Distributed Source Coding in the Presence of Byzantine Sensors

TL;DR

This paper studies how to reliably perform distributed source coding when some sensors are maliciously compromised, providing new rate characterizations and coding schemes to mitigate Byzantine attacks.

Contribution

It introduces a comprehensive analysis of distributed source coding under Byzantine attacks, including variable-rate and fixed-rate scenarios with deterministic and randomized coding.

Findings

Explicit sum rate characterization for variable-rate coding with Byzantine sensors

Achievability schemes using randomized coding to prevent traitors from causing errors

Lower rates achievable with randomized coding compared to deterministic coding

Abstract

The distributed source coding problem is considered when the sensors, or encoders, are under Byzantine attack; that is, an unknown group 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 achievable sum rates is given for any number of sensors and any groups of traitors. The converse is proved constructively by letting the traitors simulate a fake distribution and report the generated values as the true ones. This fake distribution is chosen so that the decoder cannot determine which sensors are traitors while maximizing the required rate to decode every value. Achievability is proved using a scheme in which the decoder receives small packets of information from a sensor until its message can be decoded, before moving on to the next sensor. The sensors use randomization to choose from a set of coding functions, which makes it probabilistically impossible for the traitors to cause the decoder to make an error. 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, and it is shown that lower rates can be achieved with randomized coding.