Fast and efficient coding of information sources

The author considers the problem of source coding and investigates the cases of known and unknown statistics. The efficiency of the compression codes can be estimated by three characteristics: 1) the redundancy (r), defined as the maximal difference between the average codeword length and Shannon entropy in case the letters are generated by a Bernoulli source; 2) the size (in bits) of the encoder and the encoder programs (S) when implemented on a computer; and 3) the average time required for encoding and decoding of a single letter (T). He investigates S and T as a function of r when r→0. All known methods may be divided into two classes. The Ziv-Lempel codes and their variants fall under the first class, and the arithmetic code with the Lynch-Davisson code fall under the second one. The codes from the first class need exponential memory size S=0(exp(1/r)) for redundancy r when r→O. The methods from the second class have a small memory size but a low encoding speed: S=0(1/r^const), T=0(log^const(1/r) log log (1/r)). In this paper, the author presents a code that combines the merits of both classes; the memory size is small and the speed is high: S=0(1/r^const),T=0(log ^const(1/r) log log (1/r))