Low-density parity check (LDPC) codes have experienced tremendous popularity due to their capacity-achieving performance. In this dissertation, several different aspects of LDPC coding and its applications to magnetic storage are investigated. One of the most significant issues that impedes the use of LDPC codes in many systems is the error-rate floor phenomenon associated with their iterative decoders. By delineating the fundamental principles, we extend to partial response channels algorithms for predicting the error rate performance in the floor region for the binary-input AWGN channel. We develop three classes of decoding algorithms for mitigating the error floor by directly tackling the cause of the problem: trapping sets. In our experiments, these algorithms provide multiple orders of improvement over conventional decoders at the cost of various implementation complexity increases.Product codes are widely used in magnetic recording systems where errors are both isolated and bursty. A dual-mode decoding technique for Reed-Solomon-code-based product codes is proposed, where the second decoding mode involves maximum-likelihood erasure decoding of the binary images of the Reed-Solomon codewords. By exploring a tape storage application, we demonstrate that this dual-mode decoding system dramatically improves the performance of product codes. Moreover, the complexity added by the second decoding mode is manageable. We also show the performance of this technique on a product code which has an LDPC code in the columns.Run-length-limited (RLL) codes are ubiquitous in today's disk drives. Using RLL codes has enabled drive designers to pack data very efficiently onto the platter surface by ensuring stable symbol-timing recovery. We consider a concatenation system design with an LDPC code and an RLL code as components to simultaneously achieve desirable features such as: soft information availability to the LDPC decoder, the preservation of the LDPC code's structure, and the capability of correcting long erasure bursts.We analyze the performance of LDPC-coded magnetic recording channel in the presence of media noise. We employ advanced signal processing for the pattern-dependent-noise-predictive channel detectors, and demonstrate that a gain of over 1 dB or a linear density gain of about 8% relative to a comparable Reed-Solomon is attainable by using an LDPC code.

A non-iterative receiver is proposed to achieve near capacity performance on intersymbol interference (ISI) channels. There are two main ingredients in the proposed design. i) The use of a novel BCJR-DFE equalizer which produces optimal soft estimates of the inputs to the ISI channel given all the observations from the channel and L past symbols exactly, where L is the memory of the ISI channel. ii) The use of an encoder structure that ensures that L past symbols can be used in the DFE in an error free manner through the use of a capacity achieving code for a memoryless channel. Computational complexity of the proposed receiver structure is less than that of one iteration of the turbo receiver. We also provide the proof showing that the proposed receiver achieves the i.i.d. capacity of any constrained input ISI channel. This DFE-based receiver has several advantages over an iterative (turbo) receiver, such as low complexity, the fact that codes that are optimized for memoryless channels can be used with channels with memory, and finally that the channel does not need to be known at the transmitter. The proposed coding scheme is universal in the sense that a single code of rate r; optimized for a memoryless channel, provides small error probability uniformly across all AWGN-ISI channels of i.i.d. capacity less than r: This general principle of a proposed non-iterative receiver also applies to other signal processing functions, such as timing recovery, pattern-dependent noise whiten ing, joint demodulation and decoding etc. This makes the proposed encoder and receiver structure a viable alternative to iterative signal processing. The results show significant complexity reduction and performance gain for the case of timing recovery and patter-dependent noise whitening for magnetic recording channels.

<p>U radu su predstavljene nove tehnike dekodovanja maximum<br />transition run (MTR) kodova na principu finog odlučivanja.<br />Analizirane su performanse ovih tehnika u kombinaciji sa<br />za&scaron;titnim LDPC kodom na kanalima za magnetsko memorisanje<br />informacija, sa posebnim osvrtom na model kanala sa<br />dve staze za zapisivanje i dve glave za čitanje. U modelu kanala<br />je kori&scaron;ćena idealna E2PR4 ekvalizacija staza adekvatna<br />za sisteme sa visokom gustinom magnetskog zapisa.</p> / <p>This thesis presents the novel soft-decision decoding techniques<br />for decoding of the maximum transition run (MTR)<br />codes. Performances of such techniques have been analyzed<br />in combination with error correcting LDPC code over magnetic<br />recording channels, especially the two-track two-head<br />channel model. Ideal E2PR4 track equalization suitable for<br />high density magnetic recording has been used.</p>