Probability of error for the fixed-length lossy coding of general sources
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 Verdu, 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 epsilon(n)(D) similar to e(-nr) (n -> infinity), where r is the prescribed error exponent, epsilon(n) (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 crrect decoding in lossy coding is established.
general source error exponent reliability function continuous alphabet fixed-length source coding information spectrum large-deviation rate-distortion theory