Variable-length Feedback Codes with Several Decoding Times for the Gaussian Channel

Abstract

We investigate variable-length feedback (VLF) codes for the Gaussian point-to-point channel under maximal power, average error probability, and average decoding time constraints. Our proposed strategy chooses K < ∞ decoding times n₁,n₂,…,n_K rather than allowing decoding at any time n = 0,1,2,…. We consider stop-feedback, which is one-bit feedback transmitted from the receiver to the transmitter at times n₁,n₂,… only to inform her whether to stop. We prove an achievability bound for VLF codes with the asymptotic approximation ln M ≈ NC(P)/1−ϵ − √N ln_((K−1))(N)V(P)/1−ϵ, where ln_((K))(⋅) denotes the K-fold nested logarithm function, N is the average decoding time, and C(P) and V(P) are the capacity and dispersion of the Gaussian channel, respectively. Our achievability bound evaluates a non-asymptotic bound and optimizes the decoding times n₁,…,n_K within our code architecture.