Rateless codes for AVC models

Authors:
Anand D. Sarwate;Michael Gastpar
Affiliations:
Information Theory and Applications Center, University of California, San Diego, La Jolla, CA and Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA;Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Berkeley, CA and Faculty of Electrical Engineering, Mathematics and Computer Science, Delft Universi ...
Venue:
IEEE Transactions on Information Theory
Year:
2010

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Abstract

The arbitrarily varying channel (AVC) is a channel model whose state is selected maliciously by an adversary. Fixed-blocklength coding assumes a worst-case bound on the adversary's capabilities, which leads to pessimistic results. This paper defines a variable-length perspective on this problem, for which achievable rates are shown that depend on the realized actions of the adversary. Specifically, rateless codes are constructed which require a limited amount of common randomness. These codes are constructed for two kinds of AVC models. In the first the channel state cannot depend on the channel input, and in the second it can. As a by-product, the randomized coding capacity of the AVC with state depending on the transmitted codeword is found and shown to be achievable with a small amount of common randomness. The results for this model are proved using a randomized strategy based on list decoding.