An on-line universal lossy data compression algorithm via continuous codebook refinement. I. Basic results

A new on-line universal lossy data compression algorithm is presented. For finite memoryless sources with unknown statistics, its performance asymptotically approaches the fundamental rate distortion limit. The codebook is generated on the fly, and continuously adapted by simple rules. There is no separate codebook training or codebook transmission. Candidate codewords are randomly generated according to an arbitrary and possibly suboptimal distribution. Through a carefully designed "gold washing" or "information-theoretic sieve" mechanism, good codewords and only good codewords are promoted to permanent status with high probability. We also determine the rate at which our algorithm approaches the fundamental limit.