Two-Way Relay Channels: Error Exponents and Resource Allocation

TL;DR

This paper analyzes the error exponents in two-way relay channels with amplify-and-forward relaying, deriving fundamental tradeoffs between rate and reliability, and proposes optimal resource allocation strategies to maximize the bottleneck error exponent.

Contribution

It introduces the concept of the bottleneck error exponent and provides optimal rate and power allocation methods for two-way relay channels.

Findings

Derived the random coding error exponent for each link.

Proposed optimal resource allocation strategies to maximize the bottleneck error exponent.

Numerical results confirm the effectiveness of the proposed allocations.

Abstract

In a two-way relay network, two terminals exchange information over a shared wireless half-duplex channel with the help of a relay. Due to its fundamental and practical importance, there has been an increasing interest in this channel. However, surprisingly, there has been little work that characterizes the fundamental tradeoff between the communication reliability and transmission rate across all signal-to-noise ratios. In this paper, we consider amplify-and-forward (AF) two-way relaying due to its simplicity. We first derive the random coding error exponent for the link in each direction. From the exponent expression, the capacity and cutoff rate for each link are also deduced. We then put forth the notion of the bottleneck error exponent, which is the worst exponent decay between the two links, to give us insight into the fundamental tradeoff between the rate pair and information-exchange reliability of the two terminals. As applications of the error exponent analysis, we present two optimal resource allocations to maximize the bottleneck error exponent: i) the optimal rate allocation under a sum-rate constraint and its closed-form quasi-optimal solution that requires only knowledge of the capacity and cutoff rate of each link; and ii) the optimal power allocation under a total power constraint, which is formulated as a quasi-convex optimization problem. Numerical results verify our analysis and the effectiveness of the optimal rate and power allocations in maximizing the bottleneck error exponent.