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

• Authors: John C. Kieffer;En-Hui Yang
• Venue: DCC '99 Proceedings of the Conference on Data Compression
• Year: 1999

If x is a string of finite length over a finite 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 µ(x) be the probability assigned to x by a memoryless source model. Using a very simple technique, we prove the pointwise redundancy bound LZ(x) + log 2 µ(x) = 8t(x) max{ log 2 µ(a) : a ? A}