Concatenated Coding for the AWGN Channel with Noisy Feedback

TL;DR

This paper develops an asymptotically optimal linear feedback scheme for AWGN channels with noisy feedback, demonstrating improved error performance when used as an inner code in concatenated coding schemes, supported by simulations.

Contribution

It introduces a new optimal linear feedback scheme for noisy AWGN channels and shows its effectiveness as an inner code in concatenated coding, with practical simulation results.

Findings

Improved error exponent bounds with the new scheme

Enhanced bit-error-rate and frame-error-rate performance

Inner code blocklength scales as N=O(C/R) for optimal performance

Abstract

The use of open-loop coding can be easily extended to a closed-loop concatenated code if the channel has access to feedback. This can be done by introducing a feedback transmission scheme as an inner code. In this paper, this process is investigated for the case when a linear feedback scheme is implemented as an inner code and, in particular, over an additive white Gaussian noise (AWGN) channel with noisy feedback. To begin, we look to derive an optimal linear feedback scheme by optimizing over the received signal-to-noise ratio. From this optimization, an asymptotically optimal linear feedback scheme is produced and compared to other well-known schemes. Then, the linear feedback scheme is implemented as an inner code to a concatenated code over the AWGN channel with noisy feedback. This code shows improvements not only in error exponent bounds, but also in bit-error-rate and frame-error-rate. It is also shown that the if the concatenated code has total blocklength L and the inner code has blocklength, N, the inner code blocklength should scale as N = O(C/R), where C is the capacity of the channel and R is the rate of the concatenated code. Simulations with low density parity check (LDPC) and turbo codes are provided to display practical applications and their error rate benefits.