Partial Response Channels Research Articles

An Improved Belief-Propagation Decoder for LDPC-Coded Partial-Response Channels

The traditional belief-propagation (BP) decoder for low-density parity-check (LDPC) codes assumes that the soft input information for each bit is independent of all other bits. However, for partial-response (PR) channels, the log-likelihood ratios (LLRs) generated by the channel detector are correlated. In this paper, we propose an improved BP (IBP) decoder to take into account the dependence among the LLRs produced by channel detectors. The IBP decoder needs not only the LLR for each bit but also the probability distribution of the subblock that contains this bit. Therefore, we revise the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm accordingly to generate the additional information during channel detection. We apply the proposed decoder to an ideal PR channel and, as a practical example, to equalized perpendicular magnetic recording channels (PMRCs). The IBP decoder significantly outperforms the traditional BP decoder without turbo equalization, but this gain is substantially reduced when we introduce turbo equalization. Furthermore, we extend the IBP decoder to nonbinary LDPC codes, and show that we can achieve additional gains.

Error Floor Estimation of Long LDPC Codes on Magnetic Recording Channels

The presence of error floor in low density parity check (LDPC) codes is of great concern for potential applications of LDPC codes to data storage channels, which require the code to maintain the near capacity error correcting performance down to frame error rates of 10-12. In order to investigate the error floor of LDPC codes under magnetic recording channels used in data storage systems, we extended the trapping set based estimation method to predict the error floor under magnetic recording channels. The goal is to accurately estimate the error rates in the error floor region for certain types of LDPC codes under the partial response channel. First, we use field-programmable gate array (FPGA) hardware simulation to find the trapping sets that cause the decoding failure in the error floor region. For each trapping set, we extract the parameters that are key to the decoding failure caused by this trapping set. Then we use a much simpler in situ simulation with these parameters to obtain the conditional decoding failure rate. By considering all the trapping sets, we obtain the overall frame error rate in the error floor region. The estimation results under the magnetic recording channel are within 0.3 dB of the direct simulation results.

Joint TA Suppression and Turbo Equalization for Coded Partial Response Channels

Thermal asperities (TAs) cause a crucial problem in magnetic recording systems because they can cause a burst of errors in data detection process. Without a TA detection and correction algorithm, the system performance can be unacceptable, depending on how severe the TA effect is. This paper proposes an iterative scheme to suppress the TA effect. This scheme jointly performs TA suppression and turbo equalization on the partial-response channels with error-correction codes. At each turbo iteration, an improved readback signal is obtained by subtracting the reconstructed TA signal from the TA-affected readback signal, where the reconstructed TA signal is computed based on a least-squares fitting technique with an aid of soft decisions from previous turbo iterations. Simulation results indicate that the proposed scheme outperforms the conventional receiver with separate TA suppression and turbo equalization, and is only marginally more complex than the conventional receiver.

Application of pattern-output viterbi algorithm to algebraic soft-decision decoding over partial response channels

The algebraic soft-decision decoding algorithm (ASD) requires a reliability matrix as its input. In this paper, a new method to construct the reliability matrix over partial response (PR) channels of interest in magnetic recording is proposed by using recently introduced pattern-output Viterbi algorithm (POVA). A modified bit-level generalized minimum distance (BGMD) algorithm is also proposed with the POVA to achieve performance gains over PR channels that are as large as gains as over AWGN channels.

Low-Floor Detection/Decoding of LDPC-Coded Partial Response Channels

The error-rate floor phenomenon associated with iterative LDPC decoders has delayed the use of LDPC codes in certain communication and storage systems. Error floors are known to generally be caused by so-called trapping sets which have the effect of confounding the decoder. In this paper, we introduce two techniques that lower the error-rate floors for LDPC-coded partial response (PR) channels which are applicable to magnetic and optical storage. The techniques involve, via external measures, "pinning" one of the bits in each problematic trapping set and then letting the iterative decoder proceed to correct the rest of the bits. We also extend our earlier work on generalized-LDPC (G-LDPC) decoders for error-floor mitigation on the AWGN channel to partial response channels. Our simulations on PR1 and EPR4 channels demonstrate that the floor for the code chosen for this study, a 0.78(2048,1600) quasicyclic LDPC code, is lowered by orders of magnitude, beyond the reach of simulations. Because simulation in the floor region is so time-consuming, a method for accelerating such simulations is essential for research in this area. In this paper, we present an extension of Richardson's importance sampling technique for estimating the level of error floors.

