The capacity of a class of 3-receiver broadcast channels with degraded message sets

TL;DR

This paper demonstrates that the capacity region for certain 3-receiver broadcast channels with degraded message sets exceeds the straightforward extension of the 2-receiver Korner-Marton region, introducing indirect decoding as a key technique.

Contribution

It establishes the capacity region for a class of 3-receiver broadcast channels with degraded message sets, showing it can be larger than previously conjectured, and introduces indirect decoding.

Findings

Capacity region exceeds straightforward extension in some cases

Introduces indirect decoding technique for 3-receiver channels

Bounds are tight for specific nontrivial cases

Abstract

Korner and Marton established the capacity region for the 2-receiver broadcast channel with degraded message sets. Recent results and conjectures suggest that a straightforward extension of the Korner-Marton region to more than 2 receivers is optimal. This paper shows that this is not the case. We establish the capacity region for a class of 3-receiver broadcast channels with 2 degraded message sets and show that it can be strictly larger than the straightforward extension of the Korner-Marton region. The key new idea is indirect decoding, whereby a receiver who cannot directly decode a cloud center, finds it indirectly by decoding satellite codewords. This idea is then used to establish new inner and outer bounds on the capacity region of the general 3-receiver broadcast channel with 2 and 3 degraded message sets. We show that these bounds are tight for some nontrivial cases. The results suggest that the capacity of the 3-receiver broadcast channel with degraded message sets is as at least as hard to find as the capacity of the general 2-receiver broadcast channel with common and private message.