Universal communication - Part I: Modulo additive channels

Yuval Lomnitz, Meir Feder

Research output: Contribution to journalArticlepeer-review

Abstract

Which communication rates can be attained over a channel whose output is an unknown (possibly stochastic) function of the input that may vary arbitrarily in time with no a priori model? Following the spirit of the finite-state compressibility of a sequence, defined by Lempel and Ziv, a 'capacity' is defined for such a channel as the highest rate achievable by a designer knowing the particular relation that indeed exists between the input and output for all times, yet is constrained to use a fixed finite-length block communication scheme without feedback, i.e., use the same encoder and decoder over each block. In the case of the modulo additive channel, where the output sequence is obtained by modulo addition of an unknown individual sequence to the input sequence, this capacity is upper bounded by a function of the finite state compressibility of the noise sequence. A universal communication scheme with feedback that attains this capacity universally, without prior knowledge of the noise sequence, is presented.

Original languageEnglish
Article number6557005
Pages (from-to)5488-5510
Number of pages23
JournalIEEE Transactions on Information Theory
Volume59
Issue number9
DOIs
StatePublished - 2013

Keywords

  • Arbitrarily varying channels (AVCs)
  • feedback communication
  • individual sequences
  • rateless coding
  • universal communication
  • unknown channels

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