Pattern-Flipping Chase-Type Decoders with Error Pattern Extracting Viterbi Algorithm over 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.

List Decoding Techniques for Intersymbol Interference Channels Using Ordered Statistics

In this paper, we present a generalization of the ordered statistics decoding (OSD) techniques for the class of intersymbol interference (ISI) channels, and show decoding results for the extended Bose-Chaudhuri-Hocquenghem (eBCH) [128, 64, 22] code and the [255, 239, 17] Reed-Solomon (RS) binary image, over the PR2 partial response channel. Using the generalized OSD technique, we go on to generalize the Box-and- Match Algorithm (BMA) to the class of ISI channels. The BMA is an enhancement of OSD, and prior work has shown it to provide significant performance gain over OSD for memoryless additive white Gaussian noise (AWGN) channels. We present decoding results of the BMA for ISI channels, for the same eBCH and RS (binary image) codes, and PR2 channel. Our results show that the BMA (generalized for ISI channels) is superior to the OSD in terms of its performance/complexity trade-off. More specifically, the BMA may be tuned such that both algorithms have similar complexity, whereby the BMA still outperforms the OSD by a significant margin.

Multi-Gb/s Bit-by-Bit Receiver Architectures for 1-D Partial-Response Channels

Low-complexity bit-by-bit detection techniques for 1-D partial-response channels are presented. First, a full-rate detection technique is presented which operates at 3.3 Gb/s consuming 40 mA from a 1.8-V supply with a sensitivity of 40-mV differential. The speed of the full-rate architecture is limited by the settling time of a latch circuit which has to be less than 1 UI. To eliminate this limitation, a novel demuxing technique is introduced. Using the proposed technique, a second architecture achieves 5 Gb/s data rate with the same sensitivity and consuming 62 mA (including output buffer) from 1.8-V supply. Both half-rate and full-rate architectures are also studied in 90-nm CMOS targeting chip-to-chip applications. The implemented full-rate architecture operates at 10 Gb/s consuming 32 mW, whereas the simulated half-rate architecture consumes 50 mW and operates at 16.67 Gb/s.

Optimal channel detection for nonbinary coded partial response channels

We derive a recursive algorithm to compute the joint maximum a posteriori probabilities of p consecutive bits on partial response channels. This channel detector is optimal for nonbinary soft-iterative decoding with multiple channel iterations. It is validated on a nonbinary low-density parity-check coded perpendicular magnetic recording channel.

Turbo Equalization of Run Length Limited (1,9) and Low Density Parity Check Code for Super Resolution Nearfield Structure Read Only Memory Discs with 60 nm Minimum Mark Length

Due to severe intersymbol interference and low signal-to-noise ratio of super resolution nearfield structure (SuperRENS) random read-outs, turbo equalization techniques are applied to lower bit error rates. A d1k9r5 run length limited (RLL) modulation code having minimum runlength d = 1, maximum runlength k = 9 and repeated minimum transition run limitation of r = 5 has been developed with emphasis on low joint bit detection and demodulation (super-trellis) complexity for use within turbo equalization schemes. Bit error rate (BER) performance of d1k9r5 code over partial response-channels is similar to 17pp code while the super-trellis detector complexity of d1k9r5 code is reduced. Low-frequency suppression performance of d1k9r5 code is similar to that of 17pp code under the same DC control redundancy. BER results for measured data from a 60 nm SuperRENS read only memory disc employing an InSb mask layer, using d1k9r5 modulation and a high-rate quasi-cyclic low density parity check (LDPC) code, correspond well to simulation results. Continuously decreasing BERs down to 2 ×10-5 after five iterations show that a turbo equalization scheme incorporating d1k9r5 super-trellis detection can be successfully applied in SuperRENS storage systems together with an LDPC code.

