Variable-length Coding Error Exponents for the AWGN Channel with Noisy Feedback at Zero-Rate

A one-way additive white Gaussian noise (AWGN) channel with active feedback sent over another AWGN feedback channel is considered. Achievable error exponents are presented in the finite message / zero-rate regime for a variable length coding (VLC) scheme. This coding scheme uses a form of round-robin scheduling of messages, and a simplex-based feedback code to obtain reliable feedback and remain synchronized, despite the noise in the feedback link. Our results show that this new VLC scheme under an almost-sure power constraint achieves an error exponent similar to an achievable exponent attained using a fixed block length scheme under a much more relaxed expected block power constraint, and is larger than that achieved by schemes without feedback.1