Joint Transmission and State Estimation: A Constrained Channel Coding Approach

TL;DR

This paper introduces a capacity-distortion function for joint message transmission and channel state estimation, demonstrating a fundamental tradeoff and optimal strategies for fading channels, extended to multiple access scenarios.

Contribution

It establishes a new capacity-distortion framework for joint transmission and state estimation, including a characterization for Rayleigh fading channels and extensions to multiple access channels.

Findings

Capacity-distortion function characterizes the tradeoff between rate and estimation fidelity.

Non-coherent communication with training achieves the capacity-distortion limit.

Capacity for Rayleigh fading channels is characterized within 1.443 bits at high SNR.

Abstract

A scenario involving a source, a channel, and a destination, where the destination is interested in {\em both} reliably reconstructing the message transmitted by the source and estimating with a fidelity criterion the state of the channel, is considered. The source knows the channel statistics, but is oblivious to the actual channel state realization. Herein it is established that a distortion constraint for channel state estimation can be reduced to an additional cost constraint on the source input distribution, in the limit of large coding block length. A newly defined capacity-distortion function thus characterizes the fundamental tradeoff between transmission rate and state estimation distortion. It is also shown that non-coherent communication coupled with channel state estimation conditioned on treating the decoded message as training symbols achieves the capacity-distortion function. Among the various examples considered, the capacity-distortion function for a memoryless Rayleigh fading channel is characterized to within 1.443 bits at high signal-to-noise ratio. The constrained channel coding approach is also extended to multiple access channels, leading to a coupled cost constraint on the input distributions for the transmitting sources.