Super-Trellis Based Noise Predictive Joint Bit Detection and Runlength Limited Decoding for High-Density Optical Storage

Super-trellis based noise predictive detection is investigated for high density optical storage, where runlength limited (RLL) encoder, non-return-to-zero inverted (NRZI) precoder, partial response (PR) channel, and noise predictor (NP) together are interpreted as an equivalent RLL-NRZI-PR-NP channel. Two approaches are shown to combine an RLL decoding trellis with the NRZI-PR channel by means of looking either backward or forward the RLL decoding trellis, which is extended to construct an RLL-NRZI-PR-NP super-trellis. To maintain a reasonable detector complexity, reduced-state noise predictive detectors are derived. Three different d = 1 RLL codes are compared with respect to the complexity of noise predictive detectors, showing the complexity advantage of our recently designed d = 1, k = 9 RLL code. Simulation results show that bit error rate performance gain obtained by the proposed detector increases as storage density increases.

109 Gbit/in.2 Recording on Near-Field Optical Disc Using Combination of Partial-Response Channel and Low-Density Parity-Check Code

The signal properties were examined at recording densities higher than 100 Gbit/in.2 in our solid immersion lens recording system of 1.84 numerical aperture (NA). The low-density parity-check coded partial-response (PR) 17-parity preserve/prohibit (PP) system increased the recording density by approximately 35% compared with the previous results. The recording power tolerance was ±8.1% at a recording density of 109 Gbit/in.2. We conclude that the upper limit of recording density is 109 Gbit/in.2, which is equivalent to 151 Gbytes for a 12-cm-diameter disc, assuming the same redundancy as that of the Blu-ray disc format.

Graph-Based Channel Detection for Multitrack Recording Channels

We propose a low complexity detection technique for multihead multitrack recording systems. By exploiting sparseness of two-dimensional partial response (PR) channels, we develop an algorithm which performs belief propagation (BP) over corresponding factor graphs. We consider the BP-based detector not only for partial response channels but also for more practical conventional media and bit-patterned media storage systems, with and without media noise. Compared to the maximum likelihood detector which has a prohibitively high complexity that is exponential with both the number of tracks and the number of intersymbol interference (ISI) taps, the proposed detector has a much lower complexity and a fast parallel structure. For the multitrack recording systems with PR equalization, the price is a small performance penalty (less than one dB if the intertrack interference (ITI) is not too high). Furthermore, since the algorithm is soft-input soft-output in nature, turbo equalization can be employed if there is an outer code. We show that a few turbo equalization iterations can provide significant performance improvement even when the ITI level is high.

DFT-Based Channel Estimation with Symmetric Extension for OFDMA Systems

A novel partial frequency response channel estimator is proposed for OFDMA systems. First, the partial frequency response is obtained by least square (LS) method. The conventional discrete Fourier transform (DFT) method will eliminate the noise in time domain. However, after inverse discrete Fourier transform (IDFT) of partial frequency response, the channel impulse response will leak to all taps. As the leakage power and noise are mixed up, the conventional method will not only eliminate the noise, but also lose the useful leaked channel impulse response and result in mean square error (MSE) floor. In order to reduce MSE of the conventional DFT estimator, we have proposed the novel symmetric extension method to reduce the leakage power. The estimates of partial frequency response are extended symmetrically. After IDFT of the symmetric extended signal, the leakage power of channel impulse response is self-cancelled efficiently. Then, the noise power can be eliminated with very small leakage power loss. The computational complexity is very small, and the simulation results show that the accuracy of our estimator has increased significantly compared with the conventional DFT-based channel estimator.

Simplified Neural Network Equalizer With Noise Whitening Function for GPRML System

A new design method of the simplified neural network equalizer (NNE) with the noise whitening function for a generalized partial response (GPR) channel is proposed. The long-term bit error rate performance of GPR class-I maximum likelihood (GPR1ML) system employing NNE in perpendicular magnetic recording (PMR) channel with thermal decay is also obtained by computer simulation using our thermal decay model for a CoPtCr-SiO2 PMR medium with KuV/kT=60. The performance of GPR1ML system with NNE (GPR1ML-NNE) is superior to that of GPR1ML with a transversal filter equalizer. The PR1ML system using a noise whitening NNE and a two-state Viterbi detector provides almost equivalent performance to that of GPR1ML-NNE having a 16-state detector.

