No abstract

The 3-user discrete memoryless interference channel is considered in this paper. We provide a new inner bound (achievable rate region) to the capacity region for this channel. This inner bound is based on a new class of code ensembles based on asymptotically good nested linear codes. This achievable region is strictly superior to the straightforward extension of Han-Kobayashi rate region from the case of twousers to three-users. This rate region is characterized using single-letter information quantities. We consider examples to illustrate the rate region.

Abstract-It is shown that the original construction of polar codes suffices to achieve the symmetric capacity of discrete memoryless channels with arbitrary input alphabet sizes. It is shown that in general, channel polarization happens in several, rather than only two, levels so that the synthesized channels are either useless, perfect or "partially perfect". Given a coset decomposition of the input alphabet, there exists a corresponding partially perfect channel whose outputs uniquely determine the coset where the channel input symbol belongs to. By a slight modification of the encoding and decoding rules, it is shown that perfect transmission of certain information letters over partially perfect channels is possible. It is also shown through an example that polar codes do not achieve the capacity of coset codes over arbitrary channels.

We consider the problem of communication over a three user discrete memoryless interference channel (3−IC).The current known coding techniques for communicating over an arbitrary 3−IC are based on message splitting, superposition coding and binning using independent and identically distributed (iid) random codebooks. In this work, we propose a new ensemble of codes -partitioned coset codes (PCC) -that possess an appropriate mix of empirical and algebraic closure properties. We develop coding techniques that exploit algebraic closure property of PCC to enable interference alignment over general 3−IC. We analyze the performance of the proposed coding technique to derive an achievable rate region for the general discrete 3−IC. Additive and non-additive examples are identified for which the derived achievable rate region is the capacity, and moreover, strictly larger than current known largest achievable rate regions based on iid random codebooks.

In this paper, we study the asymptotic performance of Abelian group codes for the the channel coding problem for arbitrary discrete (finite alphabet) memoryless channels as well as the lossy source coding problem for arbitrary discrete (finite alphabet) memoryless sources. For the channel coding problem, we find the capacity characterized in a single-letter information-theoretic form. This simplifies to the symmetric capacity of the channel when the underlying group is a field. For the source coding problem, we derive the achievable rate-distortion function that is characterized in a single-letter information-theoretic form. When the underlying group is a field, it simplifies to the symmetric rate-distortion function. We give several illustrative examples. Due to the non-symmetric nature of the sources and channels considered, our analysis uses a synergy of information-theoretic and group-theoretic tools.