The capacity of online (causal) q-ary error-erasure channels

Zitan Chen, Sidharth Jaggi, Michael Langberg

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


In the q-ary online (causal) channel coding model, a sender wishes to communicate a message to a receiver by transmitting a codeword x = (x1, ω, xn) ⋯ {0, 1, ω, q ™ 1}n symbol-by-symbol via a channel limited to at most pn errors (symbol changes) and pn erasures. The channel is 'online' (i.e., 'causal') in the sense that at the ith step of communication the channel decides whether to corrupt the ith symbol or not only based on its view of the symbols (x1, ω, xi). This is in contrast to the classical adversarial channel in which the corruption is chosen with full knowledge of the sent codeword x. In this work we extend the results obtained in [1]-[4] (in which the capacities of binary online bit-flip-only channels, and separately binary online erasure-only channels were characterized). We here extend those prior results in two important ways. First, we obtain the capacity of q-ary online channels for general q (rather than just q = 2). Second, we analyze combined error-erasure corruption models (rather than studying them separately). Characterization of this much broader class of symmetric online channels gives a fuller understanding of the effects of causality on jamming adversaries. The extensions in this paper require novel approaches for both optimal code designs, and matching information-theoretic converse arguments.

Original languageEnglish
Title of host publicationProceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages5
ISBN (Electronic)9781509018062
StatePublished - 10 Aug 2016
Externally publishedYes
Event2016 IEEE International Symposium on Information Theory, ISIT 2016 - Barcelona, Spain
Duration: 10 Jul 201615 Jul 2016

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095


Conference2016 IEEE International Symposium on Information Theory, ISIT 2016

Bibliographical note

Publisher Copyright:
© 2016 IEEE.


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