parent node of B and node C is child of B, then A<B<C.
The weight is merely the count of symbols transmited which codes are associated with children of that node.
A set of nodes with same weights make a block.

To get the code for every node, in case of binary tree we could just traverse all the path from the root to the node, writing down (for example)"1" if we go to the right and "0" if we go to the left.

We need some general and straightforwad metod to transmit symbols which are not yet transmitted (NYT), we could use tranmission of binary numbers for every symbol in alphabet.

Encoder and decoder start with the only the root node which has the maximum number, in the begining it is our initial NYT node. When we transmit an NYT symbol we have to transmit code for NYT node then it's generic code. For every symbol which already in the tree we only have to transmit code for it's external node.

For every symbol transmitted on both sides we must execute update procedure:

1. If current symbol is NYT, add two child nodes to NYT node, one will be a new NYT node the other is external node for our symbol, increase weight for new external node and old NYT, goto step 4
else
go to symbols external node.

3. If this node does not have the highest number in a block swap it with which has the highest number

4. Increase weight for current node

4. If this is not the root node go to parent node, goto step 3
else end

Note: swapping nodes means swapping weights, corresponding symbols bat not the numbers.