Upper bounds on the capacity of binary channels with causal adversaries

Bikash Kumar Dey, Sidharth Jaggi, Michael Langberg, Anand D. Sarwate

Research output: Contribution to journalArticlepeer-review


In this paper, we consider the communication of information in the presence of a causal adversarial jammer. In the setting under study, a sender wishes to communicate a message to a receiver by transmitting a codeword x=(x 1,..., xn) bit-by-bit over a communication channel. The sender and the receiver do not share common randomness. The adversarial jammer can view the transmitted bits xi one at a time and can change up to a p-fraction of them. However, the decisions of the jammer must be made in a causal manner. Namely, for each bit xi, the jammer's decision on whether to corrupt it or not must depend only on xj for j ≤ i. This is in contrast to the 'classical' adversarial jamming situations in which the jammer has no knowledge of x, or knows x completely. In this study, we present upper bounds (that hold under both the average and maximal probability of error criteria) on the capacity which hold for both deterministic and stochastic encoding schemes.

Original languageEnglish
Article number6516725
Pages (from-to)3753-3763
Number of pages11
JournalIEEE Transactions on Information Theory
Issue number6
StatePublished - 2013


  • Arbitrarily varying channels (AVCs)
  • channel coding
  • jamming


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