How Much Rate Splitting Is Required for a Random Coding Scheme? A new Achievable Rate Region for the Broadcast Channel with Cognitive Relays

TL;DR

This paper introduces a new achievable rate region for the broadcast channel with cognitive relays, demonstrating that splitting messages into more than two sub-messages is unnecessary, and provides a systematic, graphical approach to scheme design.

Contribution

It presents a novel, unified achievability scheme combining Han-Kobayashi and Marton coding, showing that only two sub-messages per private message suffice for optimality.

Findings

Achievable rate region includes previous results.

Splitting messages into more than two sub-messages is redundant.

Graphical illustrations facilitate scheme design for various networks.

Abstract

In this paper, it is shown that for any given single-hop communication network with two receivers, splitting messages into more than two sub-messages in a random coding scheme is redundant. To this end, the Broadcast Channel with Cognitive Relays (BCCR) is considered. A novel achievability scheme is designed for this network. Our achievability design is derived by a systematic combination of the best known achievability schemes for the basic building blocks included in the network: the Han-Kobayashi scheme for the two-user interference channel and the Marton coding scheme for the broadcast channel. Meanwhile, in our scheme each private message is split into only two sub-messages which is identically exploited also in the Han-Kobayashi scheme. It is shown that the resultant achievable rate region includes previous results as well. More importantly, the procedure of the achievability design is described by graphical illustrations based on directed graphs. Then, it is argued that by extending the proposed scheme on the MACCM plan of messages, one can derive similar achievability schemes for any other single-hop communication network.