Abstract
This chapter presents personal research on an application of the joint spectral radius to a problem in constrained coding: the computation of the capacity of codes submitted to forbidden differences constraints. We first present how the joint spectral radius appears to be the good tool to compute the capacity in this particular problem.We show how the quantity \(\hat{\rho}_{t}\) provides bounds on the joint spectral radius that are tighter than in the general case. We show how the situation is even better in some particular situations. We then provide a polynomial time algorithm that decides if the capacity is positive. We introduce a closely related problem that we prove to be NP-hard. We then prove the existence of extremal norms for sets of matrices arising in this coding problem.
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© 2009 Springer-Verlag Berlin Heidelberg
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Jungers, R. (2009). Capacity of Codes. In: The Joint Spectral Radius. Lecture Notes in Control and Information Sciences, vol 385. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-95980-9_7
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DOI: https://doi.org/10.1007/978-3-540-95980-9_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-95979-3
Online ISBN: 978-3-540-95980-9
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