Marc Andre Armand

PSK Communication with Passband Additive Symmetric α-Stable Noise

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.

On Single-Carrier Communication in Additive White Symmetric Alpha-Stable Noise

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.

Inaudible watermarking via phase manipulation of random frequencies

Watermarking technology can be beneficial in digital rights protection. However, the industry’s acceptance of the technology has been lukewarm as experts have been able to hear audible artifacts introduced during the watermarking process. In this paper, we present what we believe to be a truly inaudible solution to this problem. Our proposed watermarking technique embeds the watermark signal in the phase of an audio signal, with secrecy as to which frequency components carry the watermark bits, achieved via a pseudorandom generator. Inaudibility is realized by exploiting the human auditory system’s insensitivity to absolute phase. Further, our algorithm includes a novel mechanism for segmenting an audio signal into variable frame-lengths to provide robustness against de-synchronization attacks such as jitter and time-scaling. It uses a short-time Fourier transform to first characterize local changes in the frequency content of an audio signal, from which, pairs of frequencies satisfying specified conditions are identified, to mark the start and end of a segment. The insertion of synchronization marks adds further robustness against such attacks. Robustness against other common attacks may be further enhanced through the use of concatenated error-control codes which enable the correction of random and/or burst errors, which may be introduced during an attack.

Interleaved LDPC codes, reduced-complexity inner decoder and an iterative decoder for the Davey-MacKay construction

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.

Detection-Decoding on BPMR Channels With Written-In Error Correction and ITI Mitigation

Written-in errors and inter-track interference (ITI) are recognized as key and unique performance-limiting factors in bit-patterned media recording (BPMR). Hence, in this paper, we consider data recovery on a BPMR channel model consisting of a write channel producing data-dependent written-in errors followed by a partial response read channel with the addition of ITI. The Davey-MacKay (DM) serial concatenated coding scheme is employed to handle the written-in errors while multi-track (MT) detection and 2D-equalization are used to mitigate the inter-symbol interference (ISI) and ITI. Three detection-inner-decoding schemes are proposed to work with an outer decoder to recover the data on the BPMR channel, namely the BCJR-binary-input-inner-decoder (BCJR-BIID) algorithm, the joint detection-inner-decoder (JDD) algorithm and the BCJR-soft-input-inner-decoder (BCJR-SIID) algorithm. Media configurations leading to areal densities of 2.64 Tb/in2 and 4 Tb/in2 with comparable ISI but significantly higher ITI in the latter case are considered. Computer simulations show that at low to moderate (resp., high) signal-to-noise ratios (SNRs), BCJR-SIID (resp., BCJR-BIID) provides good performance-complexity trade-offs. It is also shown that increasing the areal density from 2.64 Tb/in2 to 4 Tb/in2 while the written-in error rates remain fixed, does not significantly affect error performance on the BPMR channel. Rather, it is the burst errors preceding and following an insertion or deletion that has a significant impact on performance.

The Davey-MacKay Coding Scheme for Channels With Dependent Insertion, Deletion, and Substitution Errors

In this paper, we propose a new channel model which introduces dependent insertion, deletion, and substitution (DIDS) errors. This channel model mimics the write channel found in bit-patterned media recording (BPMR) systems. It consists of a ternary Markov state channel and a two-state binary symmetric channel (BSC). The ternary Markov state channel produces data-dependent and paired insertion-deletion errors while the two-state BSC produces random substitution errors, as well as burst-like substitution errors in the vicinity of insertions and deletions. In addition, we modify the inner decoder of the Davey-MacKay (DM) coding scheme for the proposed channel model. For the case where there are no burst-like substitution errors, computer simulations show that our modified inner decoder (which takes into account the dependencies between synchronization errors) yields superior frame error rate (FER) performance compared to that when the symbol-level inner decoder by Briffa (which ignores the dependencies between synchronization errors) is used. As the (computational) complexity of our inner decoder increases with the length of the burst-like substitution errors, we further propose a reduced-complexity variant of our inner decoder to handle these errors. Computer simulations show that under iterative decoding, FERs below 10-5 can be achieved with the reduced-complexity variant and a code of rate 0.71, when the insertion/deletion rates are low (≤10-3) and the burst-like error lengths before and after a synchronization error are short (≤5).

List decoding of generalized Reed-Solomon codes over commutative rings

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

Multisequence shift register synthesis over commutative rings with identity with applications to decoding cyclic codes over integer residue rings

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.

A Mutual Information Approach for Comparing LLR Metrics for Iterative Decoders

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 [1] and the two-symbol-observation-interval LLR metric in [2]. The latter is shown to be superior.

Improved list decoding of generalized Reed-Solomon and alternant codes over Galois rings

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))-1rceil<sleslceiln- radic((n-w)(n-d))-1rceil with a probability determined by s, w, and the ratio of the number of nontrivial zero divisors to the number of units in the code alphabet. Focusing primarily on alternant codes over Zopf(2l), 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