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, integrating it into concatenated codes to improve error performance and demonstrate practical benefits with LDPC and turbo codes.

Contribution

It introduces a new optimal linear feedback scheme for noisy feedback channels and shows how to effectively incorporate it into concatenated coding to enhance error rates.

Findings

Improved error exponent bounds with the new scheme.

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

Simulation results confirm advantages with LDPC and turbo codes.

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 the 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 outer code. Simulations with low density parity check (LDPC) and turbo codes are provided to display these advantages.