Expansion Coding: Achieving the Capacity of an AEN Channel
A general method of coding over expansions is proposed, which allows one to reduce the highly non-trivial problem of coding over continuous channels to 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.