Fixed-length lossy compression in the finite blocklength regime: discrete memoryless sources

Abstract

This paper studies the minimum achievable source coding rate as a function of blocklength n and tolerable distortion level d. Tight general achievability and converse bounds are derived that hold at arbitrary fixed blocklength. For stationary memoryless sources with separable distortion, the minimum rate achievable is shown to be q closely approximated by R(d) + √v(d)/nQ^(-1)(ϵ), where R(d) is the rate-distortion function, V (d) is the rate dispersion, a characteristic of the source which measures its stochastic variability, Q-1 (·) is the inverse of the standard Gaussian complementary cdf, and ϵ is the probability that the distortion exceeds d. The new bounds and the second-order approximation of the minimum achievable rate are evaluated for the discrete memoryless source with symbol error rate distortion. In this case, the second-order approximation reduces to R(d) + 1/2 log n/n if the source is non-redundant.

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