Asymptotically optimal lossy Lempel-Ziv coding

A new lossy variant of the fixed-database Lempel-Ziv algorithm is proposed, for encoding memoryless sources at a fixed distortion level. Its asymptotic optimality and universality are demonstrated, with respect to bounded single-letter distortion measures. As the database size m increases to infinity, the expected compression ratio approaches the rate-distortion function. The complexity and redundancy characteristics of the algorithm are comparable to those of its lossless counterpart. A heuristic argument suggests that the redundancy is of order (loglog m)/log m, and this is also confirmed experimentally by simulation results. Also, the complexity of the algorithm is seen to be comparable to that of the corresponding lossless scheme, at least in their naive implementations