Polar Coding for Multi-level 3-Receiver Broadcast Channels

TL;DR

This paper introduces a polar coding strategy for multi-level 3-receiver broadcast channels with degraded message sets, achieving capacity without time-sharing and extending to variants with private messages.

Contribution

It proposes a two-level chaining polar coding scheme that attains the capacity region for multi-level 3-receiver broadcast channels with degraded message sets, including a variant with private messages.

Findings

Achieves capacity region without time-sharing.

Extends to scenarios with private message decoding.

Proposes a novel two-level chaining polar coding strategy.

Abstract

We consider achieving the rates in the capacity region of a multi-level 3-receiver broadcast channel, in which the second receiver is degraded with respect to the first receiver, with degraded message sets. We propose a two-level chaining strategy based on polar codes that achieves the capacity region of the considered setting without time-sharing. We also look at a slight variation of this problem, where the first receiver only requires to decode its own private message and the other two receivers require to decode another private message common to them. We observe that the capacity region does not enlarge and so the proposed polar coding strategy achieves the capacity region for this problem as well.