Paul Siegel

Paul Siegel
University of California, San Diego | UCSD · Department of Electrical and Computer Engineering

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59
Publications
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1,644
Citations

Publications

Publications (59)
Article
We study the problem of designing a rate-1 block-precoder to minimize bit/symbol error rate when storing a given source on a magnetic recording channel. A block-precoder of length b-bits is defined by a permutation π on 2b blocks. We show that the problem of finding a permutation for the block-precoder that minimizes bit/symbol error rate is equiva...
Article
Full-text available
Recent work by Divsalar has shown that properly designed protograph-based low-density parity-check codes typically have minimum (Hamming) distance linearly increasing with block length. This fact rests on ensemble arguments over all possible expansions of the base protograph. However, when implementation complexity is considered, the expansions are...
Article
Spatially coupled codes have been of interest recently owing to their superior performance over memoryless binary-input channels. The performance is good both asymptotically, since the belief propagation thresholds approach the Shannon limit, as well as for finite lengths, since degree-2 variable nodes that result in high error floors can be comple...
Conference Paper
Balanced bipolar codes consist of sequences in which the symbols '-1' and '+1' appear equally often. Several generalizations to larger alphabets have been considered in literature. For example, for the q-ary alphabet {-q + 1, -q + 3, ..., q - 1}, known concepts are symbol balancing, i.e., all alphabet symbols appear equally often in each codeword,...
Conference Paper
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We investigate the reasons behind the superior performance of belief propagation decoding of non- binary LDPC codes over their binary images when the transmission occurs over the binary erasure channel. We show that although decoding over the binary image has lower complexity, it has worse performance owing to its larger number of stopping sets rel...
Article
Full-text available
Flash memory is a nonvolatile computer memory comprised of blocks of cells, wherein each cell is implemented as either NAND or NOR floating gate. NAND flash is currently the most widely used type of flash memory. In a NAND flash memory, every block of cells consists of numerous pages; rewriting even a single page requires the whole block to be eras...
Conference Paper
Full-text available
We consider terminated LDPC convolutional codes (LDPC-CC) constructed from photographs and explore the performance of these codes on correlated erasure channels including a single-burst channel (SBC) and Gilbert-Elliott channel (GEC). We consider code performance with a latency-constrained message passing decoder and the belief propagation decoder....
Conference Paper
In this paper, we explore a novel approach to evaluate the inherent UEP (unequal error protection) properties of irregular LDPC (low-density parity-check) codes over BECs (binary erasure channels). Exploiting the finite-length scaling methodology, suggested by Amraoui et. al., we introduce a scaling approach to approximate the bit erasure rates of...
Conference Paper
Despite flash memory's promise, it suffers from many idiosyncrasies such as limited durability, data integrity problems, and asymmetry in operation granularity. As architects, we aim to find ways to overcome these idiosyncrasies while exploiting flash memory's useful characteristics. To be successful, we must understand the trade-offs between the p...
Conference Paper
The read-write process in perpendicular magnetic recording channels includes a number of nonlinear effects. Nonlinear transition shift (NLTS) arising from previously written transitions is one of these. The signal distortion induced by NLTS is reduced by use of write precompensation during data recording. In this paper, we numerically evaluate the...
Article
Upper and lower bounds on the weight distribution of overextended Reed-Solomon (OERS) codes are derived, from which tight upper and lower bounds on the probability of undetected error for OERS codes are obtained for q-ary symmetric channels
Conference Paper
The ability of linear programming (LP) decoding to detect failures, and its potential for improvement by the addition of new constraints, motivates the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we show that the application of such adaptive methods can significantly reduce the complexity o...
Conference Paper
The stopping redundancy of a linear code is defined as the minimum number of rows in its parity-check matrix such that the smallest stopping sets have size equal to the minimum distance of the code. We derive new upper bounds on the stopping redundancy of maximum distance separable (MDS) codes, and show how they improve upon previously known result...
