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

Abstract

Abstract 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.