This paper studies bit-patterned media recording channels when there exist written-in errors. Using a signal processing point of view, we consider an abstract model for the overall recording channel, incorporating errors occurred during the write process. Based on the resulting channel model, we develop various trellis structures, and propose several detection algorithms for data recovery. Furthermore, we investigate the achievable information rates for patterned media recording systems with different levels of write error probability, which provide an information theoretical performance assessment for such systems.

In this letter, we propose an iterative belief propagation (BP) channel detector (equalizer) over single-input single- output (SISO) and multiple-input multiple-output (MIMO) frequency selective fading channels as an alternative to the typically used maximuma-posteriori(MAP) or maximum likelihood (ML) detectors. The proposed detector has a parallel structure, resulting in fast hardware implementations. Moreover, BP detector is less complex than the MAP detector and it has a short decoding delay. We analyze the bit error rate and the mutual information and show that, over frequency selective fading channels, the proposed BP detector achieves a near-optimal performance, even in the presence of the length 4 cycles in the corresponding channel factor graph.

Timing recovery in communication and storage systems requires the use of Run Length Limited (RLL) or (d,k) codes. A class of such codes is constructed by a method called coded bit stuffing. The proposed encoder does not change the main part of input data bits, and just places these bits into the code word "as is". The remaining small part of data bits is encoded into a set of short nonzero words called separators. The separators are placed between the uncoded subblock of data. Due to the nonzero nature of the separators, the coded bit stream concatenated from data sub blocks and separators always satisfies the k constraint. The uncoded part of data bits can be arbitrary permuted without nullifying the k constraint. This property of the presented codes is important when an RLL code is used in the channel with an iterative detection scheme requiring interleaving. Simulations show that the designed codes have very good suppression of error propagation.

Timing recovery is crucial for magnetic recording systems. A conventional timing recovery loop (also known as the phase-locked loop) consists of a timing error detector (TED), a loop filter, and a voltage controlled oscillator (VCO), all of which process the samples in a sequential manner. This sequence of operations in the timing recovery loop performs well if the timing error is a small fraction of the bit interval. However, in the cycle-slip regions, the timing error is comparable to the bit interval, and the loop fails. In this paper, we represent the timing error in magnetic recording systems using a discrete Markov model that does not confine the timing error to only small fractions of the bit interval. By utilizing such a model, we derive an optimal baud-rate processing unit that does not perform tasks in sequence, but jointly. The derived unit has a similar structure as the classical first-order phase-locked loop (PLL). Simulation results show that the new detector outperforms the standard Mueller and Muller phase-locked loop. This performance gain is substantial if the timing error process is extremely noisy or if there is residual frequency-offset. For moderately low-noise timing errors without residual frequency-offset, the improvement over the Mueller and Müller phase-locked loop is just marginal.

Along with inter-symbol interference (ISI), many communication channels also suffer from timing errors. Traditionally, timing errors are meditated through dedicated timing recovery circuitry. In this paper, we extend a recently introduced BCJR-DFE receiver to accomplish timing recovery, ISI equalization and decoding concurrently using per-survivor processing technique. We show that the proposed BCJR-DFE receiver offers many advantages over other receiver structures, such as iterative timing recovery and detection.

A (full-complexity) per-survivor iterative timing recovery scheme, which jointly performs timing recovery, equalization, and error-correction decoding, was recently proposed [1] to deal with the problem of timing recovery operating at low signal-to-noise ratio. Although it outperforms other iterative timing recovery schemes, it has very high complexity. In this paper, we propose a reduced-complexity per-survivor iterative timing recovery scheme to make it implementable, in real-life applications. Simulation results indicate that for low to moderate complexity, the reduced-complexity scheme provides a better performance than the full-complexity scheme.

The paper gives a brief description of the data storage technologies that are expected to appear in the near future, and the challenges these new systems bring to designing robust read channels. We focus on perpendicular, heat assisted magnetic recording and probe storage systems.

We introduce iterative noise whitening for belief propagation (BP) based channel detectors over intersymbol interference (ISI) channels with correlated noise. Called noise predictive belief propagation (NPBP), the new scheme iteratively whitens the noise samples by modifying the edge probability computation of the BP algorithm. NPBP detectors based on finite impulse response (FIR) and infinite impulse response (IIR) prediction filters are introduced. In addition, we propose a novel prediction filter optimization method leading to a better noise whitening performance. Simulation results for both coded and uncoded systems and comparisons with maximum a posteriori (MAP) and BP detectors show that, significant improvements can be obtained.

