Variable-Rate Distributed Source Coding in the Presence of Byzantine Sensors

TL;DR

This paper investigates the challenges of distributed source coding when some sensors are compromised by Byzantine attacks, proposing a variable-rate coding scheme with optimal sum rate characterization and comparing it to fixed-rate approaches.

Contribution

It provides an explicit characterization of the minimum achievable sum rate for variable-rate coding under Byzantine attacks and compares fixed-rate and randomized coding strategies.

Findings

Variable-rate coding achieves the lowest sum rate.

Randomized fixed-rate coding outperforms deterministic coding.

All coding strategies are suboptimal compared to the variable-rate approach.

Abstract

The distributed source coding problem is considered when the sensors, or encoders, are under Byzantine attack; that is, an unknown number of sensors have been reprogrammed by a malicious intruder to undermine the reconstruction at the fusion center. Three different forms of the problem are considered. The first is a variable-rate setup, in which the decoder adaptively chooses the rates at which the sensors transmit. An explicit characterization of the variable-rate minimum achievable sum rate is stated, given by the maximum entropy over the set of distributions indistinguishable from the true source distribution by the decoder. In addition, two forms of the fixed-rate problem are considered, one with deterministic coding and one with randomized coding. The achievable rate regions are given for both these problems, with a larger region achievable using randomized coding, though both are suboptimal compared to variable-rate coding.