In this correspondence, we illustrate among other things the use of the stationarity property of the set of capacity-achieving inputs in capacity calculations. In particular, as a case study, we consider a bit-patterned media recording channel model and formulate new lower and upper bounds on its capacity that yield improvements over existing results. Inspired by the observation that the new bounds are tight at low noise levels, we also characterize the capacity of this model as a series expansion in the low-noise regime. The key to these results is the realization of stationarity in the supremizing input set in the capacity formula. While the property is prevalent in capacity formulations in the ergodic-theoretic literature, we show that this realization is possible in the Shannon-theoretic framework where a channel is defined as a sequence of finite-dimensional conditional probabilities, by defining a new class of consistent stationary and ergodic channels.

This paper analyzes various receiver schemes for orthogonal frequency division multiplexing (OFDM) transmission in impulsive noise. We consider Rayleigh block-fading and model the noise process by additive white symmetric α-stable noise (AWSαSN). We begin by discussing maximum-likelihood (ML) detection performance of baseband OFDM. Though optimal, the computational cost increases exponentially with the number of carriers. Alternatively, one may evaluate soft-estimates of the transmitted symbol block and employ carrier-wise detection to lower computational complexity. We analyze such schemes under the frameworks of M-estimation and compressed sensing theory. Moving on, we highlight important rules that ensure the passband AWSαSN process is converted to a baseband form suitable for the discussed schemes. Finally, it is shown that linear passband-to-baseband conversion actually reduces the signal-to-noise ratio (SNR) at the receiver and that all these rules may be avoided by applying an estimation scheme directly on the passband samples.

In this paper we analyze design aspects of a single-carrier digital communications receiver in the presence of impulsive noise. We use the additive white symmetric α-stable noise (AWSαSN) to model the channel noise. By introducing passband sampling, efficient constellations and suitable baseband detectors, we show that the uncoded error performance of the conventional (linear) receiver can be enhanced given the real and imaginary components of the transmitted symbol are decoded separately. The performance may be improved further by sacrificing the linearity of the system. Various non-linear estimation and joint-detection schemes are discussed and their error performance analyzed. It is shown that if the receiver bandwidth is large enough, impulsive noise may be effectively countered in a single-carrier communications system.

Impulsive noise is a non-Gaussian heavy-tailed random process that is encountered in various communication scenarios. If not catered for, a single impulse will corrupt several symbols in an OFDM block. In this paper we analyze the maximum-likelihood (ML) detection error performance of uncoded OFDM. Results are presented for two different models with emphasis on binary and quadrature phase-shift keying (BPSK/QPSK) constellations. As the number of carriers increases, the error performance actually tends towards the Gaussian noise error curve irrespective of the noise impulsiveness. These results provide benchmarks to validate error performance of various schemes in impulsive noise.

The performance of conventional digital communication schemes in the presence of additive white Gaussian noise (AWGN) has been widely studied and optimized. The efficiency of these systems, however, is severely hampered if the channel noise is impulsive. Impulsive noise is non-Gaussian in nature and is modeled well by random processes based on heavy-tailed symmetric α-stable (SαS) distributions. If the noise samples are identical and mutually independent, the additive white SαS noise (AWSαSN) model is used to simulate the channel. As performance is conventionally analyzed at the baseband level, we investigate characteristics of complex baseband noise derived from passband AWSαSN. The baseband noise samples are shown to be mutually independent with identical distribution. The bivariate distribution of each complex noise sample takes on a star-like geometrical configuration. We also investigate the baseband scale parameter as a function of the noise impulsiveness and system parameters.

A doubly multistage decoder (DMD) for low-density parity-check codes over ℤ2m, m>1, which fuses the multistage decoding approaches of Armand et al. and Varnica et al., is proposed. Two variants of the DMD are considered. The first (respectively, second) performs belief-propagation (BP) [respectively, offset min-sum (OMS)] decoding in each decoding stage and is referred to as DMD - BP (respectively, DMD - OMS). For the moderate-length codes considered in this study, the computer simulations show the DMD - BP (respectively, DMD - OMS) achieving coding gains of up to 0.43 dB (respectively, 0.67 dB) over standard BP decoding at a bit error rate of 10−6 on an additive-white-Gaussian-noise channel, while requiring significantly less computational power. Remarkably, DMD - OMS outperforms DMD - BP, yet has lower computational complexity than DMD - BP. Snapshots of the log-likelihood ratio densities of the decoded bits midway through the decoding process explain the superiority of the DMD over standard BP decoding.

The conventional additive white Gaussian noise (AWGN) model adequately simulates many noisy environments that hamper the performance of practical digital communication systems. However if the channel noise is impulsive, the approximation this model provides reduces significantly. The AWGN channel may then be replaced by the more general additive white symmetric α-stable noise (AWSαSN) model. When converted to its complex baseband form, the resulting noise for the non-Gaussian AWSαSN case is radically different from its Gaussian counterpart. In this paper we investigate the properties of baseband noise for the general AWSαSN case using conventional passband-to-baseband conversion schemes. The converted noise is generally not isotropic and furthermore the real and imaginary components may be dependent. By varying certain physical parameters we may attain different non-isotropic distributions. Using the variable geometry offered by these distributions, efficient placement of signal points on the constellation map for the quadrature phase-shift keying (QPSK) scheme is proposed. It is shown that efficient placement of signal points significantly improve the uncoded error performance of the system. We plot the bit error rate (BER) and symbol error rate (SER) curves against a signal-to-noise ratio (SNR) measure for a few selected rotated versions of the QPSK scheme.

