An improved Ziv‐lempel coding scheme for universal source coding

Abstract

AbstractThis paper proposes a universal information source code (improved ZL code) based on the Ziv‐Lempel (ZL) incremental parsing algorithm. It is known that a ZL code is asymptotically optimum for a stationary ergodic information source, although it does not utilize the source structure. Its convergence, however, is very slow and it cannot provide efficient compression for an input string of limited length. This paper considers the redundancy of ZL code, which is the reason for the slow convergence. In order to eliminate the redundancy a coding scheme is presented in which only the substring obtained by incremental parsing is used in the next stage. When the substrings of the incremental parsing are separately coded the improved ZL code obtained by the proposed scheme is the least redundant in the sense that the mean code length for the substrings is minimized. In the coding a data structure called modified ZL tree is introduced and its properties discussed together with two coding algorithms based on that structure. The coding is actually performed for the output string from a memory‐less binary source and binary Markov source. It is shown that sufficient compression is realized for a binary code string length of 103 to 104, indicating the possibility as a practical data compression algorithm.