Comparison between universal data-compression algorithms applied to Markov sources

A comparison between universal data compression algorithms applied to binary Markov sources is presented. Four algorithms are considered (1) The Ziv-Lempel (Z-L) algorithm proposed in 1978. (2) A state conditioned version of the Z-L algorithm. (3) Rissanen´s algorithm (1986). (4) A sequential algorithm recently presented by Weinberger, Lempel and Ziv (see IEEE Trans. on Information Theory), that performs an online estimation of the source structure and uses an arithmetic code. It is shown via simulation that, actually, the redundancy of the Ziv-Lempel (Z-L) algorithm is considerably smaller than the analytical upper bounds given in (2). Also, the average codeword length in the state conditioned version is, in most cases, smaller than in the original Z-L algorithm, even when conditioning with respect to a set of states that differs from the actual set of states of the source. The redundancy for the sequential algorithm of (4) is almost the same as that for Rissanen´s code