The inner decoder of the Davey-MacKay (DM) construction for combating insertions, deletions and substitution errors, has high complexity and produces bursts of output likelihoods of greatest uncertainty in the vicinity of insertions and deletions. We therefore propose (i) a lookup-table-based implementation of the inner decoder to reduce its complexity, (ii) the use of interleaved LDPC codes as outer codes in the DM construction to spread the uncertain likelihoods produced by the inner decoder over several constituent LDPC codewords. Simulation results show that the proposed lookup table approach reduces the complexity of the inner decoder considerably while a significant improvement in frame error rate (FER) performance can be obtained with small interleaving depths. Our lookup table approach culminates in an iterative decoding scheme which yields improved FER performance over its non-iterative counterparts, yet with only a modest increase in decoding complexity, when the insertion/deletion probability is small.

This Letter considers the finite-length analysis of iterative decoding of low-density parity-check codes under differential binary-phase-shift-keying (DBPSK) and differential quadrature-phase-shift-keying (DQPSK) over the noncoherent additive-white-Gaussian-noise channel. Specifically, we derive the weight of the pseudocodewords of a Tanner graph under these signaling schemes and use them to explain the difference in error performance between coded DBPSK and coded DQPSK.

Collaborative decoding of interleaved Reed-Solomon (RS) codes was first proposed by Krachkovsky in 1997. Their work has since sparked off a series of papers from various authors on the subject. In this paper, we study the merits of multisequence-shift-register-synthesis-based collaborative decoding of interleaved RS codes formed from RS codes over Galois rings, in terms of key performance measures such as the probabilty of decoding failure and word error probability. In particular, we show that when ¿ is even and large but not exceeding ¿(n-3+¿(n2-6n+1))/2¿, aq¿-ary interleaved code formed from ¿/2 parallel copies of a length-nRS code of rate greater than1-(¿+3+(2/¿))/nover a Galois ring of cardinalityq2, can be on par with its finite field counterpart formed from ¿ parallel copies of an RS code of the same length and rate overFq, in terms of the word error probabilities of their respective decoders, while incurring lower decoding complexity.

We develop an approach to compare different log-likelihood ratio (LLR) metrics for iterative soft decoding. We show that an LLR metric for a function of the received signals is a sufficient statistic to this function about the binary channel input. We also prove that when the function belongs to a set of specific mappings, the corresponding LLR metric can feed the maximal mutual information to the decoder. For decoding low density parity check codes with the belief-propagation decoder, we develop a method to estimate the minimal average number of iterations. The results are applied to compare the Gaussian metric in and the two-symbol-observation-interval LLR metric in. The latter is shown to be superior.

We propose an algorithm which incorporates Feng-Tzeng's fundamental iterative algorithm (FIA) for synthesizing multi-sequences containing unknown elements in the middle. This algorithm can be applied to decode the generalized Reed Solomon (GRS) codes whose associated syndrome sequences have unknown elements in the middle. We also show that the proposed algorithm can be used to decode folded Reed Solomon (FRS) codes constructed from any GRS code

In the above titled paper (ibid., vol. 51, no. 1, pp. 411-419, Jan 05), Lemma 6 is incorrect due to an error on the proof. Consequently, Proposition 2 is restated here.

This correspondence presents a multistage decoding approach for a free Zopfq-submodule of ZopfqNof rank K defined by a sparse (N-K)timesN parity-check matrix overZopfqwhere q=pm, p=2 and m>1. The proposed method involves the repeated application of belief propagation decoding to exploit the natural ring epimorphism ZopfqrarrZopfpl:r|rarr Sigmai=0l-1r(i)piwith kernel plZopfqfor each l, 1lesllesm, where Sigmai=0m-1r(i)piis the p-adic expansion of r. Computer simulations for codes of rate half and moderate length on an additive white Gaussian noise (AWGN) channel with various modulation schemes show that such a decoding strategy offers an additional coding gain of between 0.07-0.1 dB over a single-stage decoding approach

Sequential Monte Carlo (SMC) is a group of methods that use Monte Carlo simulation to solve online estimation problems in dynamic systems. SMC methods are traditionally built on the techniques of sequential importance sampling (SIS) and resampling. In this paper, we apply the SMC methodology to the problem of symbol detection in a differentially encoded orthogonal frequency division multiplexing (OFDM) system over a frequency selective fading channel. We first propose the periodical termination of differential phase trellis at predetermined indices. It is seen that accelerated weight degeneracy and impoverished trajectory diversity - problems that are encountered in traditional SMC methods - are mitigated. Using these observations, a novel SMC framework that circumvents resampling is then developed. The effect of varying termination periods on the performance of the non-resampling detector is investigated. We also present results which show that periodic termination helps to retard weight degeneracy. The performance of traditional and non-resampling SMC detectors for a convolutional-coded OFDM system is compared and simulation results suggest that the non-resampling detector performs better than its traditional counterpart. We also consider a low-density parity check (LDPC)-coded OFDM system and simulation results suggest the near bound performance of the proposed non-resampling SMC detector

