Variable-length Feedback Codes with Several Decoding Times for the Gaussian Channel
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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 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 ln M ≈N C(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 n_1, …, n_K within our code architecture.
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