Error-event detection codes for partial response channels

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.

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.

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.

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.

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.

In this work, anew approach of designing channel codes for partial band interference channels based on hidden puncturing is introduced that is not requiring explicit estimation of the interferer. We investigate the performance of specially designed rate 1/2 Viterbi decoding of convolutional codes and rate 1/2 turbo codes in an example scenario with partial band FM interference. We show by means of simulations that for Gaussian as well as for a variety of multipath fading profiles, a significant channel coding gain compared to a conventional system can be achieved. Thereby the performance of optimal combining, that is requiring optimal estimation of the interferer, can be approached very closely in various scenarios.

Abstract. Life tables were constructed for solitary and coexisting populations of univoltine Fiorinia externa Ferris and bivoltine Tsugaspidiotus tsugae (Marlatt) (Homoptera: Diaspididae), two exotic scale pests of eastern hemlock, Tsuga canadensis Carriere, in the northeastern United States. Solitary and coexisting populations of F. externa had similar survivorship and population growth rates resulting in an annual increase in density of 7–16%. Survivorship of solitary and coexisting populations of T. tsugae also was similar, but growth rates differed substantially. While solitary populations increased their density by 68% annually, populations coexisting with F. extema were reduced 74% each year. The annual reduction in T. tsugae density where it coexists with F. externa was due in part to interspecific competition which resulted in higher mortality to nymphs from dispersal and starvation and in lower fecundity of adult females relative to solitary populations. A host shift by the parasitoid, Aspidiotiphagus citrinus (Crawford) (Hymenoptera: Aphenlinidae) from F. externa to T. tsugae in autumn also accounted for 71% of the annual decrease in T. tsugae numbers. Therefore, F. externa adversely affects the growth of T. tsugae populations not only because of its superior competitive ability but also because adult para‐sitoids which emerge from it subsequently attack nymphs of T. tsugae in autumn. Parasitism and starvation of nymphs resulting from competition were the key mortality factors in the population dynamics of these exotic hemlock scales.

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.

In signal processing for high density magnetic recording systems, it is important to combine a signal detection method and an error correction scheme. Error correcting codes for magnetic recording channels are required to be easily implemented and to have high code rates. High dimensional parity check codes with high code rates satisfy these requirements. We show the error correcting performance of the high dimensional parity check codes with high code rates when we apply them to PR channels. We also show that the integrated interleaving ECC technique is useful for a PR channel.

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.

Magnetic Information Storage Technology

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.

Matched Convolutional Codes For (1+D) Partial Response Channels

New magnetic recording technologies such as bit-patterned media recording (BPMR), heat (or microwave) assisted magnetic recording (HAMR) and shingled writing (SW)/two-dimensional magnetic recording (TDMR) have been proposed to push the storage density of future hard disks beyond 1Tb/in2. However, at such high recording density, many new challenges from the magnetic recording medium, read/write head as well as writing and reading channels arise. These challenges hinder the realization of Tb/in2 hard disks and should be addressed. In this paper, we review these major challenges from a communication theory perspective, and propose ways to mitigate the channel impairments by using low-complexity two-dimensional (2D) channel detection, new low-density parity-check (LDPC) code design paradigm, as well as re-synchronizable coding schemes.

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.