On codes with local joint constraints

We study the largest number of sequences with the property that any two sequences do not contain specified pairs of patterns. We show that this number increases exponentially with the length of the sequences and that the exponent, or capacity, is the logarithm of the joint spectral radius of an appropriately defined set of matrices. We illustrate a new heuristic for computing the joint spectral radius and use it to compute the capacity for several simple collections. The problem of computing the achievable rate region of a collection of codes is introduced and it is shown that the region may be computed via a similar analysis.