A power interval perspective on additive white Gaussian noise (AWGN) channels

Abstract

We present a new perspective on additive white Gaussian noise (AWGN) channels that separates user and channel attributes. Following this separation, various questions concerning achievability and successive decoding can be reformulated as properties of the set of user attributes, which can be determined independently of the actual channel noise. To obtain these properties directly, we introduce a graphical framework called the power diagram. Based on graphical manipulations in this framework, our results on N-user multi-access channels include the following: 1. simplifying the achievability condition to an algorithm requiring 0 (N In N) computations 2. simplifying the check of whether a given rate tuple is decodable with simple successive decoding (to be defined) to an algorithm requiring 0(N ln N) computations 3. developing a technique for power-reduced successive decoding, accompanied by the set of rate tuples for which such a technique is applicable, and an algorithm that checks whether a given rate tuple is decodable with this technique requiring O(N In N) computations 4. presenting a class of graphical constructions for splitting any achievable rate tuple into a set of virtual users that allows successive decoding. These constructions deal with rate tuples not on the dominant face in a natural way, whereas previous works have viewed these rate tuples as a somewhat ad hoc extension of the dominant face results 5. presenting a class of graphical constructions that facilitate successive decoding to any achievable rate tuple using the time-sharing technique, improving the known upper bound on decoding complexity (using this combination of techniques) to 2N - !