Variable-Length Sparse Feedback Codes for Point-to-Point, Multiple Access, and Random Access Channels

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, . . . , nK 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 ≈ N C(P )1− , 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, . . . , nK within our code architecture.