The benefit of a 1bit jumpstart, and the necessity of stochastic encoding, in jamming channels
Abstract
We consider the problem of communicating a message $m$ in the presence of a malicious jamming adversary (Calvin), who can erase an arbitrary set of up to $pn$ bits, out of $n$ transmitted bits $(x_1,\ldots,x_n)$. The capacity of such a channel when Calvin is exactly causal, i.e. Calvin's decision of whether or not to erase bit $x_i$ depends on his observations $(x_1,\ldots,x_i)$ was recently characterized to be $12p$. In this work we show two (perhaps) surprising phenomena. Firstly, we demonstrate via a novel code construction that if Calvin is delayed by even a single bit, i.e. Calvin's decision of whether or not to erase bit $x_i$ depends only on $(x_1,\ldots,x_{i1})$ (and is independent of the "current bit" $x_i$) then the capacity increases to $1p$ when the encoder is allowed to be stochastic. Secondly, we show via a novel jamming strategy for Calvin that, in the singlebitdelay setting, if the encoding is deterministic (i.e. the transmitted codeword is a deterministic function of the message $m$) then no rate asymptotically larger than $12p$ is possible with vanishing probability of error, hence stochastic encoding (using private randomness at the encoder) is essential to achieve the capacity of $1p$ against a onebitdelayed Calvin.
 Publication:

arXiv eprints
 Pub Date:
 February 2016
 DOI:
 10.48550/arXiv.1602.02384
 arXiv:
 arXiv:1602.02384
 Bibcode:
 2016arXiv160202384D
 Keywords:

 Computer Science  Information Theory;
 Computer Science  Cryptography and Security
 EPrint:
 21 pages, 4 figures, extended draft of submission to ISIT 2016