A Universal Random Coding Ensemble for Sample-Wise Lossy Compression

We propose a universal ensemble for the random selection of rate–distortion codes which is asymptotically optimal in sample-wise sense. According to this ensemble, each reproduction vector, x^, selected independently at under probability distribution that proportional 2−LZ(x^), where LZ(x^) code length x^ pertaining 1978 version Lempel–Ziv (LZ) algorithm. show that, with high probability, resulting codebook gives rise an variable-rate lossy compression scheme arbitrary distortion measure, sense matching converse theorem also holds. theorem, even if decoder knew ℓ-th order type source vector advance (ℓ being large but fixed positive integer), performance above-mentioned could not have been improved essentially vast majority codewords vectors same type. Finally, we present discussion our results, includes among other things, clear indication coding outperforms one selects shortest LZ all are within allowed from vector.