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 (1999), and the other a nonbinary generalization of the binary enumeration methods of Patrovics and Immink (1996), and Gu and Fuja (1994). The construction based on permutation codes is simple and asymptotically (in block-length) 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 block-length. In the process, we 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.