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

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 < infinity decoding times n(1), n(2), ..., 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 n(1), n(2), ... only to inform her whether to stop. We prove an achievability bound for VLF codes with the asymptotic approximation In M approximate to NC(P)/1-epsilon-root N In(K-1) (N)V(P)/1-epsilon, where In-(K) (center dot) 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 n(1), ..., n(K) within our code architecture.

Automated summary

Variable-length feedback (VLF) codes for the Gaussian point-to-point channel are investigated under maximal power, average error probability, and average decoding time constraints. A proposed strategy chooses decoding times and considers stop-feedback, with an achievability bound for VLF codes optimizing decoding times within the code architecture.