Systematic construction algorithm of fixed block‐length multitrack (d, k) Codes

Abstract

AbstractThis paper notes the fact that the recording code often takes the form of a multitrack code, as well as the fact that the k‐constraint in the (d, k)‐constraint is considerably relaxed, which increases the capacity. Then the paper proposes a systematic construction algorithm for the fixed block‐length multitrack (d, k) code and discusses the coding characteristics. A simple idea is applied in the code construction to apply the (d, ∞) code to all tracks except for one in order to reflect the relaxation of the k‐constraint on the improvement of the coding rate. the (d, ∞) code is applied to the left track if the vector obtained by the elementwise logical sum of the code words satisfies the k‐constraint and, if not, the (d, k) code is applied. the author has already proposed a systematic construction algorithm for the efficient fixed block‐length (d, k) code.This paper discusses mainly the systematic construction algorithm and the coding characteristics for the fixed block‐length (d, ∞) code, based on the unique ordering technique of the binary sequence by the Schalkwijk algorithm, as the systematic construction algorithm for the fixed block‐length multitrack (d, k) code based on the forementioned idea. the coding rate and the coding efficiency are examined, and the result indicates that the characteristics are very close to those of the (d, ∞) code.