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21
Codes for Digital Recorders
 IEEE TRANS. INFORM. THEORY
, 1998
"... Constrained codes are a key component in the digital recording devices that have become ubiquitous in computer data storage and electronic entertainment applications. This paper surveys the theory and practice of constrained coding, tracing the evolution of the subject from its origins in Shannon&ap ..."
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Cited by 84 (16 self)
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Constrained codes are a key component in the digital recording devices that have become ubiquitous in computer data storage and electronic entertainment applications. This paper surveys the theory and practice of constrained coding, tracing the evolution of the subject from its origins in Shannon's classic 1948 paper to presentday applications in highdensity digital recorders. Open problems and future research directions are also addressed.
Binary intersymbol interference channels: Gallager codes, density evolution and code performance bounds
 IEEE TRANS. INFORM. THEORY
, 2003
"... We study the limits of performance of Gallager codes (lowdensity paritycheck (LDPC) codes) over binary linear intersymbol interference (ISI) channels with additive white Gaussian noise (AWGN). Using the graph representations of the channel, the code, and the sum–product messagepassing detector/d ..."
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Cited by 68 (8 self)
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We study the limits of performance of Gallager codes (lowdensity paritycheck (LDPC) codes) over binary linear intersymbol interference (ISI) channels with additive white Gaussian noise (AWGN). Using the graph representations of the channel, the code, and the sum–product messagepassing detector/decoder, we prove two error concentration theorems. Our proofs expand on previous work by handling complications introduced by the channel memory. We circumvent these problems by considering not just linear Gallager codes but also their cosets and by distinguishing between different types of message flow neighborhoods depending on the actual transmitted symbols. We compute the noise tolerance threshold using a suitably developed density evolution algorithm and verify, by simulation, that the thresholds represent accurate predictions of the performance of the iterative sum–product algorithm for finite (but large) block lengths. We also demonstrate that for high rates, the thresholds are very close to the theoretical limit of performance for Gallager codes over ISI channels. If g denotes the capacity of a binary ISI channel and if g � � � denotes the maximal achievable mutual information rate when the channel inputs are independent and identically distributed (i.i.d.) binary random variables @g � � � gA, we prove that the maximum information rate achievable by the sum–product decoder of a Gallager (coset) code is upperbounded by g � � �. The last topic investigated is the performance limit of the decoder if the trellis portion of the sum–product algorithm is executed only once; this demonstrates the potential for trading off the computational requirements and the performance of the decoder.
New precoding for intersymbol interference cancellation using nonmaximally decimated multirate filterbanks with ideal FIR equalizers
 Systems and Filter Banks (Englewood Cliffs, NJ: PrenticeHall
, 1997
"... Abstract—In this paper, we propose a new precoding method for intersymbol interference (ISI) cancellation by using nonmaximally decimated multirate filterbanks. Unlike the existing precoding methods, such as the TH and trellis precodings, the new precoding i) may be independent of the ISI channel; i ..."
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Cited by 48 (3 self)
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Abstract—In this paper, we propose a new precoding method for intersymbol interference (ISI) cancellation by using nonmaximally decimated multirate filterbanks. Unlike the existing precoding methods, such as the TH and trellis precodings, the new precoding i) may be independent of the ISI channel; ii) is linear and does not have to implement any modulo operation; iii) gives the ideal FIR equalization at the receiver for any FIR ISI channel including spectralnull channels; iv) expands the transmission bandwidth in a minimum amount. The precoding is built on nonmaximally decimated multirate filterbanks. Based on multirate filterbank theory, we present a necessary and sufficient condition on an FIR ISI transfer function in terms of its zero set such that there is a linear FIR N 2 K precoder so that an ideal FIR equalizer exists, where the integers K and N are arbitrarily fixed. The condition is easy to check. As a consequence of the condition, for any given FIR ISI transfer function (not identically 0), there always exist such linear FIR precoders. Moreover, for almost all given FIR ISI transfer functions, there exist linear FIR precoders with size N 2 (N 0 1), i.e., the bandwidth is expanded by 1=N. In addition to the conditions on the ISI transfer functions, a method for the design of the linear FIR precoders and the ideal FIR equalizers is also given. Numerical examples are presented to illustrate the theory. I.