Conference Paper
We derive upper and lower bounds on the weight distribution of Over-Extended Reed-Solomon (OERS) codes. Using these bounds, we obtain tight upper and lower bounds on the probability of undetected error for OERS codes on q-ary symmetric channels.
Article
In magnetic recording, a standard code architecture consists of an outer Reed-Solomon code in concatenation with an inner parity code. The inner parity code is used to detect and correct common error events. Generally, a parity code with short block length performs better, as multiple error events within one block and, consequently, miscorrection a...
Conference Paper
Two-dimensional intersymbol interference channels are models for two-dimensional optical storage and holographic recording systems. We describe analytical bounds and simulation-output estimates for achievable rates of such channels, as well as signal processing and coding algorithms that approach these information-theoretic limits
Chapter
Theoretical bounds for maximum likelihood sequence estimation (MLSE) for intensity modulated fiber-optic links using an integrate and dump receiver structure are derived. These bounds are used to compare performance of different modulation formats. We show that while significant performance differences exist when bit-by-bit detection is used, the p...
Conference Paper
Just as the Hamming weight spectrum of a linear block code sheds light on the performance of a maximum likelihood decoder, the pseudo-weight spectrum provides insight into the performance of a linear programming decoder. Using properties of polyhedral cones, we find the pseudo-weight spectrum of some short codes. We also present two general lower b...
Conference Paper
Full-text available
The achievable information rates for multilevel coding (MLC) systems with multistage decoding (MSD) are examined on two-dimensional binary-input intersymbol interference (ISI) channels. One MSD scheme employs trellis-based detection, while another involves zero-forcing equalization and linear noise prediction. Information rates are determined by ex...
Conference Paper
Full-text available
We present bit-stuffing schemes which encode arbitrary data sequences into two-dimensional (2-D) constrained arrays. We consider the class of 2-D runlength-limited (RLL) (d, infin) constraints as well as the 'no isolated bits' (n.i.b.) constraint, both defined on the square lattice. The bit stuffing technique was previously introduced and applied t...
Conference Paper
We consider hard-decision iterative decoders for product codes over the erasure channel, which employ repeated rounds of decoding rows and columns alternatingly. We derive the exact asymptotic probability of decoding failure as a function of the error-correction capabilities of the row and column codes, the number of decoding rounds, and the channe...
Conference Paper
We derive lower bounds on the capacity of asymmetric two-dimensional (d, infin)-constraints from bounds on the output entropy of bit-stuffing encoders for general asymmetric (d, infin)-constraints on both the square lattice and the hexagonal lattice. For the (d, infin; 1, infin)-constraint on the square lattice and the (d, infin; 1, infin; 1, infin...
Conference Paper
Full-text available
Biinfinite sequences X=(x<sub>k</sub>)<sub>k∈Z</sub> over the alphabet {0,1,...,q-1}, for an arbitrary q≥2, that satisfy the following q-ary ghost pulse (qGP) constraint: for all k,l,m∈Z such that x<sub>k</sub>,x<sub>l</sub>,x<sub>m</sub> are nonzero and equal, x<sub>k+l-m</sub> is also nonzero is studied in this paper. This constraint arises in th...
Conference Paper
Full-text available
We present a near-capacity coding system for higher-order partial-response channels, consisting of an outer set of interleaved low-density parity-check codes, an inner rate-1 shaping code, and a multistage decoder. The inner shaping code, which may be noninvertible, is designed to generate an output process similar to a binary Markov process that m...
Conference Paper
This paper describes the analysis of convolutional codes on the erasure channel. We compare the maximum likelihood (ML) sequence decision and the maximum a posteriori (MAP) symbol decision for codes, which are transmitted over the erasure channel. When a codeword from a linear error correcting code with elements from the field GF is transmitted ove...
