Achievable Error Exponents in the Gaussian Channel With Rate-Limited Feedback

DOI10.1109/TIT.2013.2280918zbMATH Open1364.62008arXiv1007.1986OpenAlexW2096658028MaRDI QIDQ5346215

Andrea J. Goldsmith, Reza Mirghaderi, Tsachy Weissman

Publication date: 8 June 2017

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

Abstract: We investigate the achievable error probability in communication over an AWGN discrete time memoryless channel with noiseless delay-less rate-limited feedback. For the case where the feedback rate R_FB is lower than the data rate R transmitted over the forward channel, we show that the decay of the probability of error is at most exponential in blocklength, and obtain an upper bound for increase in the error exponent due to feedback. Furthermore, we show that the use of feedback in this case results in an error exponent that is at least RF B higher than the error exponent in the absence of feedback. For the case where the feedback rate exceeds the forward rate (R_FB geq R), we propose a simple iterative scheme that achieves a probability of error that decays doubly exponentially with the codeword blocklength n. More generally, for some positive integer L, we show that a L-th order exponential error decay is achievable if R_FB geq (L-1)R. We prove that the above results hold whether the feedback constraint is expressed in terms of the average feedback rate or per channel use feedback rate. Our results show that the error exponent as a function of R_FB has a strong discontinuity at R, where it jumps from a finite value to infinity.

Full work available at URL: https://arxiv.org/abs/1007.1986

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Statistical aspects of information-theoretic topics (62B10) Channel models (including quantum) in information and communication theory (94A40)

Related Items (5)

Achievable Rates for Nonlinear Volterra Channels ⋮ On Gaussian MACs With Variable-Length Feedback and Non-Vanishing Error Probabilities ⋮ On the Computational Cutoff Rate, R₀for the Peak-Power-Limited Gaussian Channel ⋮ On the zero-rate error exponent for a BSC with noisy feedback ⋮ Finite-size effects and error-free communication in Gaussian channels

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