Upper Bounds on the Capacity of Binary Channels with Causal Adversaries

TL;DR

This paper establishes upper bounds on the capacity of binary channels with a causal adversary who can flip up to a fraction of bits, considering both deterministic and stochastic encoding schemes.

Contribution

It introduces new upper bounds on channel capacity under causal adversarial jamming, contrasting with classical non-causal models.

Findings

Upper bounds hold for both average and maximal error probabilities.

Results apply to deterministic and stochastic encoding schemes.

Capacity limits are characterized for causal adversarial settings.

Abstract

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 $(x_1,...,x_n)$ 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 $x_i$ 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 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 $(x_1,...,x_n)$, or knows $(x_1,...,x_n)$ completely. In this work, 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.