We propose a new iterative timing recovery scheme based on per-survivor processing that jointly performs timing recovery and turbo equalization on partial response channels with error-correction codes. The scheme embeds the timing recovery process inside the Bahl, Cocke, Jelinek, and Raviv (BCJR) equalizer, using per-survivor processing. This per-survivor BCJR equalizer then iteratively exchanges soft information with an error-correction decoder. Results indicate that the proposed scheme yields a better performance than a conventional receiver that performs timing recovery and turbo equalization separately, especially when the channel encounters severe timing jitter noise. We also present evidence that suggests that the proposed scheme can correct a cycle slip much more efficiently than the others.

A conventional receiver performs timing recovery and equalization separately. Specifically, conventional timing recovery is based on a phase-locked loop that relies on the decision provided by its own symbol detector. We propose a new timing recovery scheme based on per-survivor processing (PSP) that jointly performs timing recovery and equalization for uncoded partial response channels. In the proposed scheme, each survivor of the Viterbi algorithm maintains its own estimate of the timing offset, and this estimate is updated according to the history data associated with the survivor path. As compared to conventional timing recovery at BER = 10/sup -4/, the proposed scheme can provide a 0.5 dB gain in SNR.

We propose a simulation-based method to compute the achievable information rates for general multiple-input multiple-output (MIMO) intersymbol interference (ISI) channels with inputs chosen from a finite alphabet. This method is applicable to both deterministic and stochastic channels. As an example of the stochastic MIMO ISI channels, we consider the multiantenna systems over frequency-selective fading channels, and quantify the improvement in the achievable information rates provided by the additional frequency diversity (for both ergodic and nonergodic cases). In addition, we consider the multiaccess multiantenna system and present some results on the achievable information-rate region. As for the deterministic MIMO ISI channels, we use the binary-input multitrack magnetic recording system as an example, which employs multiple write and read heads for data storage. Our results show that the multitrack recording channels have significant advantages over the single-track channels, in terms of the achievable information rates when the intertrack interference is considered. We further consider practical coding schemes over both stochastic and deterministic MIMO ISI channels, and compare their performance with the information-theoretical limits. Specifically, we demonstrate that the performance of the turbo coding/decoding scheme is only about 1.0 dB away from the information-theoretical limits at a bit-error rate of 10/sup -5/ for large interleaver lengths.

In this paper, we introduce a simulation-based method to compute the information rates of intersymbol interference (ISI) channels with signal-dependent Gaussian noise when the inputs are binary and independent identically distributed. The method extends the idea in Arnold et al. (2001), which focuses on the ISI channels with additive white Gaussian noise (AWGN). With the new method, we can compute the information rates of the Lorentzian channels with media noise that represents a suitable model for practical magnetic recording channels.

This paper evaluates two-dimensional turbo product codes based on single-parity check codes (TPC/SPC) and low-density parity check (LDPC) codes for use in digital magnetic recording systems. It is first shown that the combination of a TPC/SPC code and a precoded partial response (PR) channel results in a good distance spectrum due to the interleaving gain. Then, density evolution is used to compute the thresholds for TPC/SPC codes and LDPC codes over PR channels. Analysis shows that TPC/SPC codes have a performance close to that of LDPC codes for large codeword lengths. Simulation results for practical block lengths show that TPC/SPC codes perform as well as LDPC codes in terms of bit error rate, but possess better burst error statistics which is important in the presence of an outer Reed-Solomon code. Further, the encoding complexity of TPC/SPC codes is only linear in the codeword length and the generator matrix does not have to be stored explicitly. Based on. the results in the paper and these advantages, TPC/SPC codes seem like a viable alternative to LDPC codes.

Following the trend of turbo codes and low density parity check (LDPC) codes, single-parity turbo product codes (TPC/SPC) are being seriously considered for application in future high-density recording systems. Recent work on TPC/SPC codes has focused on ideal partial response channels with additive white Gaussian noise. This work extends the investigation to a more realistic equalized Lorentzian channel model where imperfect channel shaping, colored noise and recording density effect are taken into consideration. The effect of precoding is discussed and the interleaving gain is quantified. Simulation results of the turbo decoding system with both channel models are presented. A comprehensive evaluation is conducted, including BER performance, code rate selection, equalization targets and error statistics, which demonstrate TPC/SPC codes to be a promising candidate for future high-density recording systems.

