Interval and recency rank source coding: Two on-line adaptive variable-length schemes

In the schemes presented the encoder maps each message into a codeword in a prefix-free codeword set. In interval encoding the codeword is indexed by the interval since the last previous occurrence of that message, and the codeword set must be countably infinite. In recency rank encoding the codeword is indexed by the number of distinct messages in that interval, and there must be no fewer codewords than messages. The decoder decodes each codeword on receipt. Users need not know message probabilities, but must agree on indexings, of the codeword set in an order of increasing length and of the message set in some arbitrary order. The average codeword length over a communications bout is never much larger than the value for an off-line scheme which maps the th most frequent message in the bout into the th shortest codeword in the given set, and is never too much larger than the value for off-line Huffman encoding of messages into the best codeword set for the bout message frequencies. Both schemes can do much better than Huffman coding when successive selections of each message type cluster much more than in the independent case.