Finite-Blocklength Performance of Sequential Transmission over BSC with Noiseless Feedback
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In this paper, we consider the expected blocklength of variable-length coding over the binary symmetric channel (BSC) with noiseless feedback. Horstein first proposed a simple one-phase scheme to achieve the capacity of BSC. Naghshvar et al. used a novel extrinsic Jensen-Shannon (EJS) divergence in a sequential transmission scheme that maximizes EJS (MaxEJS) and provided a non-asymptotic upper bound on the expected blocklength for MaxEJS. Simulations in this paper show that MaxEJS provides lower expected blocklengths than the original Horstein scheme, but the non-asymptotic bound of Naghshvar et al. is loose enough that lies above the simulated performance of Horstein scheme for a BSC with a small crossover probability. This paper proposes a new expression for MaxEJS expected blocklength that is a tight approximation of simulated performance. This expression is developed by exploring a genie-aided decoder (GAD) whose expected blocklength will always be larger than MaxEJS and can be approximated by two random walks. We conjecture that even with these two approximations, the expression may still be an upper bound on blocklength as suggested by the simulation results.
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