In this paper, we study the problem of turbo coding for magnetic recording channels from a theoretical perspective. In particular we assume that the magnetic recording channel is modeled as a Lorentzian channel, and we develop performance bounds on the bit error probability of turbo codes (parallel or serial) with maximum likelihood decoding. The bound is also applicable to any (uniformly interleaved) binary linear code. This work is an extension of our recent work on performance bounds for partial response channels. The use of the bound is illustrated via some numerical examples, and comparisons based on the simulation results are provided.

We investigate the performance of low density parity check (LDPC) codes, single-parity turbo product codes (TPC/SPC) and multi-parity turbo product codes (TPC/MPC) over various partial response channels (PR) encountered in magnetic and magneto-optical (MO) recording systems, like PR4/EPR4 and PR1/PR2 channels. The codes have similarity in structures and can be decoded using simple message-passing algorithms. We show that the combination of a TPC/SPC code and a precoded PR channel results in good distance spectrum due to interleaving gain. Density evolution is then used to compute the thresholds for TPC/SPC and LDPC codes over PR channels. Through analysis and through simulations, we show the three types of codes yield comparable bit error rate performance with similar complexity, but they exhibit quite different error statistics, which in turn may result in sharp differences in block failure rate after the Reed-Solomon error correction code (RS-ECC).

Turbo codes and low-density parity check (LDPC) codes with iterative decoding have received significant research attention because of their remarkable near-capacity performance for additive white Gaussian noise (AWGN) channels. Previously, turbo code and LDPC code variants are being investigated as potential candidates for high-density magnetic recording channels suffering from low signal-to-noise ratios (SNR). We address the application of turbo codes and LDPC codes to magneto-optical (MO) recording channels. Our results focus on a variety of practical MO storage channel aspects, including storage density, partial response targets, the type of precoder used, and mark edge jitter. Instead of focusing just on bit error rates (BER), we also study the block error statistics. Our results for MO storage channels indicate that turbo codes of rate 16/17 can achieve coding gains of 3-5 dB over partial response maximum likelihood (PRML) methods for a 10/sup -4/ target BER. Simulations also show that the performance of LDPC codes for MO channels is comparable to that of turbo codes, while requiring less computational complexity. Both LDPC codes and turbo codes with iterative decoding are seen to be robust to mark edge jitter.

We develop union bounds for high-rate linear codes used for partial-response equalized channels with additive white Gaussian noise. The bounds assume uniform interleaving and are based on an approximation which is valid for high-rate linear codes. Furthermore, the derivation of the bounds assumes that maximum-likelihood decoding is employed. One particular application of the present setting is the computation of bounds for magnetic recording systems using turbo codes. The results can be considered as a generalization of the results of M. Oberg and P.H. Siegel (see Proc. Allerton Conf. Communications, Control and Computing, Sept. 1998) which develops the union bound for the dicode channel; however, our approach is completely different. We present several examples of the bounds developed together with the simulation results.

Turbo codes have been investigated for magnetic recording channels as potential candidates to succeed the current Viterbi-based partial response maximum likelihood (PRML) approaches. In contrast, relatively less attention has been devoted to the investigation of turbo decoding methods for optical data storage channels. In this paper, we present the simulation results of applying turbo decoding to an optical data storage channel. Our results focus on a variety of practical optical storage channel aspects including storage density, partial response targets, and the type of precoder used.

The remarkable performance of turbo codes for low SNRs in AWGN channels has encouraged the application of turbo codes to systems operating in different kind of channels. In this paper we consider an IS-95-based CDMA system operating in a multipath Rayleigh fading channel. We replace the convolutional encoder by a parallel and a serial turbo encoding scheme, and by a serial concatenation of an outer convolutional and an inner parallel turbo code, and instead of the Viterbi decoder we use iterative decoding based on the MAP algorithm. We perform BER and FER comparisons by varying system parameters such as the constraint length of the component convolutional codes, the interleaver lengths, and the wireless channel fading rate. The results obtained show that the concatenated schemes outperform the more complex convolutional scheme even for relatively short interleaving lengths, especially when FER is the desired figure of merit.

In this correspondence we consider the coding for multitrack magnetic recording systems. We provide analytical results related to uncoded and coded multitrack systems which constitute the basis of the code construction. We have designed matched spectral null codes for multitrack recording systems which give coding gains from 3 to 4.8 dB over uncoded systems.