CROSSTALK-RESILIANT CODING FOR HIGH DENSITY DIGITAL RECORDING

Increasing the track density in magnetic systems is very difficult due to inter-track interference (ITI) caused by the magnetic field of adjacent tracks. This work presents a two-track partial response class 4 magnetic channel with linear and symmetrical ITI; and explores modulation codes, signal processing methods and error correction codes in order to mitigate the effects of ITI. Recording codes were investigated, and a new class of two-dimensional run-length limited recording codes is described. The new class of codes controls the type of ITI and has been found to be about 10% more resilient to ITI compared to conventional run-length limited codes. A new adaptive trellis has also been described that adaptively solves for the effect of ITI. This has been found to give gains up to 5dB in signal to noise ratio (SNR) at 40% ITI. It was also found that the new class of codes were about 10% more resilient to ITI compared to conventional recording codes when decoded with the new trellis. Error correction coding methods were applied, and the use of Low Density Parity Check (LDPC) codes was investigated. It was found that at high SNR, conventional codes could perform as well as the new modulation codes in a combined modulation and error correction coding scheme. Results suggest that high rate LDPC codes can mitigate the effect of ITI, however the decoders have convergence problems beyond 30% ITI

EQUALISATION TECHNIQUES FOR MULTI-LEVEL DIGITAL MAGNETIC RECORDING

A large amount of research has been put into areas of signal processing, medium design, head and servo-mechanism design and coding for conventional longitudinal as well as perpendicular magnetic recording. This work presents some further investigation in the signal processing and coding aspects of longitudinal and perpendicular digital magnetic recording. The work presented in this thesis is based upon numerical analysis using various simulation methods. The environment used for implementation of simulation models is C/C + + programming. Important results based upon bit error rate calculations have been documented in this thesis. This work presents the new designed Asymmetric Decoder (AD) which is modified to take into account the jitter noise and shows that it has better performance than classical BCJR decoders with the use of Error Correction Codes (ECC). In this work, a new method of designing Generalised Partial Response (GPR) target and its equaliser has been discussed and implemented which is based on maximising the ratio of the minimum squared euclidean distance of the PR target to the noise penalty introduced by the Partial Response (PR) filter. The results show that the new designed GPR targets have consistently better performance in comparison to various GPR targets previously published. Two methods of equalisation including the industry's standard PR, and a novel Soft-Feedback- Equalisation (SFE) have been discussed which are complimentary to each other. The work on SFE, which is a novelty of this work, was derived from the problem of Inter Symbol Interference (ISI) and noise colouration in PR equalisation. This work also shows that multi-level SFE with MAP/BCJR feedback based magnetic recording with ECC has similar performance when compared to high density binary PR based magnetic recording with ECC, thus documenting the benefits of multi-level magnetic recording. It has been shown that 4-level PR based magnetic recording with ECC at half the density of binary PR based magnetic recording has similar performance and higher packing density by a factor of 2. A novel technique of combining SFE and PR equalisation to achieve best ISI cancellation in a iterative fashion has been discussed. A consistent gain of 0.5 dB and more is achieved when this technique is investigated with application of Maximum Transition Run (MTR) codes. As the length of the PR target in PR equalisation increases, the gain achieved using this novel technique consistently increases and reaches up to 1.2 dB in case of EEPR4 target for a bit error rate of 10-5

Design of low-density parity-check codes for magnetic recording channels.

A technique for designing low-density parity-check (LDPC) error correcting codes for use with the partial-response channels commonly used in magnetic recording is presented. This technique combines the well-known density evolution method of Richardson and Urbanke for analyzing the performance of the LDPC decoder with a newly developed method for doing density evolution analysis of the Bahl-Cocke-Jelinek-Raviv (BCJR) channel decoder to predict the performance of LDPC codes in systems that employ both LDPC and BCJR decoders, and to search for good codes. We present examples of codes that perform 0.3dB to 0.5dB better than the regular column weight three codes employed in previous work.A new algorithm is also presented, which we call "MTR enforcement". Typical magnetic recording systems employ not just an error correcting code, but also some form of run-length-limited code or maximum-transition-run (MTR) code. The MTR enforcement algorithm allows us to exploit the added redundancy imposed by the MTR code to increase performance over that of a magnetic recording system which does not employ the MTR enforcer. We show a gain of approximately 0.5dB from the MTR enforcer in a typical magnetic recording system. We also discuss methods of doing so-called "soft-error estimates", which attempt to extrapolate the bit-error-rate (BER) curve from Monte Carlo simulations down below the limits for which the traditional BER results are valid. The recent work by Yedidia on generalizations of the belief propagation algorithm is discussed, and we consider problems that arise in using this generalized belief propagation method for decoding LDPC codes

Applications of iterative decoding to magnetic recording channels.

