A Simple Technique for Bounding the Pointwise Redundancy of the 1978 Lempel-Ziv Algorithm

Abstract: If x is a string of nite length over a nite alphabet A, let LZ(x) denote the length of the binary codeword assigned to x by the 1978 version of the Lempel-Ziv data compression algorithm, let t(x) be the number of phrases in the Lempel-Ziv parsing of x, and let (x) be the probability assigned to x by a memoryless source model. Using a very simple technique, we prove the pointwise redundancy bound