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arXiv · 2307.04222

Derandomizing Codes for the Binary Adversarial Wiretap Channel of Type II

Eric Ruzomberka·Homa Nikbakht·Christopher G. Brinton·David J. Love·H. Vincent Poor
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Abstract

We revisit the binary adversarial wiretap channel (AWTC) of type II in which an active adversary can read a fraction $r$ and flip a fraction $p$ of codeword bits. The semantic-secrecy capacity of the AWTC II is partially known, where the best-known lower bound is non-constructive, proven via a random coding argument that uses a large number (that is exponential in blocklength $n$) of random bits to seed the random code. In this paper, we establish a new derandomization result in which we match the best-known lower bound of $1-H_2(p)-r$ where $H_2(\cdot)$ is the binary entropy function via a random code that uses a small seed of only $O(n^2)$ bits. Our random code construction is a novel application of pseudolinear codes -- a class of non-linear codes that have $k$-wise independent codewords when picked at random where $k$ is a design parameter. As the key technical tool in our analysis, we provide a soft-covering lemma in the flavor of Goldfeld, Cuff and Permuter (Trans. Inf. Theory 2016) that holds for random codes with $k$-wise independent codewords.

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Eric Ruzomberka, Homa Nikbakht, Christopher G. Brinton, David J. Love, H. Vincent Poor. 2023-07-09. Derandomizing Codes for the Binary Adversarial Wiretap Channel of Type II. https://arxiv.org/abs/2307.04222

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