Oblivious channels

Michael Langberg

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


Let C = {x1, . . ., xN} ⊂ {0, 1}n be an [n,N] binary error correcting code (not necessarily linear). Let e ∈ {0, 1}n be an error vector. A codeword x ∈ C is said to be disturbed by the error e if the closest codeword to x ⊕ e is no longer x. Let Ae be the subset of codewords in C that are disturbed by e. In this work we study the size of Ae in random codes C (i.e. codes in which each codeword xi is chosen uniformly and independently at random from {0, 1}n). Using recent results of Vu [Random Structures and Algorithms 20(3)] on the concentration of non-Lipschitz functions, we show that |Ae| is strongly concentrated for a wide range of values of N and ||e||. We apply this result in the study of communication channels we refer to as oblivious. Roughly speaking, a channel W(y|x) is said to be oblivious if the error distribution imposed by the channel is independent of the transmitted codeword x. For example, the well studied Binary Symmetric Channel is an oblivious channel. In this work, we define oblivious and partially oblivious channels and present lower bounds on their capacity. The oblivious channels we define have connections to Arbitrarily Varying Channels with state constraints.

Original languageEnglish
Title of host publicationProceedings - 2006 IEEE International Symposium on Information Theory, ISIT 2006
Number of pages5
StatePublished - 2006
Externally publishedYes
Event2006 IEEE International Symposium on Information Theory, ISIT 2006 - Seattle, WA, United States
Duration: 9 Jul 200614 Jul 2006

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8101


Conference2006 IEEE International Symposium on Information Theory, ISIT 2006
Country/TerritoryUnited States
CitySeattle, WA


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