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High-rate low-density parity-check (LDPC) codes are the focus of intense research in magnetic recording because, when decoded by the iterative sum-product algorithm, they show decoding performance close to the Shannon capacity. However, cycles, especially short cycles, are harmful to LDPC codes. The paper describes the partition-and-shift LDPC (PS-LDPC) codes, a new class of regular, structured LDPC codes that can be designed with large girth and arbitrary large minimum distance. Large girth leads to more efficient iterative decoding and codes with better error-floor properties than random LDPC codes. PS-LDPC codes can be designed for any desired column weight and with flexible code rates. The paper details the girth and distance properties of the codes and their systematic construction and presents analytical and simulation performance results that show that, in the high signal-to-noise ratio region, PS-LDPC codes out- perform random codes, alleviating the error floor phenomenon. [ABSTRACT FROM AUTHOR]

A parity code and a distance enhancing constrained code are often concatenated with a Reed-Solomon code to form a coding system for magnetic recording. The tensor-product parity coding scheme helps to improve efficiency of the parity code while retaining the same level of performance. In this paper, we present two methods for combining a tensor-product parity code with a distance-enhancing constrained code. The first method incorporates a constrained code with unconstrained positions. The second method uses a new technique, which we call word-set partitioning, to achieve a higher code rate relative to the first method. We simulate the performance of several coding systems based upon the two combination methods on a perpendicular recording channel, and we compare their symbol error rates and sector error rates with those of a system that uses only a Reed-Solomon code. [ABSTRACT FROM AUTHOR]