Iterative soft detection and decoding for data storage channels

Error correcting codes (ECC) with iterative soft decoding algorithm, such as turbo codes and low density parity check (LDPC) codes, have shown extremely good performance, operating near Shannon capacity on additive white Gaussian noise (AWGN) channels. This thesis explores the potential application of LDPC codes with iterative soft decoding for use in high-density magnetic recording systems. One of the challenges in using LDPC codes for hard disk drives is that the implementations should be simple enough to permit data rates of the order Gbps.; Realizing that some subclasses of self-orthogonal codes have low-density parity check matrices which essentially define 4-cycle-free LDPC codes, we modify two construction methods for self-orthogonal codes to construct regular LDPC codes, including disjoint difference sets (DDS)-based LDPC codes and permutation matrix-based LDPC codes. Such structured LDPC codes can be represented with a small set of integers, thus, lending them to a low complexity implementation. Systematic construction also holds the promise of evaluating the performance of LDPC codes analytically. We analyze the girth and distance properties of these codes and propose methods to avoid short cycles as well as efficient encoding algorithms. Monte Carlo simulation results reveal that the structured codes perform as well as random LDPC codes both for AWGN channels and magnetic recording channels.; In order to investigate the compatibility of inner LDPC codes with an outer ECC, we construct and analyze a class of low complexity LDPC codes with column weight j = 2 in contrast to the often-used j ≥ 3 codes. The j = 2 codes possess several significant features in addition to their structure. Firstly, they can achieve the lower bound on the block length for a given girth and code rate. Secondly, they can be encoded with linear complexity. Thirdly, iterative soft decoding with sum-product algorithm is very close to maximum likelihood decoding in AWGN channels for these codes. Finally, they exhibit block error statistics (significantly different from LDPC codes with j ≥ 3) that are more compatible with outer error correction codes (ECC).; Density evolution is employed to analyze the performance of serial concatenated partial response (PR) systems, which provides insight for system designs. Under the framework of turbo equalization, LDPC codes outperform Reed-Solomon (RS) codes by 1∼1.7dB SNR gain at sector error rate (SER) of 10 −4, depending on the column weight and the code rate of the codes. A concatenated LDPC coding scheme is proposed for magnetic recording systems, which exhibits about 1.4dB gain over RS code at SER of 10 −4, while holding the potential to maintain similar coding gain at 10−15 BERs.