Conference Paper
An (n,k) Reed-Solomon (RS) code is used in a magnetic recording system to help reduce the word failure rate (WFR). If the channel signal-to-noise ratio (SNR) exceeds a certain value, the full power of a given RS code may be needed only on a few occasions to guarantee a target WFR. When this occurs, a parity-sharing scheme can be used to group a num...
Conference Paper
Since the discovery of turbo codes, iterative decoding has gained enormous momentum. The idea of repeatedly passing information between components of a receiver or decoder to increase the overall system performance has attracted much research effort. In this work, we present an iterative soft-decision decoding architecture for Reed-Solomon (RS) cod...
Conference Paper
Analytic expressions for the exact probability of erasure for systematic, rate- 1/2 convolutional codes used to communicate over the binary erasure channel and decoded using the soft-input, soft-output (SISO) and a posteriori probability (APP) algorithms are given. An alternative forward-backward algorithm which produces the same result as the SISO...
Conference Paper
In this paper, the uplink of an asynchronous direct sequence code division multiple access (DS-CDMA) system with multiple antennas at both the transmitter and the receiver is considered. We analyze the system performance over a spatially correlated Rayleigh fading channel with multiple access interference (MAI). Assuming perfect channel knowledge a...
Article
We design multilevel coding (MLC) and bit-interleaved coded modulation (BICM) schemes based on low-density parity-check (LDPC) codes. The analysis and optimization of the LDPC component codes for the MLC and BICM schemes are complicated because, in general, the equivalent binary-input component channels are not necessarily symmetric. To overcome th...
Article
For a discrete-time, binary-input Gaussian channel with finite intersymbol interference (ISI), we prove that reliable communication can be achieved if and only if E b =N0 > log 2=Gopt , for some constant Gopt that depends on the channel. To determine this constant, we consider the finite-state machine which represents the output sequences of the ch...
Conference Paper
We evaluate truncated union bounds on the frame error rate performance of space-time (ST) codes operating over the quasistatic fading channel and compare them to the results from computer simulation. Both ST trellis and block codes are considered. We calculate these bounds by characterizing the set of codeword differences from a general expression...
Conference Paper
Parallel message-passing detectors for partial-response channels have the property that a bit is estimated using channel symbols in a window of size W centered upon that bit. Distinct input sequences that produce the same output sequence result in undesirable failure of window decoders, but preceding can eliminate this input-to-output mapping ambig...
Conference Paper
Full-text available
In this paper, we consider the problem of determining when the capacities of distinct 1-dimensional (d,k)-constrained systems can be equal. If we let C(d,k) denote the capacity of a (d, k)-constrained system, then it is known that C(d,2d)=C(d+1,3d+1), and C(d,2d+1)=C(d+1,∞). Repeated application of these two identities also yields the chain of equa...
Conference Paper
The capacity and the symmetric information rate (SIR, when the channel inputs are i.i.d., equiprobable) of the channel are investigated. Many of the results can be further extended to multidimensional ISI channels.
Conference Paper
We compare the performance of list-type soft-decision Reed-Solomon (RS) decoding algorithms to that of classical hard-decision RS decoding on partial response (PR) channels. The two soft-decision RS decoding approaches that we consider, the list-GMD and the Koetter-Vardy (see Proc. IEEE Int. Symp. Information Theory, (Sorrento, Italy), IEEE, June 2...
Article
The performance of turbo-coded asynchronous direct sequence code division multiple access (DS-CDMA) using long and short spreading sequences is compared by both analysis and simulation. For coded systems with a conventional matched filter (MF) receiver, three analytical methods with different complexity are compared: the standard Gaussian approxima...
Article
The performance of maximum-likelihood decoding of a serial concatenation comprising a high-rate block code, convolutional code, or a turbo code, a uniform interleaver, and a partial response channel with additive white Gaussian noise is addressed. The effect of a channel precoder on the system performance is also considered. Bit- and word-error rat...
Conference Paper
We consider maximum-likelihood decoder performance in additive white Gaussian noise for the serial concatenation of an outer code comprising multiple, independent odd-parity-check codes and an inner precoded dicode partial-response channel through a random interleaver. Using a technique proposed in Oberg and Siegel (1998, 2001) we derive an approxi...
