Generating functions and lower bounds on rates for limited error-correcting codes

Runlength-limited (RLL) and digital-sum-limited (DSL) codes are considered. For these codes the finite and asymptotic lower bounds on achievable rates for the given minimum Hamming distance are derived. Using generating functions and trellis diagram techniques, the authors prove the existence of RLL- and DSL-codes of rate R and minimum distance d= delta n, such that R>or=2.log lambda ₁(0)-min(log lambda ₁(z)- delta .log z), 01(z) is the maximum modulus eigenvalue of a certain matrix that is dependent on the limitations and some parameter z. The bounds for the limited codes improve the lower bound of H. C. Ferreira (1984).