Performance and Complexity of 32 k-bit Binary LDPC Codes for Magnetic Recording Channels

Recently, 32 k-bit sector size for hard disk drives is being investigated to take advantage of the superior performance of long error correcting codes. Meanwhile, low-density parity-check (LDPC) codes have been actively investigated for obtaining coding gains over conventional Reed-Solomon (RS) codes mainly for 4 k-bit sectors. In this paper, the coding gain of a 32 k-bit LDPC code over a 4 k-bit LDPC code, a 32 k-bit RS code, and a 4 k-bit RS code in magnetic recording channels is investigated. The decoding complexity of 32 k-bit LDPC codes and 4 k-bit LDPC codes is also discussed. It is important to evaluate whether the coding gains are enough to justify the increased complexity. Using the 32 k-bit LDPC code, 0.8-dB gain over the 32 k-bit RS code or the 4 k-bit LDPC code (the two schemes coincidentally showed similar performance) at 32 k-bit block error rate (BLER) $10^{-3}$ , and 1.6-dB gain over the 4 k-bit RS code were obtained. It is shown that 32 k-bit LDPC codes require a larger number of iterations than the 4 k-bit LDPC codes. It is also shown that there is much room to improve the design of 32 k-bit LDPC codes than the code used in the simulation. To illustrate the potential, quasicyclic LDPC codes with column weights up to 13 with girth 6 are investigated.