The Error-Pattern-Correcting Turbo Equalizer

The error-pattern correcting code (EPCC) is incorporated in the design of a turbo equalizer (TE) with aim to correct dominant error events of the inter-symbol interference (ISI) channel at the output of its matching Viterbi detector. By targeting the low Hamming-weight interleaved errors of the outer convolutional code, which are responsible for low Euclidean-weight errors in the Viterbi trellis, the turbo equalizer with an error-pattern correcting code (TE-EPCC) exhibits a much lower bit-error rate (BER) floor compared to the conventional non-precoded TE, especially for high rate applications. A maximum-likelihood upper bound is developed on the BER floor of the TE-EPCC for a generalized two-tap ISI channel, in order to study TE-EPCC's signal-to-noise ratio (SNR) gain for various channel conditions and design parameters. In addition, the SNR gain of the TE-EPCC relative to an existing precoded TE is compared to demonstrate the present TE's superiority for short interleaver lengths and high coding rates.Comment: This work has been submitted to the special issue of the IEEE Transactions on Information Theory titled: "Facets of Coding Theory: from Algorithms to Networks". This work was supported in part by the NSF Theoretical Foundation Grant 0728676

On Coding and Detection Techniques for Two-Dimensional Magnetic Recording

Edited version embargoed until 15.04.2020 Full version: Access restricted permanently due to 3rd party copyright restrictions. Restriction set on 15/04/2019 by AS, Doctoral CollegeThe areal density growth of magnetic recording systems is fast approaching the superparamagnetic limit for conventional magnetic disks. This is due to the increasing demand for high data storage capacity. Two-dimensional Magnetic Recording (TDMR) is a new technology aimed at increasing the areal density of magnetic recording systems beyond the limit of current disk technology using conventional disk media. However, it relies on advanced coding and signal processing techniques to achieve areal density gains. Current state of the art signal processing for TDMR channel employed iterative decoding with Low Density Parity Check (LDPC) codes, coupled with 2D equalisers and full 2D Maximum Likelihood (ML) detectors. The shortcoming of these algorithms is their computation complexity especially with regards to the ML detectors which is exponential with respect to the number of bits involved. Therefore, robust low-complexity coding, equalisation and detection algorithms are crucial for successful future deployment of the TDMR scheme. This present work is aimed at finding efficient and low-complexity coding, equalisation, detection and decoding techniques for improving the performance of TDMR channel and magnetic recording channel in general. A forward error correction (FEC) scheme of two concatenated single parity bit systems along track separated by an interleaver has been presented for channel with perpendicular magnetic recording (PMR) media. Joint detection decoding algorithm using constrained MAP detector for simultaneous detection and decoding of data with single parity bit system has been proposed. It is shown that using the proposed FEC scheme with the constrained MAP detector/decoder can achieve a gain of up to 3dB over un-coded MAP decoder for 1D interference channel. A further gain of 1.5 dB was achieved by concatenating two interleavers with extra parity bit when data density along track is high. The use of single bit parity code as a run length limited code as well as an error correction code is demonstrated to simplify detection complexity and improve system performance. A low-complexity 2D detection technique for TDMR system with Shingled Magnetic Recording Media (SMR) was also proposed. The technique used the concatenation of 2D MAP detector along track with regular MAP detector across tracks to reduce the complexity order of using full 2D detection from exponential to linear. It is shown that using this technique can improve track density with limited complexity. Two methods of FEC for TDMR channel using two single parity bit systems have been discussed. One using two concatenated single parity bits along track only, separated by a Dithered Relative Prime (DRP) interleaver and the other use the single parity bits in both directions without the DRP interleaver. Consequent to the FEC coding on the channel, a 2D multi-track MAP joint detector decoder has been proposed for simultaneous detection and decoding of the coded single parity bit data. A gain of up to 5dB was achieved using the FEC scheme with the 2D multi-track MAP joint detector decoder over un-coded 2D multi-track MAP detector in TDMR channel. In a situation with high density in both directions, it is shown that FEC coding using two concatenated single parity bits along track separated by DRP interleaver performed better than when the single parity bits are used in both directions without the DRP interleaver.9mobile Nigeri

ON REDUCING THE DECODING COMPLEXITY OF SHINGLED MAGNETIC RECORDING SYSTEM

Shingled Magnetic Recording (SMR) has been recognised as one of the alternative technologies to achieve an areal density beyond the limit of the perpendicular recording technique, 1 Tb/in2, which has an advantage of extending the use of the conventional method media and read/write head. This work presents SMR system subject to both Inter Symbol Interference (ISI) and Inter Track Interference (ITI) and investigates different equalisation/detection techniques in order to reduce the complexity of this system. To investigate the ITI in shingled systems, one-track one-head system model has been extended into two-track one-head system model to have two interfering tracks. Consequently, six novel decoding techniques have been applied to the new system in order to find the Maximum Likelihood (ML) sequence. The decoding complexity of the six techniques has been investigated and then measured. The results show that the complexity is reduced by more than three times with 0.5 dB loss in performance. To measure this complexity practically, perpendicular recording system has been implemented in hardware. Hardware architectures are designed for that system with successful Quartus II fitter which are: Perpendicular Magnetic Recording (PMR) channel, digital filter equaliser with and without Additive White Gaussian Noise (AWGN) and ideal channel architectures. Two different hardware designs are implemented for Viterbi Algorithm (VA), however, Quartus II fitter for both of them was unsuccessful. It is found that, Simulink/Digital Signal Processing (DSP) Builder based designs are not efficient for complex algorithms and the eligible solution for such designs is writing Hardware Description Language (HDL) codes for those algorithms.The Iraqi Governmen

