Optimal block codes for M-ary runlength-constrained channels

In this work, 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 shall also extend a result due to Zehavi and Wolf (1988) on the capacity of binary (d, k) constraints to M-ary channels. Finally, we present examples of template codes: remarkably low-complexity (M,d,k) block codes which achieve the optimal rate without the use of enumeration.