Permutation (d,k) Codes: Efficient Enumerative Coding and Phrase Length Distribution Shaping

In this paper, we introduce a new coding scheme for use in higher order partial response (PR) magnetic as well as optical recording channels. The proposed codes are constructed by reducing the frequency of occurrence of long phrases in maxentropic runlength limited sequences. In magnetic recording systems this leads to a decrease of the frequency of patterns that account for most of the errors. In optical recording systems, the new coding method reduces the effects of thermal flow in optical media, thus preventing undesirable mark stretching. For the presented codes, it is possible to construct practical coders of high rate by employing enumerative coding techniques. The enumerative encoding algorithm presented here is conceptually simpler and computationally less expansive than the method in [4].