Efficient codes for Limited View adversarial channels

Abstract

We introduce randomized Limited View (LV) adversary codes that provide protection against an adversary that uses their partial view of the channel to construct an adversarial error vector that is added to the channel. For a codeword of length N, the adversary selects a subset of size <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ρr</sub> N of components to “see”, and then “adds” an adversarial error vector of weight <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ρw</sub> N to the codeword. Performance of the code is measured by the probability of the decoder failure in recovering the sent message. An (N, q <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RN</sup> , δ)-limited view adversary is a code of rate R that ensures that the success chance of the adversary in making decoder to fail is bounded by δ. Our main motivation to study these codes is providing protection for wireless communication at the physical layer of networks. We formalize the definition of adversarial error and decoder failure, construct a code with efficient encoding and decoding that allows the adversary to, depending on the code rate, read up to half of the sent codeword and add error on the same coordinates. The code is non-linear, has an efficient decoding algorithm, and is constructed using a message authentication code (MAC) and a Folded Reed-Solomon (FRS) code. The decoding algorithm uses an innovative approach that combines the list decoding algorithm of the FRS codes and the MAC verification algorithm to eliminate the exponential size of the list output from the decoding algorithm. We discuss our results and future work.