Channel matched iterative decoding for magnetic recording systems

The perpendicular magnetic recording channel (PMRC) is corrupted by sever inter-symbol interference and data-dependent media noise, in addition to a variety of other bursty impairments. Thus far, the hard decodable symbol correcting Reed-Solomon (RS) code has been the industry standard for outer error control coding (ECC). This thesis proposes two novel ECC schemes in the migration toward next generation high density recording. The first scheme is a two-level concatenation of channel-matched turbo equalization (TE) and outer RS, replacing current inner parity correction codes. Conventional TE is matched to the channel via the incorporation of the error pattern correction code (EPCC), which works iteratively with the other constituent code in TE, whether block or convolutional, to suppress the occurrence of low-Euclidean-distance errors at the output of the channel detector. To understand this mechanism, and with no loss of generality, we derive the error Euclidean distance distribution of TE-EPCC for the Dicode channel, and show that EPCC substantially increases the interleaver gain exponent of low Euclidean weight errors. Furthermore, we derive an upper bound on the BER of TE-EPCC, and employ it to show that TE-EPCC delivers significant gains in the error floor and cliff regions compared to conventional precoded and unprecoded TE for a variety of channel conditions and code rates. The second proposed ECC system is a tensor product concatenation of EPCC and Q-ary LDPC (T-EPCC-QLDPC). This concatenation scheme enables the use of byte-long component EPCC without jeopardizing the overall code rate. Hence, the multiple error correction capability of EPCC is maintained at very low signal-to-noise ratios, while the component non-binary LDPC insures correct syndromes are available for the decoding of tensor symbols (EPCC code-blocks). We introduce a low complexity iterative soft decoder of T-EPCC-QLDPC, in which the component EPCC and QLDPC exchange multi-level log-likelihood ratios (mlLLR) that represent their beliefs on the reliability of error-syndromes. Moreover, we show that the two-level decoder provides a better performance-complexity tradeoff compared to single-level binary and Q-ary LDPC.