Syndrome-source-coding and its universal generalization

Abstract

A method of using error-correcting codes to obtain data compression, called syndrome-source-coding, is described in which the source sequence is treated as an error pattern whose syndrome forms the compressed data. It is shown that syndrome-source-coding can achieve arbitrarily small distortion with the number of compressed digits per source digit arbitrarily close to the entropy of a binary memoryless source. A 'universal' generalization of syndrome-source-coding is formulated which provides robustly effective distortionless coding of source ensembles. Two examples are given, comparing the performance of noiseless universal syndrome-source-coding to (1) run-length coding and (2) Lynch-Davisson-Schalkwijk-Cover universal coding for an ensemble of binary memoryless sources.