Nonasymptotic coding-rate bounds for binary erasure channels with feedback
Paper in proceeding, 2016

We present nonasymptotic achievability and converse bounds on the maximum coding rate (for a fixed average error probability and a fixed average blocklength) of variable-length full-feedback (VLF) and variable-length stop-feedback (VLSF) codes operating over a binary erasure channel (BEC). For the VLF setup, the achievability bound relies on a scheme that maps each message onto a variable-length Huffman codeword and then repeats each bit of the codeword until it is received correctly. The converse bound is inspired by the meta-converse framework by Polyanskiy, Poor, and Verdú (2010) and relies on binary sequential hypothesis testing. For the case of zero error probability, our achievability and converse bounds match. For the VLSF case, we provide achievability bounds that exploit the following feature of BEC: the decoder can assess the correctness of its estimate by verifying whether the chosen codeword is the only one that is compatible with the erasure pattern. One of these bounds is obtained by analyzing the performance of a variable-length extension of random linear fountain codes. The gap between the VLSF achievability and the VLF converse bound, when number of messages is small, is significant: 23% for 8 messages on a BEC with erasure probability 0.5. The absence of a tight VLSF converse bound does not allow us to assess whether this gap is fundamental.


Rahul Devassy

Chalmers, Signals and Systems, Communication, Antennas and Optical Networks

Giuseppe Durisi

Chalmers, Signals and Systems, Communication, Antennas and Optical Networks

Benjamin Lindquist

Chalmers, Signals and Systems, Communication, Antennas and Optical Networks

Wei Yang

Princeton University

Marco Dalai

University of Brescia

IEEE Information Theory Workshop (ITW), Cambridge, ENGLAND, SEP 11-14, 2016

86-90 7606801
978-1-5090-1091-2 (ISBN)

Areas of Advance

Information and Communication Technology

Subject Categories


Communication Systems


C3SE (Chalmers Centre for Computational Science and Engineering)





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