On the Joint Source-Channel Coding Error Exponent for Discrete Memoryless Systems: Computation and Comparison with Separate Coding

TL;DR

This paper analyzes the joint source-channel coding error exponent for discrete memoryless systems, providing computational methods, bounds comparison, and demonstrating potential power savings over separate coding schemes.

Contribution

It introduces explicit formulas and algorithms for computing the JSCC error exponent and compares it systematically with separate coding error exponents.

Findings

E_J is generally greater than E_T and can approach 2E_T.

Power savings over separate coding can exceed 2 dB.

Numerical examples confirm E_J's proximity to 2E_T in many cases.

Abstract

We investigate the computation of Csiszar's bounds for the joint source-channel coding (JSCC) error exponent, E_J, of a communication system consisting of a discrete memoryless source and a discrete memoryless channel. We provide equivalent expressions for these bounds and derive explicit formulas for the rates where the bounds are attained. These equivalent representations can be readily computed for arbitrary source-channel pairs via Arimoto's algorithm. When the channel's distribution satisfies a symmetry property, the bounds admit closed-form parametric expressions. We then use our results to provide a systematic comparison between the JSCC error exponent E_J and the tandem coding error exponent E_T, which applies if the source and channel are separately coded. It is shown that E_T <= E_J <= 2E_T. We establish conditions for which E_J > E_T and for which E_J = 2E_T. Numerical examples indicate that E_J is close to 2E_T for many source-channel pairs. This gain translates into a power saving larger than 2 dB for a binary source transmitted over additive white Gaussian noise channels and Rayleigh fading channels with finite output quantization. Finally, we study the computation of the lossy JSCC error exponent under the Hamming distortion measure.