On Codes That Avoid Specified Differences
 IEEE Transactions on Information Theory
, 2001
"... Certain magnetic recording applications call for a large number of sequences whose differences do not include certain disallowed binary patterns. We show that the number of such sequences increases exponentially with their length and that the exponent, or capacity, is the logarithm of the joint spec ..."
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Cited by 32 (2 self)
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Certain magnetic recording applications call for a large number of sequences whose differences do not include certain disallowed binary patterns. We show that the number of such sequences increases exponentially with their length and that the exponent, or capacity, is the logarithm of the joint spectral radius of an appropriately defined set of matrices. We derive a new algorithm for determining the joint spectral radius of sets of nonnegative matrices and combine it with existing algorithms to determine the capacity of several sets of disallowed differences that arise in practice.
Matched information rate codes for partial response channels
 IEEE TRANS. INFORM. THEORY
, 2005
"... In this paper we design capacityapproaching codes for partial response channels. The codes are constructed as concatenations of inner trellis codes and outer lowdensity paritycheck (LDPC) codes. Unlike previous constructions of trellis codes for partial response channels, we disregard any algebra ..."
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Cited by 16 (3 self)
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In this paper we design capacityapproaching codes for partial response channels. The codes are constructed as concatenations of inner trellis codes and outer lowdensity paritycheck (LDPC) codes. Unlike previous constructions of trellis codes for partial response channels, we disregard any algebraic properties (e.g., the minimum distance or the runlength limit) in our design of the trellis code. Our design is purely probabilistic in that we construct the inner trellis code to mimic the transition probabilities of a Markov process that achieves a high (capacityapproaching) information rate. Hence, we name it a matched information rate (MIR) design. We provide a set of 5 design rules for constructions of capacityapproaching MIR inner trellis codes. We optimize the outer LDPC code using density evolution tools specially modified to fit the superchannel consisting of the inner MIR trellis code concatenated with the partial response channel. Using this strategy, we design degree sequences of irregular LDPC codes whose noise tolerance thresholds are only fractions of a decibel away from the capacity. Examples of code constructions are shown for channels both with and without spectral nulls.
Constrained Coding for Binary Channels with High Intersymbol Interference
 IEEE TRANS. INFORM. THEORY
, 1999
"... Partialresponse (PR) signalling is used to model communications channels with intersymbol interference (ISI) such as the magnetic recording channel and the copper wire channel for digital subscriber lines. Coding for improving noise immunity in higherorder partial response channels, such as the &q ..."
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Cited by 16 (8 self)
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Partialresponse (PR) signalling is used to model communications channels with intersymbol interference (ISI) such as the magnetic recording channel and the copper wire channel for digital subscriber lines. Coding for improving noise immunity in higherorder partial response channels, such as the "extended" class4 channels denoted EPR4, E 2 PR4, E 3 PR4, has become an important subject as the linear densities in magnetic recording approach those at which these partialresponse channels are the best models of real channels. In this paper, we consider partialresponse channels for which ISI is so severe that the channels fail to achieve the matchedfilterbound (MFB) for symbol error rate, assuming maximum likelihood decoding. We show that their performance can be improved to the MFB by high rate codes based on constrained systems, some of which may even simplify the Viterbi detectors relative to the uncoded channels. We present several examples of highrate constrained codes for E ...
A Modified Concatenated Coding Scheme, with Applications to Magnetic Data Storage
 IEEE Trans. Inform. Theory
, 1997
"... When block modulation codes are concatenated with an errorcorrection code (ECC) in the standard way, the use of long block lengths results in errorpropagation. This paper analyzes the performance of modified concatenation, which involves reversing the order of modulation and ECC. This modified ..."
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Cited by 14 (3 self)
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When block modulation codes are concatenated with an errorcorrection code (ECC) in the standard way, the use of long block lengths results in errorpropagation. This paper analyzes the performance of modified concatenation, which involves reversing the order of modulation and ECC. This modified scheme reduces error propagation, provides greater flexibility in the choice of parameters, and facilitates softdecision decoding, with little or no loss in transmission rate. In particular, examples are presented which show how this technique can allow fewer interleaves per sector in hard disk drives, and permit the use of sophisticated block modulation codes which are better suited to the channel. Index terms: concatenated codes, ReedSolomon codes, modulation codes, magnetic data storage 1 Introduction This paper is concerned with the interaction between the modulation code and the errorcorrecting code (ECC). The idea of modulation is to ensure that the sequence of bits transm...
