Capacity Bounds for Diamond Networks with an Orthogonal Broadcast Channel

TL;DR

This paper derives new capacity bounds for diamond networks with orthogonal broadcast channels, improving existing bounds and establishing capacity in key cases for Gaussian and binary adder MACs.

Contribution

It introduces generalized upper bounds and tight lower bounds for this network class, extending previous techniques and establishing capacity in several scenarios.

Findings

Bounds are tighter than previous results for Gaussian MACs.

Capacity is established for all ranges of bit-pipe capacities in binary adder MACs.

The proof techniques generalize existing methods for Gaussian networks.

Abstract

A class of diamond networks is studied where the broadcast component is orthogonal and modeled by two independent bit-pipes. New upper and lower bounds on the capacity are derived. The proof technique for the upper bound generalizes bounding techniques of Ozarow for the Gaussian multiple description problem (1981) and Kang and Liu for the Gaussian diamond network (2011). The lower bound is based on Marton's coding technique and superposition coding. The bounds are evaluated for Gaussian and binary adder multiple access channels (MACs). For Gaussian MACs, both the lower and upper bounds strengthen the Kang-Liu bounds and establish capacity for interesting ranges of bit-pipe capacities. For binary adder MACs, the capacity is established for all ranges of bit-pipe capacities.