Channels with Synchronization/Substitution Errors and Computation of Error Control Codes

Abstract

We introduce the concept of an f -maximal errordetecting block code, for some parameter f between 0 and 1, in order to formalize the situation where a block code is close to maximal with respect to being error-detecting. Our motivation for this is that constructing a maximal error-detecting code is a computationally hard problem. We present a randomized algorithm that takes as input two positive integers N, l, a probability value f , and a specification of the errors permitted in some application, and generates an error-detecting, or errorcorrecting, block code having up to N codewords of length l. If the algorithm finds less than N codewords, then those codewords constitute a code that is f -maximal with high probability. The error specification (also called channel) is modelled as a transducer, which allows one to model any rational combination of substitution and synchronization errors. We also present some elements of our implementation of various error-detecting properties and their associated methods. Then, we show several tests of the implemented randomized algorithm on various channels. A methodological contribution is the presentation of how various desirable error combinations can be expressed formally and processed algorithmically.

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Cite this paper

@article{Konstantinidis2016ChannelsWS, title={Channels with Synchronization/Substitution Errors and Computation of Error Control Codes}, author={Stavros Konstantinidis and Nelma Moreira and Rog{\'e}rio Reis}, journal={CoRR}, year={2016}, volume={abs/1601.06312} }