CHANNEL CODING TECHNIQUES FOR A MULTIPLE TRACK DIGITAL MAGNETIC RECORDING SYSTEM

In magnetic recording greater area) bit packing densities are achieved through increasing track density by reducing space between and width of the recording tracks, and/or reducing the wavelength of the recorded information. This leads to the requirement of higher precision tape transport mechanisms and dedicated coding circuitry. A TMS320 10 digital signal processor is applied to a standard low-cost, low precision, multiple-track, compact cassette tape recording system. Advanced signal processing and coding techniques are employed to maximise recording density and to compensate for the mechanical deficiencies of this system. Parallel software encoding/decoding algorithms have been developed for several Run-Length Limited modulation codes. The results for a peak detection system show that Bi-Phase L code can be reliably employed up to a data rate of 5kbits/second/track. Development of a second system employing a TMS32025 and sampling detection permitted the utilisation of adaptive equalisation to slim the readback pulse. Application of conventional read equalisation techniques, that oppose inter-symbol interference, resulted in a 30% increase in performance. Further investigation shows that greater linear recording densities can be achieved by employing Partial Response signalling and Maximum Likelihood Detection. Partial response signalling schemes use controlled inter-symbol interference to increase recording density at the expense of a multi-level read back waveform which results in an increased noise penalty. Maximum Likelihood Sequence detection employs soft decisions on the readback waveform to recover this loss. The associated modulation coding techniques required for optimised operation of such a system are discussed. Two-dimensional run-length-limited (d, ky) modulation codes provide a further means of increasing storage capacity in multi-track recording systems. For example the code rate of a single track run length-limited code with constraints (1, 3), such as Miller code, can be increased by over 25% when using a 4-track two-dimensional code with the same d constraint and with the k constraint satisfied across a number of parallel channels. The k constraint along an individual track, kx, can be increased without loss of clock synchronisation since the clocking information derived by frequent signal transitions can be sub-divided across a number of, y, parallel tracks in terms of a ky constraint. This permits more code words to be generated for a given (d, k) constraint in two dimensions than is possible in one dimension. This coding technique is furthered by development of a reverse enumeration scheme based on the trellis description of the (d, ky) constraints. The application of a two-dimensional code to a high linear density system employing extended class IV partial response signalling and maximum likelihood detection is proposed. Finally, additional coding constraints to improve spectral response and error performance are discussed.Hewlett Packard, Computer Peripherals Division (Bristol

A communications system perspective for dynamic mode atomic force microscopy, with applications to high-density storage and nanoimaging

In recent times, the atomic force microscope (AFM) has been used in various fields like biology, chemistry, physics and medicine for obtaining atomic level images. The AFM is a high-resolution microscope which can provide the resolution on the order of fractions of a nanometer. It has applications in the field of material characterization, probe based data storage, nano-imaging etc. The prevalent mode of using the AFM is the static mode where the cantilever is in continuous contact with the sample. This is harsh on the probe and the sample. The problem of probe and sample wear can be partly addressed by using the dynamic mode operation with the high quality factor cantilevers. In the dynamic mode operation, the cantilever is forced sinusoidally using a dither piezo. The oscillating cantilever gently taps the sample which reduces the probe-sample wear. In this dissertation, we demonstrate that viewing the dynamic mode operation from a communication systems perspective can yield huge gains in nano-interrogation speed and fidelity. In the first part of the dissertation, we have considered a data storage system that operates by encoding information as topographic profiles on a polymer medium. A cantilever probe with a sharp tip (few nm radius) is used to create and sense the presence of topographic profiles, resulting in a density of few Tb per square inch. The usage of the static mode is harsh on the probe and the media. In this work, the high quality factor dynamic mode operation, which alleviates the probe-media wear, is analyzed. The read operation is modeled as a communication channel which incorporates system memory due to inter-symbol interference and the cantilever state. We demonstrate an appropriate level of abstraction of this complex nanoscale system that obviates the need for an involved physical model. Next, a solution to the maximum likelihood sequence detection problem based on the Viterbi algorithm is devised. Experimental and simulation results demonstrate that the performance of this detector is several orders of magnitude better than the performance of other existing schemes. In the second part of the dissertation, we have considered another interesting application of the dynamic mode AFM in the field of nano-imaging. Nano-imaging has played a vital role in biology, chemistry and physics as it enables interrogation of material with sub-nanometer resolution. However, current nano-imaging techniques are too slow to be useful in the high speed applications of interest such as studying the evolution of certain biological processes over time that involve very small time scales. In this work, we present a high speed one-bit imaging technique using the dynamic mode AFM with a high quality factor cantilever. We propose a communication channel model for the cantilever based nano-imaging system. Next, we devise an imaging algorithm that incorporates a learned prior from the previous scan line while detecting the features on the current scan line. Experimental results demonstrate that our proposed algorithm provides significantly better image resolution compared to current nano-imaging techniques at high scanning speed. While modeling the probe-based data storage system and the cantilever based nano-imaging system, it has been observed that the channel models exhibit the behavior similar to intersymbol-interference (ISI) channel with data dependent time-correlated noise. The Viterbi algorithm can be adapted for performing maximum likelihood sequence detection in such channels. However, the problem of finding an analytical upper bound on the bit error rate of the Viterbi detector in this case has not been fully investigated. In the third part of the dissertation, we have considered a subset of the class of ISI channels with data dependent Gauss-Markov noise. We derive an upper bound on the pairwise error probability (PEP) between the transmitted bit sequence and the decoded bit sequence that can be expressed as a product of functions depending on current and previous states in the (incorrect) decoded sequence and the (correct) transmitted sequence. In general, the PEP is asymmetric. The average BER over all possible bit sequences is then determined using a pairwise state diagram. Simulations results demonstrate that analytic bound on BER is tight in high SNR regime

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

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