On Pseudolinear Codes for Correcting Adversarial Errors

Eric Ruzomberka, Homa Nikbakht, Christopher G. Brinton, H. Vincent Poor

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We consider error-correction coding schemes for adversarial wiretap channels (AWTCs) in which the channel can a) read a fraction of the codeword bits up to a bound r and b) flip a fraction of the bits up to a bound p. The channel can freely choose the locations of the bit reads and bit flips via a process with unbounded computational power. Codes for the AWTC are of broad interest in the area of information security, as they can provide data resiliency in settings where an attacker has limited access to a storage or transmission medium. We investigate a family of non-linear codes known as pseudolinear codes, which were first proposed by Guruswami and Indyk (FOCS 2001) for constructing list-decodable codes independent of the AWTC setting. Unlike general non-linear codes, pseudolinear codes admit efficient encoders and have succinct representations. We focus on unique decoding and show that random pseudolinear codes can achieve rates up to the binary symmetric channel (BSC) capacity 1-H_2(p) for any p, r in the less noisy region: p<1/2 and r<1-H_2(p) where H_2(·) is the binary entropy function. Thus, pseudolinear codes are the first known optimal-rate binary code family for the less noisy AWTC that admit efficient encoders. The above result can be viewed as a derandomization result of random general codes in the AWTC setting, which in turn opens new avenues for applying derandomization techniques to randomized constructions of AWTC codes. Our proof applies a novel concentration inequality for sums of random variables with limited independence which may be of interest as an analysis tool more generally.

Original languageEnglish (US)
Title of host publicationProceedings - 2023 IEEE 64th Annual Symposium on Foundations of Computer Science, FOCS 2023
PublisherIEEE Computer Society
Number of pages12
ISBN (Electronic)9798350318944
StatePublished - 2023
Event64th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2023 - Santa Cruz, United States
Duration: Nov 6 2023Nov 9 2023

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)0272-5428


Conference64th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2023
Country/TerritoryUnited States
CitySanta Cruz

All Science Journal Classification (ASJC) codes

  • General Computer Science


  • adversarial channels
  • uniquely decodable codes
  • wiretap channels


Dive into the research topics of 'On Pseudolinear Codes for Correcting Adversarial Errors'. Together they form a unique fingerprint.

Cite this