Bounds On The Rate Of Codes Which Forbid Specified Difference Sequences
 In Proc. 1999 IEEE Global Telecommun. Conf. (GLOBECOM ’99
, 1999
"... Certain magnetic recording applications call for a large number of sequences whose differences do not include certain disallowed patterns. We show that the number of such sequences increases exponentially with their length and that the exponent, or capacity, is the logarithm of the joint spectral ra ..."
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Cited by 7 (0 self)
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Certain magnetic recording applications call for a large number of sequences whose differences do not include certain disallowed patterns. We show that the number of such sequences increases exponentially with their length and that the exponent, or capacity, is the logarithm of the joint spectral radius of an appropriately defined set of matrices. We derive new algorithms for determining the joint spectral radius of sets of nonnegative matrices and combine them with existing algorithms to determine the capacity of several sets of disallowed differences that arise in practice.
Filterbank precoders for blind equalization: polynomial ambiguity resistant precoders (PARP
 IEEE Trans. Circuits and Systems, I
, 2001
"... Abstract—Filterbank precoding in the intersymbol interference (ISI) mitigation has recently attracted much attention. Two main areas of such research have been explored. One of them is on filterbank precoding when the ISI channel is known to both the transmitter and the receiver, while the other is ..."
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Cited by 6 (0 self)
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Abstract—Filterbank precoding in the intersymbol interference (ISI) mitigation has recently attracted much attention. Two main areas of such research have been explored. One of them is on filterbank precoding when the ISI channel is known to both the transmitter and the receiver, while the other is on filterbank precoding when the ISI channel is not known to the transmitter or the receiver. This paper is in the second area and the aim is twofold. We first summarize some recent results on ambiguity resistant filterbank precoders for the ISI mitigation when the ISI channel is not known at the transmitter or the receiver, i.e., for blind equalization. We then present some new results on the construction and characterization of such precoders. The theory presented in this paper applies to both single antenna (SISO) systems and multiple antenna (MIMO) systems as space–time precoding. Index Terms—Blind equalization, filterbank precoding, intersymbol interference mitigation, polynomial ambiguity resistant precoders, space–time precoding. I.
Highorder spectralnull codes: Constructions and bounds
 IEEE Trans. Inform. Theory
, 1989
"... AbstractLet Y(n, k) denote the set of all words of length n over the alphabet { + 1, 11, having a kth order spectralnull at zero frequency. A subset of Y’(n,k) is a spectralnull code of length n and order k. Upper and lower bounds on the cardinality of 9(n, k) are derived. In particular we prove ..."
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Cited by 4 (1 self)
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AbstractLet Y(n, k) denote the set of all words of length n over the alphabet { + 1, 11, having a kth order spectralnull at zero frequency. A subset of Y’(n,k) is a spectralnull code of length n and order k. Upper and lower bounds on the cardinality of 9(n, k) are derived. In particular we prove that (k 1) log, (n/k) I n log, lY(n, k)l I log, n) for infinitely many values of n. On the other hand, we show that Y (n, k) is empty unless n is divisible by 2m, where m = [log,k] + 1. Furthermore, bounds on the minimum Hamming distance d of Y(n,k) are provided, showing that 2k 5 d I k(k 1) + 2 for infinitely many n. We also investigate the minimum number of sign changes in a word x EY’(n, k) and provide an equivalent definition of Y(n,k) in terms of the positions of these sign changes. An efficient algorithm for encoding arbitrary information sequences into a secondorder spectralnull code of redundancy 3 log, n + O(log log n) is presented. Furthermore, we prove that the first nonzero moment of any word in 9’(n,k) is divisible by k! and then show how to construct a word with a spectral null of order k whose first nonzero moment is any even multiple of k!. This leads to an encoding scheme for spectralnull codes of length n and any fixed order k, with rate approaching unity as n W. Index TermsInputconstrained spectral encoders. channels, spectralnull codes, I.