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Register a new userLow Complexity Algorithms for Transmission of Short Blocks over the BSC with Full Feedback
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Added by
Hengjie Yang
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Building on the work of Horstein, Shayevitz and Feder, and Naghshvar emph{et al.}, this paper presents algorithms for low-complexity sequential transmission of a $k$-bit message over the binary symmetric channel (BSC) with full, noiseless feedback. To lower complexity, this paper shows that the initial $k$ binary transmissions can be sent before any feedback is required and groups messages with equal posteriors to reduce the number of posterior updates from exponential in $k$ to linear in $k$. Simulation results demonstrate that achievable rates for this full, noiseless feedback system approach capacity rapidly as a function of average blocklength, faster than known finite-blocklength lower bounds on achievable rate with noiseless active feedback and significantly faster than finite-blocklength lower bounds for a stop feedback system.
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In this paper, we consider the problem of sequential transmission over the binary symmetric channel (BSC) with full, noiseless feedback. Naghshvar et al. proposed a one-phase encoding scheme, for which we refer to as the small-enough difference (SED) encoder, which can achieve capacity and Burnashevs optimal error exponent for symmetric binary-input channels. They also provided a non-asymptotic upper bound on the average blocklength, which implies an achievability bound on rates. However, their achievability bound is loose compared to the simulated performance of SED encoder, and even lies beneath Polyanskiys achievability bound of a system limited to stop feedback. This paper significantly tightens the achievability bound by using a Markovian analysis that leverages both the submartingale and Markov properties of the transmitted message. Our new non-asymptotic lower bound on achievable rate lies above Polyanskiys bound and is close to the actual performance of the SED encoder over the BSC.
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