Computer Science > Information Theory
[Submitted on 8 Jul 2024]
Title:Tight bounds for stream decodable error-correcting codes
View PDF HTML (experimental)Abstract:In order to communicate a message over a noisy channel, a sender (Alice) uses an error-correcting code to encode her message $x$ 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 $x$ 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.
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