689 research outputs found
An Iteratively Decodable Tensor Product Code with Application to Data Storage
The error pattern correcting code (EPCC) can be constructed to provide a
syndrome decoding table targeting the dominant error events of an inter-symbol
interference channel at the output of the Viterbi detector. For the size of the
syndrome table to be manageable and the list of possible error events to be
reasonable in size, the codeword length of EPCC needs to be short enough.
However, the rate of such a short length code will be too low for hard drive
applications. To accommodate the required large redundancy, it is possible to
record only a highly compressed function of the parity bits of EPCC's tensor
product with a symbol correcting code. In this paper, we show that the proposed
tensor error-pattern correcting code (T-EPCC) is linear time encodable and also
devise a low-complexity soft iterative decoding algorithm for EPCC's tensor
product with q-ary LDPC (T-EPCC-qLDPC). Simulation results show that
T-EPCC-qLDPC achieves almost similar performance to single-level qLDPC with a
1/2 KB sector at 50% reduction in decoding complexity. Moreover, 1 KB
T-EPCC-qLDPC surpasses the performance of 1/2 KB single-level qLDPC at the same
decoder complexity.Comment: Hakim Alhussien, Jaekyun Moon, "An Iteratively Decodable Tensor
Product Code with Application to Data Storage
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
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
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
Relaxation Bounds on the Minimum Pseudo-Weight of Linear Block Codes
Just as the Hamming weight spectrum of a linear block code sheds light on the
performance of a maximum likelihood decoder, the pseudo-weight spectrum
provides insight into the performance of a linear programming decoder. Using
properties of polyhedral cones, we find the pseudo-weight spectrum of some
short codes. We also present two general lower bounds on the minimum
pseudo-weight. The first bound is based on the column weight of the
parity-check matrix. The second bound is computed by solving an optimization
problem. In some cases, this bound is more tractable to compute than previously
known bounds and thus can be applied to longer codes.Comment: To appear in the proceedings of the 2005 IEEE International Symposium
on Information Theory, Adelaide, Australia, September 4-9, 200
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