Automata for Solid Codes

Show simple item record Jürgensen, H en Staiger, L en 2022-01-14T03:42:10Z 2022-01-14T03:42:10Z 2021 en
dc.identifier.citation CDMTCS Research Reports CDMTCS-550 (2021) en
dc.identifier.issn 1178-3540 en
dc.description.abstract Solid codes provide outstanding fault-tolerance when used for information transmission through a noisy channel involving not only symbol substitutions, but also synchronisation errors and black-outs. In this paper we provide an automaton theoretic characterisation of solid codes which takes this fault-tolerance into account. The fault-tolerance afforded by a solid code L can be summarised as follows: Consider messages, encoded using L, being sent through a noisy channel. Any code words in L, which are present in the received message, will be decoded correctly, unless they themselves happen to be the results of errors. Thus, errors in the received message will not lead to incorrect decodings of those parts which are error-free. In this paper we consider acceptors which are fault-tolerant in this sense when analysing such received messages. These acceptors characterise the class of solid codes. For finite solid codes an automaton characterisation was published in the sixties by Levenshtein and Romanov. The characterisation uses state-invariant finite-state transducers which act as decoders in such a way that an output is generated exactly when a code word has been read completely. State-invariance means that acceptance does not depend on the initial state - every state can be used as the initial state. The results of Levenshtein and Romanov depend strongly on the fact that the code is finite. In this paper we provide a general automaton theoretic characterisation of arbitrary solid codes without any such restriction. Moreover, the solid code is regular as a language if and only if the automaton used in the characterisation can be reduced to an equivalent finite automaton with equivalent properties. The main results of this paper are as follows: Every acceptor defines a solid code. For every solid code there is a fault-tolerant acceptor defining the code. Such acceptors expose the decomposition of potentially faulty received messages according to the code. For solid codes which are regular as languages these acceptors can be chosen to be finite while preserving all important combinatorial properties.
dc.publisher Department of Computer Science, The University of Auckland, New Zealand en
dc.relation.ispartofseries CDMTCS Research Report Series en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. en
dc.rights.uri en
dc.source.uri en
dc.title Automata for Solid Codes en
dc.type Technical Report en
dc.subject.marsden Fields of Research en
dc.rights.holder Copyright: The author(s) en
dc.rights.accessrights en

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