When Variable-Length Codes Meet the Field of Error Detection

08/31/2022

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by   Jean Néraud, et al.

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Given a finite alphabet A and a binary relation τ⊆ A^*× A^*, a set X is τ-independent if τ(X)∩ X=∅. Given a quasi-metric d over A^* (in the meaning of <cit.>) and k≥ 1, we associate the relation τ_d,k defined by (x,y)∈τ_d,k if, and only if, d(x,y)≤ k <cit.>.In the spirit of <cit.>, the error detection-correction capability of variable-length codes can be expressed in term of conditions over τ_d,k. With respect to the prefix metric, the factor one, and every quasi-metric associated to (anti-)automorphisms of the free monoid, we examine whether those conditions are decidable for a given regular code.