Channels with Synchronization/Substitution Errors and Computation of Error Control Codes
Stavros Konstantinidis, Nelma Moreira, Rogerio Reis

TL;DR
This paper introduces a probabilistic method for constructing near-maximal error-detecting and error-correcting codes for channels with substitution and synchronization errors, using a transducer-based error model.
Contribution
It presents a randomized algorithm for generating error-detecting codes close to maximal, modeled with transducers for complex error types, and demonstrates its implementation and testing.
Findings
Algorithm successfully generates near-maximal codes
Transducer model effectively captures complex errors
Implementation shows promising results on various channels
Abstract
We introduce the concept of an \ff-maximal error-detecting block code, for some parameter \ff{} 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 , a probability value \ff, and a specification of the errors permitted in some application, and generates an error-detecting, or error-correcting, block code having up to codewords of length . If the algorithm finds less than codewords, then those codewords constitute a code that is \ff-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…
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Taxonomy
Topicssemigroups and automata theory · DNA and Biological Computing · Algorithms and Data Compression
