Finite-Blocklength Performance of Sequential Transmission over BSC with Noiseless Feedback

Hengjie Yang, Richard D. Wesel

In this paper, we consider the problem of sequential transmission over the binary symmetric channel (BSC) with full, noiseless feedback. Naghshvar \emph{et al.} proposed a deterministic encoding scheme, for which we refer to as the small-enough difference (SED) encoder, which can achieve Burnashev's optimal error exponent for any symmetric binary-input channels. They also provided a non-asymptotic upper bound on the average blocklength, which implies a lower bound on achievable rate. However, this lower bound is loose compared to the simulated performance of SED encoder, and even lies beneath Polyanskiy's lower bound on the achievable rate of a system limited to stop feedback. This paper provides an improved lower bound on achievable rate by using a Markovian analysis that leverages both the submartingale and Markov properties of the transmitted message. Our new bound on achievable rate lies above Polyanskiy's bound and close to the actual performance of the SED encoder over the BSC.

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