On the Dispersions of the Gel'fand-Pinsker Channel and Dirty Paper Coding

TL;DR

This paper analyzes second-order coding rates for channels with known states, improving existing bounds for finite and Gaussian cases, and demonstrating that second-order effects match those of standard Gaussian channels.

Contribution

It provides new achievability results for second-order rates in Gel'fand-Pinsker channels, including finite alphabet and Gaussian cases, using novel coding strategies.

Findings

Second-order rates are improved over previous bounds for finite alphabets.

Gaussian case second-order asymptotics match those of standard Gaussian channels.

Achievability is demonstrated using constant-composition and sphere surface coding methods.

Abstract

This paper studies second-order coding rates for memoryless channels with a state sequence known non-causally at the encoder. In the case of finite alphabets, an achievability result is obtained using constant-composition random coding, and by using a small fraction of the block to transmit the type of the state sequence. For error probabilities less than 1/2, it is shown that the second-order rate improves on an existing one based on i.i.d. random coding. In the Gaussian case (dirty paper coding) with an almost-sure power constraint, an achievability result is obtained used using random coding over the surface of a sphere, and using a small fraction of the block to transmit a quantized description of the state power. It is shown that the second-order asymptotics are identical to the single-user Gaussian channel of the same input power without a state.