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].
We consider the problem of communicating over a classical-quantum (CQ) multiple access channel with random classical states non-causally available at the transmitter, referred to as a QMSTx. QMSTx is a classical-quantum multiple access analogue of the channel considered by Gelfand and Pinsker in 1980. We undertake a Shannon-theoretic study and focus on the problem of characterizing inner bounds to the capacity region of a QMSTx. We propose a new coding scheme based on \textit{union coset codes} - codes possessing algebraic properties and derive a new inner bound that subsumes the inner based o…
We consider the problem of communicating a general bivariate function of two classical sources observed at the encoders of a classical-quantum multiple access channel. Building on the techniques developed for the case of a classical channel, we propose and analyze a coding scheme based on coset codes. The proposed technique enables the decoder recover the desired function without recovering the sources themselves. We derive a new set of sufficient conditions that are weaker than the current known for identified examples. This work is based on a new ensemble of coset codes that are proven to ac…
We consider the problem of characterizing an inner bound to the capacity region of a $3-$user classical-quantum interference channel ($3-$CQIC). The best known coding scheme for communicating over CQICs is based on unstructured random codes and employs the techniques of message splitting and superposition coding. For classical $3-$user interference channels (ICs), it has been proven that coding techniques based on coset codes - codes possessing algebraic closure properties - strictly outperform all coding techniques based on unstructured codes. In this work, we develop analogous techniques bas…
