SYSTEMATIC CONSTRUCTION ALGORITHM OF FIXED BLOCK-LENGTH (D,K) CODES

This paper proposes a systematic construction algorithm for the fixed block-length (d, k) code, which is important as the code for magnetic recording. The coding rate (coding efficiency) and the encoding/decoding algorithms are discussed. As a result of numerical calculation for the coding rate of the finite block-length (d, k) code, it is very close to the capacity limit even for a relatively short block-length code. It is shown also that the coding rate for the infinite block length agrees with the capacity. A systematic encoding/decoding algorithm for the finite block-length (d, k) code is proposed, and it is shown that the algebraic encoding/decoding can be realized. By introducing the concept of state, the coding efficiency of fd, k) code can be improved drastically and the coding rate approaches very close to the capacity while observing the constraint for the (d, k) code. Although it can be applied for the peak-shift error correcting (d, k) code, it is left for future study.