Partition-and-shift LDPC codes for high density magnetic recording

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. LDPC codes can be described by a bipartite graph called Tanner graph. The length g of the shortest cycle in a Tanner graph is referred to as the girth g of the graph. Since large girth leads to more efficient decoding and large minimum distance, LDPC codes with large girth are particularly desired. We propose a class of structured LDPC codes with large girth and flexible code rates, called partition-and-shift LDPC codes (PS-LDPC).