Sum capacity of multi-source linear finite-field relay networks with fading

TL;DR

This paper investigates the sum capacity of multi-source linear finite-field relay networks with fading, proposing a scheme that leverages channel variations to improve decoding and characterizing capacity in certain scenarios.

Contribution

It introduces a block Markov encoding scheme that exploits fading channel variations and derives capacity bounds for specific network classes.

Findings

Sum capacity equals the minimum average rank of channel matrices for uniform channels.

Capacity characterization achieved for certain network topologies and channel distributions.

Proposed scheme effectively utilizes channel variations to enhance decoding performance.

Abstract

We study a fading linear finite-field relay network having multiple source-destination pairs. Because of the interference created by different unicast sessions, the problem of finding its capacity region is in general difficult. We observe that, since channels are time-varying, relays can deliver their received signals by waiting for appropriate channel realizations such that the destinations can decode their messages without interference. We propose a block Markov encoding and relaying scheme that exploits such channel variations. By deriving a general cut-set upper bound and an achievable rate region, we characterize the sum capacity for some classes of channel distributions and network topologies. For example, when the channels are uniformly distributed, the sum capacity is given by the minimum average rank of the channel matrices constructed by all cuts that separate the entire sources and destinations. We also describe other cases where the capacity is characterized.