Combined concatenated coding and nonlinear equalization for magnetic recording channels

Turbo codes are applied to magnetic recoding channels by treating the channel as a rate-one convolutional code that requires a soft a posteriori probability (APP) detector for channel inputs. The complexity of conventional APP detectors, such as the BCJR algorithm or the soft-output Viterbi algorithm (SOVA), grows exponentially with the channel memory length. This paper derives a new APP module for binary intersymbol interference (ISI) channels based on minimum mean squared error (MMSE) decision-aided equalization (DAE), whose complexity grows linearly with the channel memory length, and it shows that the MMSE DAE is also optimal by the maximum a posteriori probability (MAP) criterion. The performance of the DAE is analyzed, and an implementable turbo-DAE structure is proposed. The reduction of channel APP detection complexity reaches 95% for a five-tap ISI channel when the DAE is applied. Simulations performed on partial response channels show close to optimum performance for this turbo-DAE structure. Error propagation of the DAE is also studied, and two fixed-delay solutions are proposed based on combining the DAE with the BCJR algorithm.

We compare the asymptotic performance of parallel concatenated codes (PCCs) and serial concatenated codes (SCCs) over GF(4). We construct such codes using optimal nonbinary convolutional codes where optimality is in the sense of achieving the largest minimum distance for a fixed number of encoder states. Code rates of the form K/sub 0//(K/sub 0/ + 1) for K/sub 0/ = 1, 8, and 64 are considered. For all of these code rates, we find the minimum distance and its multiplicity for both concatenated code systems. This is accomplished by feeding the encoder with all possible weight-two and weight-three input information patterns and monitoring, at the output of the encoder, the weight of the corresponding codewords and their multiplicity. Our analytical results indicate that the SCC codes outperform their counterpart PCC codes with much lower complexity.

We present a turbo decoder that is based on a low complexity soft output Viterbi algorithm (SOVA) introduced by Claude Berrou et al. in ICC'93. It is conceptually different from the conventional turbo decoders, where the iteration is based on the a posteriori probabilities (APP). The constituent Berrou SOVA decoders make the maximum likelihood (ML) decision on the correct path in the trellis, and they have lots of similarities with a conventional hard decision Viterbi decoder—their complexity is double that of the Viterbi due to extraction of the soft output. The iterative Berrou SOVA decoder is able to achieve a relatively high speed: the constituent decoders can work at the same pace as their conventional Viterbi counterparts, and no back tracing is needed. The performance is competitive with the traditional decoding algorithms. In comparison with Max-Log-MAP, we have attained a slightly better performance. Copyright © 2003 AEI.

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.

We present a systematic way to construct multilevel concatenated codes for partial response (PR) channels using: (1) a structured set partition (SSP) of multiple channel output sets and (2) a set of conventional block codes with different error correcting capabilities. A lower bound on the minimum squared Euclidean distance of the constructed codes is given. This bound is based on the interset minimal Euclidean distances of the SSP and the minimum Hamming distances of the used block codes. An example of SSP for the extended class 4 partial response channel (EPR4) is presented. Iterative suboptimal decoding, which combines Viterbi detection on the trellis of the PR channel with algebraic error detection/correction, can be applied to the constructed concatenated codes. Truncated versions of the iterative decoding scheme are simulated and compared with each other.

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.

This paper concerns the soft-in soft-out detection in a coded communication system, where the transmitted symbols are discrete valued, and the exact a posteriori probability (APP) detection often involves prohibitive complexity. By using the properties of Gaussian functions, an approximate approach to the APP detection is devised with the idea that, in the computation of the APP of each symbol, the remaining symbols are distinguished based on their contributions to the APP of the concerned symbol, and the symbols with less contributions are approximated as (continuous) Gaussian variables [hence the name partial Gaussian approximation (PGA)] to reduce the computational complexity. The connection between the PGA detector and the reduced dimension maximum a posteriori detector (RDMAP) is investigated. It is shown that, PGA is equivalent to RDMAP, but it has a complexity much lower than that of RDMAP, i.e., PGA can be regarded as an efficient implementation of RDMAP. In addition, the application of PGA in intersymbol interference (ISI) channel equalization is also investigated. We show that PGA allows further significant complexity reduction by exploiting the circulant structure of the system transfer matrix, which makes PGA very attractive in handling severe ISI channels with large memory length.

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 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.

The High Performance Waveform (HPW) was developed before parallel concatenated codes (PCCC) and serial concatenated codes (SCCC) were in wide use and so it makes sense to take advantage of the advancements in communication theory and processor computation speed that have taken place since its inception. In its current form, HPW transmits a Raised-Cosine Continuous Phase Modulation (1RC CPM) modulation with a trellis code that is designed to provide, with the use of a Cyclic Redundancy Check Code error detection (CRC), error free transmission over a single, narrowband UHF satellite communications channel. In this paper we present an additional set of coding and modulation schemes which take advantage of serial concatenated code (SCCC) technology to simultaneously improve throughput at the lower end of the signal-to-noise ratio (SNR) range while increasing the highest throughput at the highest SNR available on UHF satellites. The overall bit error rate and throughput of each individual modulation type is analyzed and the framework for the adaptive modulation protocol is provided. To provide for a gradual release of a newer revision of HPW, a framework for a PHY layer is provided which will allow a heterogeneous network of legacy and updated radio terminals.

When estimating channel parameters in linearly modulated communication systems, the iterative expectation-maximization (EM) algorithm can be used to exploit the signal energy associated with the unknown data symbols. It turns out that the channel estimation requires at each EM iteration the a posteriori probabilities (APPs) of these data symbols, resulting in a high computational complexity when channel coding is present. In this paper, we present a new approximation of the APPs of trellis-coded symbols, which is less complex and requires less memory than alternatives from literature. By means of computer simulations, we show that the Viterbi decoder that uses the EM channel estimate resulting from this APP approximation experiences a negligible degradation in frame error rate (FER) performance, as compared to using the exact APPs in the channel estimation process.

The previously modified two-dimensional (2D) soft output Viterbi algorithm (SOVA) for holographic data storage (HDS) consists of four one-dimensional (1D) SOVAs in accordance with two different 1D partial response (PR) targets (vertical and horizontal directions). In this study, we propose a detection method in structural accordance with a 2D PR target through the use of the modified 2D SOVA. The proposed method shows superior bit error rate performance owing to the use of a 2D PR target that contains more information than the 1D PR target. Moreover, a reduction in power consumption, computational complexity, and the system-on-chip size for HDS system can be expected as a result of the use of only one 2D equalizer.

Duobinary partial response (PR) filtered single-carrier frequency-domain multi-access (SC-FDMA) uplink has a potential to achieve higher spectral efficiency (SE) by allowing spectrum overlapping between adjacent users. However, strong multiuser interference (MUI) degrades the bit-error rate (BER) and throughput performances. In this paper, we present two types of frequency-domain MUI cancellation technique for duobinary PR filtered SC-FDMA, which are frequency-domain iterative parallel MUI cancellation (FD-IPMUIC) and frequency-domain iterative successive MUIC (FD-ISMUIC). A series of minimum mean-square error based frequency-domain equalization (MMSE-FDE), FD-MUIC, and soft-decision decoding using soft output Viterbi algorithm (SOVA) is repeated for a sufficient number of times. By using the SOVA, MMSE-FDE weight and MUI replica are updated. Computer simulation results show that both the BER performance and SE can be improved.