Structured set partitions and multilevel concatenated coding for partial response channels

This paper addresses the design of a protograph-based LDPC code which can approach the independent and uniformly distributed (i.u.d.) capacity of partial response channels. We propose a method to calculate the iterative decoding threshold of a joint graph between a protograph and the state structure of a partial response channel using the extrinsic information transfer (EXIT) chart. We then describe a simple method to search for a protograph code whose threshold is close to the i.u.d. capacity limit. This new class of codes is needed because experiments show a protograph that is capacity approaching in the AWGN channel may not perform well in partial response channels. In particular, protographs with punctured nodes are often used to produce good AWGN codes, but they perform poorly with the BCJR equalizer. Numerical results support our analysis.

Combination of turbo codes with partial response (PR) channels was comprehensively studied in magnetic recording systems. In this paper, we investigate a decoding scheme called 'iterative tri-stage decoding' for the turbo code as the outer code and the precoded PR channel as the inner code. This decoding scheme reduces the computational complexities by reducing the number of iterations without degrading the coding gain.

A number of papers have recently been published on the concatenation of an outer code with a partial response (PR) channel, where the outer code is a turbo code, a convolutional code, or a low density parity check code. This paper deals with the second case assuming EPR4 and modified extended EPR4 (MEEPR4) partial response targets. The goal in this work is the joint optimization of interleaver and precoder for a fixed outer convolutional code and PR target. We introduce mathematical and algorithmic tools for accomplishing this goal and present simulation results which support our approach. Among the positive results is the ability to lower the well-known error rate floor of these concatenated schemes for arbitrary partial response channels.

Towards the goal of achieving better error correction performance in data storage systems, iterative soft decoding of low density parity check (LDPC) codes and soft-decision decoding of Reed-Solomon (RS) codes have started receiving increasing research attention. However, even with increased computing power, complexities of soft-decision decoding algorithms are still too high for real products which require high throughput and small hardware area. Another problem is that the performance gains of those approaches are smaller for magnetic recording channels than they are for memoryless additive white Gaussian noise (AWGN) channels. We propose a new soft-decision decoding algorithm (based on the Chase algorithm), which takes advantage of pattern reliability instead of symbol reliability or bit reliability. We also present a modified Viterbi algorithm that provides probable error patterns with corresponding reliabilities. Simulation results of the proposed algorithms over the partial response (PR) channel show attractive performance gains. The proposed algorithm dramatically reduces the number of iterations compared to the conventional Chase2 algorithm over the PR channel.

With an annual increase in density of 100% approaching superparamagnetic limits much stronger error control systems are required in read channels for hard drives. A technique is presented for correcting long errors that are the result of highly colored noise typical for modern magnetic heads and media. We introduce a sofic system-based construction of very high rate codes for correcting errors from a given list, and demonstrate a substantial SNR gain when these codes are used in a scheme that combines the error event detection and the list soft decoding.

We construct codes that can closely approach (and possibly ultimately achieve) the i.i.d. capacity of an intersymbol interference (ISI) channel with inputs confined to binary values. We use the low-density-parity-check (LDPC) degree sequences optimization method proposed by Richardson, Shokrollahi and Urbanke (see IEEE Trans. Inform. Theory, vol.47, p.619-37, February 2001) and appropriately modify it for ISI channels.

Recording media written-in transition jitter noise can limit magnetic recording systems. Read channel intersymbol interference (ISI) modulates media jitter in a head/disk/channel, attenuating jitter at low linear density due to classical ISI but amplifying at high density. This paper assesses whether jitter modulation is significant in typical disk drive peak detect (PD) and partial response (PR) channel design, where maximum linear bit density is sought at a specified bit error rate (BER). Experimental isolated pulse data, transition noise, and electronic noise measurements from a 65 mm head/disk recording design are used as inputs to a Matlab simulation of PD and PR Lorentzian channel low pass and boost filters, PD differentiator filter, PR digital filter, and PD/PR bit detectors. The goal of such models is optimizing the designable PD and PR channel parameters for realistic maximum linear density prediction. However their complexity obscures the jitter modulation contribution, which is demonstrated here by the shift in the EER versus density curves, when the jitter modulation is mathematically turned off. Jitter modulation is thereby shown to be significant but not dominant in (1,7) PD density limits. About an order of magnitude BER loss due to jitter modulation can occur at typical PD linear channel bit densities P/sub 50//T/spl ap/2. Jitter amplification in PD channels can occur at channel density 3.8 (above usable PD limits). PR channels only amplify media jitter, degrading EER by about an order of magnitude at typical (0, k) PR4 densities, and degrading timing channel accuracy twice as fast as channel density increases. Lorentzian isolated pulse (ISOP) modeling is compared to recording physics mathematical pulses, and simulation statistical validity checks are made.

