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Abstract

A general rate N/(N+1) (0, G), code construction, e.g., for a magnetic recording system, allows for encoding or decoding of a dataword having N elements, N preferably being an integer multiple of eight. The dataword is divided into N/8 bytes of binary data that are encoded as a run-length limited (RLL) codeword in accordance with the general rate N/(N+1) (0, G) code construction. The general rate N/(N+1) (0, G) code construction is characterized by the constraints (d=0, G=(N/4)+1, l=N/8, r=N/8). the N/(N+1) (0 (N/4)+1, N/8, N/8) RLL codeword is constructed from the dataword in accordance with 1) pivot bits identifying code violations related to the constraints, 2) correction bits set to correct code violations, and 3) preserved elements having values not included in the code violations. The corrections by correction bits correspond to corrections of predefined code violations that limit the number of consecutive zeros received by, for example, a magnetic record channel to (N/4)+1. The codewords generated in accordance with the general rate N/(N+1) (0, G) code construction may exhibit a high transition density. The high transition density allows for more frequent timing and gain control updates, and so results in lower required channel input signal to noise ratio for a given level of magnetic recording channel performance.

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