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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]

We have three main goals in this paper. First, we will show the equivalences and relationships among some of the well-known classes of structured low density parity check (LDPC) codes. Second, we consider application of these codes to magnetic recording channel. We will make performance comparisons not only with bit-error-rate (BER) metric but also with sector failure rate (SFR) as the comparison dimension. Such a comparison is more meaningful from a system analysis perspective. Finally, we consider the case of these structured LDPC codes concatenated with conventional Reed-Solomon (RS) codes. We believe LDPC codes will not completely replace RS codes in the future storage devices. From this perspective, for LDPC codes to be contenders for future architectures, they will need to work in harmony with the outer RS codes. This implies that we have to take into account the redundancy introduced by the overall coding scheme, that is, RS code in concatenation with LDPC code, to reach meaningful comparisons from a system design perspective. [ABSTRACT FROM AUTHOR]