Expansion coding: Achieving the capacity of an AEN channel
Abstract
A general method of coding over expansions is proposed, which allows one to reduce the highly nontrivial problem of coding over continuous channels to a much simpler discrete ones. More specifically, the focus is on the additive exponential noise (AEN) channel, for which the (binary) expansion of the (exponential) noise random variable is considered. It is shown that each of the random variables in the expansion corresponds to independent Bernoulli random variables. Thus, each of the expansion levels (of the underlying channel) corresponds to a binary symmetric channel (BSC), and the coding problem is reduced to coding over these parallel channels while satisfying the channel input constraint. This optimization formulation is stated as the achievable rate result, for which a specific choice of input distribution is shown to achieve a rate which is arbitrarily close to the channel capacity in the high SNR regime. Remarkably, the scheme allows for lowcomplexity capacityachieving codes for AEN channels, using the codes that are originally designed for BSCs. Extensions to different channel models and applications to other coding problems are discussed.
 Publication:

arXiv eprints
 Pub Date:
 February 2012
 arXiv:
 arXiv:1202.1572
 Bibcode:
 2012arXiv1202.1572O
 Keywords:

 Computer Science  Information Theory