Performance and Decoding Complexity of Nonbinary LDPC Codes for Magnetic Recording

We consider a group of high-performance q-ary low-density parity-check (LDPC) coded perpendicular magnetic recording channels (PMRCs) with optimized targets and codes over various field sizes. We show that the nonbinary LDPC-coded PMRCs provide 1-dB coding gain over a practical implementation of a good binary LDPC-coded PMRC at user density of 1.22, and evaluate the decoding complexities of these systems in terms of both the number of floating-point (FLP) operations and the computational time. Decoding complexity ratios of nonbinary LDPC-coded PMRCs to the binary LDPC-coded system are presented. After careful analysis, we conclude that the time complexity ratios are always smaller than the ratios obtained by the number of FLP operations, which do not exceed 7.42. Furthermore, experimental results show that the size of the Galois field does not affect the decoding complexity.