Tight bounds for stream decodable error-correcting codes
Abstract
In order to communicate a message over a noisy channel, a sender (Alice) uses an error-correcting code to encode her message into a codeword. The receiver (Bob) decodes it correctly whenever there is at most a small constant fraction of adversarial error in the transmitted codeword. This work investigates the setting where Bob is computationally bounded. Specifically, Bob receives the message as a stream and must process it and write in order to a write-only tape while using low (say polylogarithmic) space. We show three basic results about this setting, which are informally as follows: (1) There is a stream decodable code of near-quadratic length. (2) There is no stream decodable code of sub-quadratic length. (3) If Bob need only compute a private linear function of the input bits, instead of writing them all to the output tape, there is a stream decodable code of near-linear length.
Cite
@article{arxiv.2407.06446,
title = {Tight bounds for stream decodable error-correcting codes},
author = {Meghal Gupta and Venkatesan Guruswami and Mihir Singhal},
journal= {arXiv preprint arXiv:2407.06446},
year = {2024}
}