Finally, Q-ary LDPC (Q-LDPC) codes are considered for MRCs. Belief propagation decoding for binary LDPC codes is extended to Q-LDPC codes and a reduced-complexity decoding algorithm for Q-LDPC codes is developed. Q-LDPC coded systems perform very well with random noise as well as with burst erasures. Simulations show that Q-LDPC systems outperform RS systems.Secondly, binary low-density parity-check (LDPC) codes are proposed for MRCs. Random binary LDPC codes, finite-geometry LDPC codes and irregular LDPC codes are considered. With belief propagation decoding, LDPC systems are shown to have superior performance over current Reed-Solomon (RS) systems at the range possible for computer simulation. The issue of RS-LDPC concatenation is also addressed.Three coding schemes are investigated for magnetic recording systems. Firstly, block turbo codes, including product codes and parallel block turbo codes, are considered on MRCs. Product codes with other types of component codes are briefly discussed.Magnetic recoding channels (MRCs) are subject to noise contamination and error-correcting codes (ECCs) are used to keep the integrity of the data. Conventionally, hard decoding of the ECCs is performed. In this dissertation, systems using soft iterative decoding techniques are presented and their improved performance is established

Error-correction coding for high-density magnetic recording channels.

Finally, a promising algorithm which combines RS decoding algorithm with LDPC decoding algorithm together is investigated, and a reduced-complexity modification has been proposed, which not only improves the decoding performance largely, but also guarantees a good performance in high signal-to-noise ratio (SNR), in which area an error floor is experienced by LDPC codes.The soft-decision RS decoding algorithms and their performance on magnetic recording channels have been researched, and the algorithm implementation and hardware architecture issues have been discussed. Several novel variations of KV algorithm such as soft Chase algorithm, re-encoded Chase algorithm and forward recursive algorithm have been proposed. And the performance of nested codes using RS and LDPC codes as component codes have been investigated for bursty noise magnetic recording channels.Future high density magnetic recoding channels (MRCs) are subject to more noise contamination and intersymbol interference, which make the error-correction codes (ECCs) become more important. Recent research of replacement of current Reed-Solomon (RS)-coded ECC systems with low-density parity-check (LDPC)-coded ECC systems obtains a lot of research attention due to the large decoding gain for LDPC-coded systems with random noise. In this dissertation, systems aim to maintain the RS-coded system using recent proposed soft-decision RS decoding techniques are investigated and the improved performance is presented

Low-density parity-check coding for high-density magnetic recording systems.

Our strategy is to combine advanced signal processing techniques, the core of which is soft-decision iterative channel detection, with powerful low-density parity-check (LDPC) coding techniques.Magnetic recording channels (MRCs), including both longitudinal and perpendicular ones, are subject to a number of physical impairments, such as electronic/media noise, intersymbol interference (ISI), erasure, and intertrack interference (ITI). These impairments, if not appropriately handled, are barriers to achieving ultra-high densities. The goal of this dissertation is to study the impact of these multiple impairments on system performance, and to develop techniques to mitigate this impact such that the performance is as close to the theoretical limit of the channel as can be achieved by practical and implementable means.Specifically, the performance of regular LDPC codes on MRCs is first evaluated. Both randomly and structurally constructed codes are considered. Secondly, density evolution is used to analyze and design LDPC codes for MRCs. Results show that better irregular codes can be obtained. Afterwards, this algorithm is modified to include erasures, and erasure detection algorithms are studied. Fourthly, an improved algorithm for LDPC decoding, called signal-to-noise ratio (SNR) mismatch is unveiled. This algorithm may be useful for future practical applications. Finally, a channel detection algorithm for handling ITI in perpendicular recording is optimized, the eventual goal of which is to maximize the attainable track density

Non-iterative joint decoding and signal processing: universal coding approach for channels with memory

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