Conference Paper
We design multilevel coding (MLC) schemes with low-density parity-check (LDPC) codes as component codes at each level. We develop a method to analyze the performance of an LDPC code at any level as the codeword length goes to infinity, even if the equivalent binary-input component channels are not symmetric. By joint optimization of code rates and...
Conference Paper
We study the number of binary 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 a new algorithm for determi...
Conference Paper
An iterative receiver is proposed for a wireless communication system employing multiple transmit and receive antennas. The transmitted symbol sequences are space-time encoded. By exploiting the inherent structure in the space-time encoded data sequence, the receiver is able to significantly improve the initial estimate of the unknown channel leadi...
Article
Full-text available
Partial-response (PR) signaling 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 higher order partial-response channels, such as the “extended” class-4 channels denoted EPR4, E<sup>2</su...
Article
This paper addresses the performance of maximum-likelihood decoding of a serial concatenation comprising a high-rate convolutional code or a turbo code, a uniform interleaver, and a dicode partial-response channel. The effect of a channel precoder on the system performance is also considered. Bit- and word-error-rate estimates based upon properties...
Article
Two algorithms for characterization of input error events producing specified distance at the output of certain binary-input partial-response (PR) channels are presented. Lists of error events are tabulated for PR channels of interest in digital recording
Conference Paper
The use of turbo coding and decoding techniques in digital magnetic recording is now being given serious consideration. Major technical concerns are implementation complexity and decoding delay. In this paper, we present and analyze the performance of a simple, serial concatenation scheme comprising an outer parity check code, interleaver, and a pr...
Conference Paper
An area and computational-time efficient turbo decoder implementation on a reconfigurable processor is presented. The turbo decoder takes advantage of the latest sliding window algorithms to produce a design with minimal storage requirements as well as offering the ability to configure key system parameters via software. The parameter programmabili...
Article
Constrained codes are a kev 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 present-day applications in...
Conference Paper
Bit-stuffing constructions of binary 2-dimensional constrained arrays satisfying (d,∞) or (0,k) runlength constraints in both horizontal and vertical dimensions are described. Lower bounds on the capacity of these constrained arrays are derived
Conference Paper
Full-text available
Coding methods to enhance the performance of sequence estimators for an intersymbol interference (ISI) channel are presented. The ISI channel considered is modeled with a Lorentzian step response, and equalized to a finite-duration, discrete impulse response. The coding follows from a characterization of the dominant error events for a suboptimal s...
Article
We study via simulation the effect of different combinations of three puncturing patterns and three classes of interleavers on the performance of turbo-coded systems. The interleaver types are conventional pseudorandom, odd-even pseudo-random and modified S-random. The impact of the unequal parity-bit distribution induced by puncturing is evaluated...
Conference Paper
This paper continues the investigation of methods for computing exact bounds on the path metric differences in maximum-likelihood sequence detectors based upon the Viterbi algorithm. New upper and lower estimates for these bounds are presented and recast in terms of a collection of linear programming problems. These estimates improve upon previousl...
Conference Paper
Issues related to determining the state-space of survivor path metric differences in applications of the Viterbi algorithm are explored. In particular, the problem of characterizing the entire space of path metric differences, achievable from a given initial state, and calculating the probability density for the differences as a function of the dis...
Article
Many of the types of modulation codes designed for use in storage devices using magnetic recording are discussed. The codes are intended to minimize the negative effects of intersymbol interference. The channel model is first presented. The peak detection systems used in most commercial disk drives are described, as are the run length-limited (d,k)...
Article
A technique for determining worst case run-length-limited (RLL) code patterns for data-to-servo coupling in magnetic buried servos is presented. The problem is reduced to a general dynamic programming problem, whose solution is described. The general problem can require large amounts of computation, so a method is also developed to determine approx...
Article
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