Coset codes for communicating over non-additive channels

TL;DR

This paper advocates for using coset codes with algebraic closure properties to improve communication rates over non-additive multi-terminal channels, demonstrating their advantages over iid codes in various scenarios.

Contribution

It introduces the application of coset codes to non-additive channels and proves they achieve larger rate regions than iid codes in multiple multi-terminal communication scenarios.

Findings

Coset codes outperform iid codes in certain non-additive channels.

Achievable rate regions are strictly larger with coset codes.

Results motivate moving beyond iid codes in multi-terminal information theory.

Abstract

We present a case for the use of codes possessing algebraic closure properties - coset codes - in developing coding techniques and characterizing achievable rate regions for generic multi-terminal channels. In particular, we consider three diverse communication scenarios - $3-$user interference channel (many-to-many), $3-$user broadcast channel (one-to-many), and multiple access with distributed states (many-to-one) - and identify non-additive examples for which coset codes are analytically proven to yield strictly larger achievable rate regions than those achievable using iid codes. On the one hand, our findings motivate the need for multi-terminal information theory to step beyond iid codes. On the other, it encourages current research of linear code-based techniques to go beyond particular additive communication channels. Detailed proofs of our results are available in [1]-[3].