Iterative reduced-search decoding for coded partial-response channels

The full-complexity soft-input/soft-output (SISO) detector based on the BCJR algorithm for coded partial-response channels has a computational complexity growing exponentially with channel memory length. In this letter, we propose a low complexity soft-output channel detector based on the Chase decoding algorithm, which was previously applied to decode turbo product codes. At each iteration, the proposed detector forms a candidate list using all possible combinations of bit patterns in the weakest indices based on tentative hard estimates and a priori information fed back from the outer decoder. To demonstrate the performance/complexity tradeoff of the proposed detector, simulation results over rate-8/9 turbo-coded EPR4 and ME/sup 2/PR4 channels are presented, respectively. It is shown that the proposed detector can significantly reduce the computational complexity with only a small performance loss compared to the BCJR algorithm.

Low-Density Parity-Check Coded Recording Systems With Run-Length-Limited Constraints

We propose two techniques for the low-density parity-check (LDPC) coded partial response channel with run-length-limited (RLL) constraints. The first is a modification of the selective flipping technique so that side information is not needed. The second is based on the estimation of flipped bits for the selective flipping technique. The second technique can achieve significant performance improvement over the simple selective flipping technique either with side information or without side information. We also incorporate these two techniques into a known technique to design LDPC coded recording systems that can meet strict RLL constraints without performance degradation.

Finite-Length Extrinsic Information Transfer (EXIT) Analysis for Coded and Precoded ISI Channels

In this paper, we consider the classic problem of accessing coded and precoded intersymbol interference (ISI) channels, and particularly partial response (PR) channels, which are widely used in modeling magnetic recording systems. Previous work has either treated the binary precoder as an exclusive function of the channel characteristics, disregarding possible impact from the channel code, or, in performing the iterative analysis of this concatenated system, assumed an unbounded length. Our approach here is to extend the conventional infinite-length extrinsic information transfer (EXIT) charts to ISI systems of limited lengths, and to explicitly account for the effect of the channel nonergodicity. We found that short-length channel codes may exhibit distinctively different EXIT behaviors in different rate regions, and it is important to couple the precoder and the channel code. We show that infinite- and finite-length EXIT behaviors do not always agree, and hence the results obtained from the infinite-length analysis may not hold for practical short-length systems.

Interior point decoding for linear vector channels

In this paper, a novel decoding algorithm for low-density parity-check (LDPC) codes based on convex optimization is presented. The decoding algorithm, called interior point decoding, is designed for linear vector channels. The linear vector channels include many practically important channels such as inter-symbol interference channels and partial response channels. It is shown that the maximum likelihood decoding (MLD) rule for a linear vector channel can be relaxed to a convex optimization problem, which is called a relaxed MLD problem.

Optimization of Information Rate Upper and Lower Bounds for Channels With Memory

We consider the problem of minimizing upper bounds and maximizing lower bounds on information rates of stationary and ergodic discrete-time channels with memory. The channels we consider can have a finite number of states, such as partial response channels, or they can have an infinite state space, such as time-varying fading channels. We optimize recently proposed information rate bounds for such channels, which make use of auxiliary finite-state machine channels (FSMCs). Our main contribution in this paper is to provide iterative expectation-maximization (EM) type algorithms to optimize the parameters of the auxiliary FSMC to tighten these bounds. We provide an explicit, iterative algorithm that improves the upper bound at each iteration. We also provide an effective method for iteratively optimizing the lower bound. To demonstrate the effectiveness of our algorithms, we provide several examples of partial response and fading channels where the proposed optimization techniques significantly tighten the initial upper and lower bounds. Finally, we compare our results with results obtained by the conjugate gradient optimization algorithm and an improved variation of the simplex algorithm, called Soblex. While the computational complexities of our algorithms are similar to the conjugate gradient method and less than the Soblex algorithm, our algorithms robustly find the tightest bounds. Interestingly, from a channel coding/decoding perspective, optimizing the lower bound is related to increasing the achievable mismatched information rate, i.e., the information rate of a communication system where the decoder at the receiver is matched to the auxiliary channel, and not to the original channel.