Upper Bounds on the Capacity of Binary Channels with Causal Adversaries

Details Upper Bounds on the Capacity of Binary Channels with Causal Adversaries Upper Bounds on the Capacity of Binary Channels with Causal Adversaries

2012-04-11

arxiv.org/abs/1204.2587v1

Computer Science

Information Theory

Submitted to the IEEE Transactions on Information Theory; shortened version submitted to ISIT 2012

Scientific paper

In this work 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 $\mathbf{x}=(x_1,...,x_n)$ bit-by-bit over a communication channel. The sender and receiver do not share common randomness. The adversarial jammer can view the transmitted bits $x_i$ 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 $x_i$ the jammer's decision on whether to corrupt it or not (and on how to change it) must depend only on $x_j$ for $j \leq i$. This is in contrast to the "classical" adversarial jamming situations in which the jammer has no knowledge of $\mathbf{x}$ or complete knowledge of $\mathbf{x}$. In this work, we present upper bounds on the capacity which hold for both deterministic and stochastic encoding schemes.

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