In this paper, we propose a sequential Monte Carlo (SMC) symbol detector for differentially encoded multi-input multi-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. We first propose the periodic termination of differential phase trellis and it is seen that this method yields advantages that allow us to simplify the pilot-aided SMC detector. Specifically, the resampling step that is present in conventional SMC methods is circumvented, and the multi-dimensional distribution required for sequence imputations reduces to a simple product of one-dimensional likelihood functions and a priori probabilities that are easily obtained from the decoder. This non-resampling SMC detector is applied to both convolutional-coded and low-density parity check (LDPC)-coded MIMO-OFDM systems and simulation results suggest the promising performance of our proposed detector

In this paper, we consider the problem of symbol detection in a differentially encoded orthogonal frequency division multiplexing (OFDM) system over frequency selective fading channel. We first propose the periodical termination of differential phase trellis at predetermined indices. When the sequential Monte Carlo (SMC) methodology is applied to symbol detection in the proposed system, it is seen that accelerated weight degeneracy and impoverished trajectory diversity-problems that are encountered in conventional SMC methods-are mitigated. Furthermore, the terminated indices may also act as pilots, thus enabling pilot-aided SMC detection. Using these observations, we then propose a pilot-aided SMC detector that circumvents resampling. The effect of varying termination periods on the performance of the non-resampling detector is investigated. We also consider a low-density parity check (LDPC)-coded OFDM system and simulation results suggest the near bound performance of the proposed pilot-aided non-resampling SMC detector.

We show that the list decoding procedure of Guruswami and Sudan may be used to decode generalized Reed-Solomon (RS) codes defined over commutative rings with identity. An algorithm for performing the first of the two phases of this decoding procedure is also given. In particular, we show that for generalized RS codes over chain rings, the probability of picking an incorrect codeword from a given list can be reduced by increasing the size of the code alphabet while keeping the length and minimum (Hamming) distance of the code constant

We present a two-stage list decoder comprising an errors-only Guruswami-Sudan (GS) decoder and an errors-and-erasures GS decoder as component decoders in the first and second stage, respectively. The two stages are coupled via a post-processor which selects a codeword from the output list of the first component decoder, from which erasure locations are obtained for the second stage. When applied to a generalized Reed-Solomon (RS) code over a Galois ring R that maps into a generalized RS code of the same length n and minimum (Hamming) distance d over the corresponding residue field, the proposed decoder exploits the presence of zero divisors in R to correct s errors where w=lceiln-radic(n(n-d))-1rceill), an important class of subring subcodes of generalized RS codes over GR(2l,a), we demonstrate that the GS decoding radius w can be exceeded by a substantial margin with significant probability

We present a simple modification to the Guruswami-Sudan list decoding algorithm to exceed the decoding radius of the original algorithm. It exploits the presence of nontrivial zero divisors in the code alphabet and is applicable, but not limited to, generalized Reed-Solomon codes over Galois rings and their subring subcodes

An efficient adaptive list decoder for Reed-Solomon (RS) codes by adaptively adjusting the list size is presented. Simulations show that it performs better than the Koetter-Vardy decoder (KVD) for small list sizes, with only a marginal increase in complexity. For larger list sizes, we propose an iterative decoder which, when applied to a parallel concatenated RS code, performs significantly better than the KVD, applied to an RS code of the same rate.

We present a new algorithm for solving the multisequence shift register synthesis problem over a commutative ring R with identity. Given a finite set of R-sequences, each of length L, the complexity of our algorithm in terms of R-multiplications is O(L/sup 2/) as L /spl rarr/ /spl infin/. An important application of this algorithm is in the decoding of cyclic codes over Z/sub q/ up to the Hartmann-Tzeng bound, where q is a prime power. Characterization of the set of monic characteristic polynomials of a prescribed set of multiple syndrome sequences leads to an efficient decoding procedure, which we further extend to decode cyclic codes over Z/sub m/ where m is a product of prime powers.

We propose a new decoding procedure for Bose-Chaudhuri-Hocquenghem (BCH) and Reed-Solomon (RS) codes over Z/sub m/ where m is a product of prime powers. Our method generalizes the remainder decoding technique for RS codes originally introduced by Welch and Berlekamp and retains its key feature of not requiring the prior evaluation of syndromes. It thus represents a significant departure from other algorithms that have been proposed for decoding linear block codes over integer residue rings. Our decoding procedure involves a Welch-Berlekamp (WB)-type algorithm for solving a generalized rational interpolation problem over a commutative ring R with identity. The solution to this problem includes as a special case, the solution to the WB key equation over R which is central to our decoding procedure. A remainder decoding approach for decoding cyclic codes over Z/sub m/ up to the Hartmann-Tzeng bound is also presented.