Optimal block codes for M-ary runlength-limited channels

In this paper we consider the analysis and design of optimal block-decodable M-ary runlength-limited (RLL) codes. We present two general construction methods: one based on permutation codes due to Datta and McLaughlin, and the other a nonbinary generalization of the binary enumeration methods of Patrovics and Immink, and Gu and Fuja. The construction based on permutation codes is simple and asymptotically (in blocklength) optimal, while the other construction is optimal in the sense that the resulting codes have the highest rate among all block-decodable codes for any blocklength. In the process, we shall also prove a new result on the capacity of(M,d,k) constraints. Finally, we present examples of remarkably low-complexity (M,d,k) block codes which achieve the optimal rate without the use of enumeration.