Equality of asymptotic redundancy factors for multiple bursts and substitutions

Let qq, tt, and bb be constant positive integers with q2q\geqslant 2. For the multiple burst-substitution channel ch(t,b)\mathfrak{ch}(t,b) and the multiple substitution channel ch(t)\mathfrak{ch}(t), write rasy(ch,1)r^*_{\operatorname{asy}}(\mathfrak{ch},-1) for the asymptotic redundancy factor.

Multiple burst-substitution redundancy conjecture.

rasy(ch(t,b),1)=rasy(ch(t),1).r^*_{\operatorname{asy}}(\mathfrak{ch}(t,b),-1)=r^*_{\operatorname{asy}}(\mathfrak{ch}(t),-1).

This extends the known equality between the asymptotic redundancy factors for a single burst and a single substitution channel to the case of multiple substitutions and bursts; the equality remains conjectural in the source.

Sources & referencesView supporting material

Primary source

Wenjun Yu, Yubo Sun, Zixiang Xu, Gennian Ge and Moshe Schwartz, “Optimal Reconstruction Codes with Given Reads in Multiple Burst-Substitutions Channels”, arXiv:2506.12924 (2025).

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