Joint Source-Channel Coding of Gaussian Sources over Block Erasure Channels: Nonasymptotic Bounds and Channel-Uniform Normal Approximations

Abstract

We study finite-blocklength lossy transmission of a Gaussian memoryless source over memoryless, possibly nonstationary block erasure channels under an excess mean-squared distortion criterion. We derive computable nonasymptotic achievability and converse bounds and establish matching third-order, channel-uniform normal approximations. Our achievability bound exactly evaluates the ensemble-average excess-distortion probability of a specified random coding scheme and improves corresponding specializations of known general one-shot bounds. Our converse conditions on the erasure pattern and source energy and combines spherical-cap and volume bounds, with the spherical-cap term providing the geometric prefactor needed for the matching third-order term. In our channel-uniform normal approximation, we show that for fixed distortion ratio, target excess-distortion probability, and block size, the sufficient and necessary information-balance conditions have the same dispersion and $\frac{1}{2}\log k$ terms, where $k$ is the source blocklength, and differ only by bounded remainders that are uniform over the channel blocklength and erasure-probability profile. Numerical evaluations compare the nonasymptotic JSCC bounds and their common third-order normal approximation with an optimized symmetrized SSCC achievability benchmark.