Information Spectrum Approach to Second-Order Coding Rate in Channel Coding

TL;DR

This paper uses the information spectrum method to determine the optimal second-order coding rates for various channels, highlighting limitations of the Gallager bound in this context.

Contribution

It extends the information spectrum approach to second-order coding rates across multiple channel models, providing a unified framework.

Findings

Derived the optimal second-order transmission rate for general channels.

Applied results to DMC, Markovian, and Gaussian channels with constraints.

Showed Gallager bound is suboptimal for second-order rate evaluation.

Abstract

Second-order coding rate of channel coding is discussed for general sequence of channels. The optimum second-order transmission rate with a constant error constraint $\epsilon$ is obtained by using the information spectrum method. We apply this result to the discrete memoryless case, the discrete memoryless case with a cost constraint, the additive Markovian case, and the Gaussian channel case with an energy constraint. We also clarify that the Gallager bound does not give the optimum evaluation in the second-order coding rate.