Optimal Linear Joint Source-Channel Coding with Delay Constraint

TL;DR

This paper derives an optimal linear, causal joint source-channel coding scheme for Gaussian sources and channels with delay constraints, using spectral factorization and convex optimization, and discusses its properties and limitations.

Contribution

It introduces a convex optimization framework for designing optimal LTI encoders and decoders under delay constraints for Gaussian sources and channels.

Findings

Optimal LTI encoders/decoders minimize a convex functional combining Wiener filter cost and channel noise effects.

The optimal solution generally requires infinite memory, necessitating approximations.

Numerical results show performance close to rate-distortion lower bounds.

Abstract

The problem of joint source-channel coding is considered for a stationary remote (noisy) Gaussian source and a Gaussian channel. The encoder and decoder are assumed to be causal and their combined operations are subject to a delay constraint. It is shown that, under the mean-square error distortion metric, an optimal encoder-decoder pair from the linear and time-invariant (LTI) class can be found by minimization of a convex functional and a spectral factorization. The functional to be minimized is the sum of the well-known cost in a corresponding Wiener filter problem and a new term, which is induced by the channel noise and whose coefficient is the inverse of the channel's signal-to-noise ratio. This result is shown to also hold in the case of vector-valued signals, assuming parallel additive white Gaussian noise channels. It is also shown that optimal LTI encoders and decoders generally require infinite memory, which implies that approximations are necessary. A numerical example is provided, which compares the performance to the lower bound provided by rate-distortion theory.