The dependence of MSE and marginalized BER on amplitude asymmetry for two partial response channels is reported. To eliminate the impact of variations in other head parameters, we varied the bias point of a given head using an external magnetic field. We find that the MSE degrades continuously as the magnitude of the amplitude asymmetry is increased; the marginalized BER is at most weakly dependant on amplitude asymmetry for magnitudes less than 15%. At larger magnitudes the channel performance is more severely impacted, Finally, we were able to simulate these results using a simplified model of the read channel.

This paper is concerned with the applications of majority-logic decodable nonbinary low-density parity-check (LDPC) codes to partial response (PR) channels. We propose a joint detection/decoding algorithm that works in an iterative manner by exchanging messages between the Viterbi detector and a generalized majority logic decoder (GMLGD). The Viterbi detector is implemented over a sectionalized trellis. The hard-decisions made by the Viterbi detector are then passed to the decoder. The decoder delivers as output estimates of each coded symbols, which will be utilized in next iteration to update the branch metrics of the trellis. Since the proposed algorithm requires only integer operations and finite field operations, it can be implemented with simple combinational logic circuits. Simulation results and complexity analysis show that, when compared with the conventional turbo equalizer implemented with the BCJR algorithm and the Q-ary sum-product algorithm (BCJR-QSPA), the proposed algorithm has a much lower complexity but suffers from a little performance degradation. So the proposed algorithm provides a good candidate for trade-offs between performance and complexity.

Transmitter and receiver filter design plays a key role in communication systems with partial response channels. For a partial response system, a nonmaximally decimated multirate filter bank can be used as a precoder. Based on the MMSE criterion, a closed-form solution to the joint transmitter-receiver optimization problem for noisy partial response channels is presented in this paper. It is found that the redundancy introduced by the nonmaximally decimated filter bank precoder can compensate for spectral nulls in partial response channels that can impair several known joint optimization methods. Simulation results corroborate the analysis that joint transmitter-receiver optimization can achieve significant performance improvement over inverse filter receiver and receiver optimization schemes.

The partial response channel can be viewed as a rate-1 encoder in which the output alphabet differs from the input alphabet. In serially concatenated coding schemes, the partial response channel can serve as the inner encoder. Recent works on the application of turbo decoding techniques to partial response channels have used channel models to investigate system performance. While the models provided some insight into the performance of turbo decoding techniques, performance in a real system, with electronic and signal-dependent media noise, remained unknown. This paper will demonstrate the performance of turbo decoding techniques using real and modeled spinstand data. A simple serial concatenation system will be presented that uses as its outer code a single convolutional code and as its inner code the partial response channel. Significant gains will be shown over QMTR coded systems.

This paper introduces a combinatorial construction of high rate low-density parity check codes based on two-dimensional integer lattices. A class of codes with a wide range of lengths, column weights and minimum distances is obtained. The resulting codes are doubly circulant, i.e. the matrix of parity checks is an array of circulant matrices. The bounds on the minimum distance are established and the performance of these codes in partial response channels is investigated.

This paper addresses a new scheme by Vasic and Pedagani to combine low-density parity-check (LDPC) codes with run length limited (RLL) constraints. In this method, the RLL constraints are embedded into the LDPC codewords by deliberately flipping the bits of LDPC codewords that violate the RLL constraints. It is important to keep the number of flipped bits small in order to not overburden the LDPC decoder. In this paper, we introduce a method to control the number of flipped bits by using pseudorandom sequences. We present a new low-complexity iterative decoding and detection scheme to correct both the flipped bits and channel errors in a partial response channel. Analyses and simulation results show that the proposed method has good performance and reasonable complexity for (0,k) RLL constraints.

Summary form only given. Following the work done by Ryan (Proc. ICC Int. Conf. on Communications, 1998), considerable research has been reported on the application of concatenated codes to partial response (PR) channels. Both parallel concatenated codes (PCC) and serial concatenated codes (SCC) have been studied. In all of those works, a linear model for the channel was assumed, which is a valid assumption for low recording densities. However, as the recording density increases, the channel becomes nonlinear where nonlinearity arises from closely spaced recorded transitions. In this paper, we combine concatenated coding and nonlinear equalization for PR channels that suffer from nonlinear distortion (or intersymbol interference) according to the setup shown in Fig 1. We extend the RAM-search/Viterbi-detector concept to the a posteriori probability (APP) and soft-output Viterbi algorithm (SOVA) detectors that are used with turbo-coded partial response channels. The modified APP and SOVA are called RS-APP and RS-SOVA, respectively.

The partial response channel can be viewed as a rate-1 encoder in which the output alphabet differs from the input alphabet. In serially concatenated coding schemes, the partial response channel can serve as the inner encoder. Recent work has focused on convolutional codes and parity-check codes as the outer code in such serial concatenation schemes. This work focuses instead on the use of product codes as the outer code. Systems using both hard and soft decoding, with both iterative and non-iterative decoding, are presented. Simulation results are presented comparing performance of product codes which use Reed-Solomon and BCH codes as the constituent codes.