Upper bounds on the size of error-correcting runlength-limited codes

The maximum achievable rate of an error-correcting runlength-limited code is considered. Runlength-limited codes find wide applications in magnetic and optical recording, baseband pulse transmission, and fiber optic communications. When a runlength-limited code is used on a noisy channel, error-correction control is often needed in order to obtain the desired system reliability. It is well-known that the error-correcting capability of a code is closely related to its distance properties. In this paper, asymptotic upper bounds for the maximum achievable rate of a runlength-limited code are derived as a function of the code's minimum Hamming distance.