Bounds on the rate of codes which forbid specified difference sequences

Certain magnetic recording applications call for a large number of sequences whose differences do not include certain disallowed patterns. We show that the number of such sequences increases exponentially with their length and that the exponent, or capacity, is the logarithm of the joint spectral radius of an appropriately defined set of matrices. We derive new algorithms for determining the joint spectral radius of sets of nonnegative matrices and combine them with existing algorithms to determine the capacity of several sets of disallowed differences that arise in practice.