Combination coding: a new entropy coding technique

Summary form only given. Entropy coding is defined to be the compression of a stream of symbols taken from a known symbol set where the probability of occurrence of any symbol from the set at any given point in the stream is constant and independent of any known occurrences of any other symbols. Shannon and Fano showed that the information of such a sequence could be calculated. When measured in bits the information represents the optimum compressed length of the original sequence. If information about sequential redundancy is known better compression may be possible by one of the substitution coding techniques of Ziv and Lempel. In the absence of any such information, entropy coding provides an optimum coding strategy. Huffman posed an optimal variable word length coding technique. Many years later the arithmetic coding technique was formulated by IBM which provided compression close to the optimum. Combination coding is as efficient as arithmetic coding and is very fast as it only requires basic integer operations for both the compression and decompression stages. The technique is in fact for the entropy coding of a binary sequence but by the use of a binary tree, the entropy coding of a sequence of any number of symbols can be reduced to the entropy coding of a number of binary sequences.