Probability of error for the fixed-length source coding of general sources

Abstract

In this correspondence, we are interested in the error exponent of fixed-length lossy source coding, where the sources are general sources, in the sense of Han and Verduacute, including all nonstationary and/or nonergodic sources. The aim of the correspondence is to establish a unified formula for the minimum (D, r)-achievable rate which is the minimum achievable coding rate under asymptotic constraints of the form epsivn(D) ~ e-nr (n rarr infin), where r is the prescribed error exponent, epsivn(D) is the probability of the distortion exceeding a level D, and n is the code-length. For the stationary memoryless source with finite alphabet, Marton (1974) obtained a formula for the reliability function which is expressed in terms of the minimum (D,r)- achievable rate. Recently, Ihara and Kubo proved that the Marton's formula remains true for the stationary memoryless Gaussian source under a mean-squared fidelity criterion. In this correspondence, it is shown that a formula similar to Marton's formula holds for the general sources. The error exponent of correct decoding is also investigated and a formula for the minimum achievable rate of correct decoding in lossy coding is established