Ofer Amrani

The Leech lattice and the Golay code: bounded-distance decoding and multilevel constructions

Multilevel constructions of the binary Golay code and the Leech lattice are described. Both constructions are based upon the projection of the Golay code and the Leech lattice onto the (6,3,4) hexacode over GF(4). However, unlike the previously reported constructions, the new multilevel constructions make the three levels independent by way of using a different set of coset representatives for one of the quaternary coordinates. Based upon the multilevel structure of the Golay code and the Leech lattice, efficient bounded-distance decoding algorithms are devised. The bounded-distance decoder for the binary Golay code requires at most 431 operations. As compared to 651 operations for the best known maximum-likelihood decoder. Efficient bounded-distance decoding of the Leech lattice is achieved by means of partitioning it into four cosets of Q/sub 24/, beyond the conventional partition into two H/sub 24/ cosets. The complexity of the resulting decoder is only 953 real operations on the average and 1007 operations in the worst case, as compared to about 3600 operations for the best known in maximum-likelihood decoder. It is shown that the proposed algorithms decode correctly at least up to the guaranteed error-correction radius of the maximum-likelihood decoder. Thus, the loss in coding-gain is due primarily to an increase in the effective error-coefficient, which is calculated exactly for both algorithms. Furthermore, the performance of the Leech lattice decoder on the AWGN channel is evaluated experimentally by means of a comprehensive computer simulation. The results show a loss in coding-gain of less than 0.1 dB relative to the maximum-likelihood decoder for BER ranging from 10/sup -1/ to 10/sup -7/. >

Bit loading algorithms for OFDM

Adaptive bit loading algorithms are proposed for multicarrier transmission systems. Constant power allocation is assumed over all subchannels while the (subchannel) bit error rate is unconstrained. The algorithms are computationally efficient and their performance compare favorably with the prior art

PLC systems for electric vehicles and Smart Grid applications

In this paper an extensive set of measurements, simulations and testing of a commercial modem are performed in an electric vehicle to evaluate the performance of PLC. The noise of the motor drive is measured and characterized in the time and frequency domains. Also, the noise generated by the AC/DC converter is measured and described. The symbol-error-rate performance of a multicarrier communication scheme is analyzed via simulation by employing the above modeled channels and noise.

Augmented product codes and lattices: Reed-Muller codes and Barnes-Wall lattices

This paper concerns the construction of the so-called augmented product codes and augmented product lattices. These are obtained by augmenting product codes or product lattices from certain classes thus obtaining higher dimensional codes or lattices from the same class, respectively. Certain properties of the augmented product construction are derived, and specific construction examples are given. In particular, it is shown that the Reed-Muller codes, the Golay code, the Barnes-Wall lattices, as well as the Leech lattice all have various augmented product constructions.

Contention Detection and Resolution for Multiple-Access Power-Line Communications

Contention-detection and contention-resolution procedures are presented. This procedure is not only tailored for use over the direct-current power lines in automotive applications but is also applicable for other multiple-access networks where the users cannot simultaneously transmit and receive. Bus arbitration is accomplished by each user that is randomly switching between carrier-sense and carrier-transmission modes prior to sending data. If the bus is sensed as busy during this process, then the user switches to a packet-reception mode. Typically, contention detection and contention resolution are two separate procedures. The proposed scheme effectively combines the two while maintaining a controlled probability of collision. A detailed analysis of this scheme is given, revealing that the collision probability can be made arbitrarily small for the price of slightly increased packet overhead.

Bounded-distance decoding: algorithms, decision regions, and pseudo nearest neighbors

For a code C, bounded distance decoding algorithms perform as optimal algorithms within the balls B(c), centered at the codewords c/spl isin/C, with radius equal to half the minimum Euclidean distance of the code. Thus distinct bounded-distance algorithms vary in performance due to their different behavior outside the balls B(c). We investigate this issue by analyzing the decision regions of some known (e.g., GMD) and some new bounded-distance algorithms presented in this work. In particular, we show that there are three distinct types of nearest neighbors and classify them according to their influence on the decision region. Simulation results and computer-generated images of the decision regions are provided to illustrate the analytical results for block and lattice codes on additive white Gaussian noise (AWGN) channels.

A Method for Generating Arbitrary Optical Signal Constellations Using Direct Digital Drive

A digitally operated optical quadrature-amplitude modulation (QAM) modulator based on a single multielectrode Mach-Zehnder modulator is presented. Generation and performance of 64QAM are studied in detail. Simulation results show that a single modulator with 13 electrodes, each of which is driven by either one of the voltages 0 or 1.68 vπ, provides close-to-ideal 64QAM constellation despite the inherent nonlinearity of the modulator. Moreover, employing a sufficient number of electrodes, close to ideal error performance can be obtained for any constellation order, or shape. Simulations results are demonstrated for several different square constellations: 16QAM and 256QAM, and nonsquare constellations: 32QAM and 128QAM. A brief discussion on the utilization of the proposed scheme as a predistorter is also given.

Geometrical and performance analysis of GMD and Chase decoding algorithms

The overall number of nearest neighbors in bounded distance decoding (BDD) algorithms is given by N/sub 0,eff/=N/sub 0/+N/sub BDD/. Where NBDD denotes the number of additional, non-codeword, neighbors that are generated during the (suboptimal) decoding process. We identify and enumerate the nearest neighbors associated with the original generalized minimum distance (GMD) and Chase (1972) decoding algorithms. After careful examination of the decision regions of these algorithms, we derive an approximated probability ratio between the error contribution of a noncodeword neighbor (one of N/sub BDD/ points) and a codeword nearest neighbor. For Chase algorithm 1 it is shown that the contribution to the error probability of a noncodeword nearest neighbor is a factor of 2/sup d-1/ less than the contribution of a codeword, while for Chase algorithm 2 the factor is 2/sup [d/2]-1/, d being the minimum Hamming distance of the code. For Chase algorithm 3 and GMD, a recursive procedure for calculating this ratio, which turns out to be nonexponential in d, is presented. This procedure can also be used for specifically identifying the error patterns associated with Chase algorithm 3 and GMD. Utilizing the probability ratio, we propose an improved approximated upper bound on the probability of error based on the union bound approach. Simulation results are given to demonstrate and support the analytical derivations.

Nonlinear Codes: The Product Construction

The standard product construction is discussed with respect to nonlinear codes. Thus, so-called nonlinear product codes are obtained that are better than linear product codes of similar length and code rate, and at the same time, amenable for encoding/decoding. On the other hand, it is shown that certain notorious nonlinear codes have an augmented product construction, namely, they can be constructed by taking the union of a product code and certain of its cosets. The binary Hamming codes are shown to have similar construction. A simple two-stage decoder is proposed for nonlinear product (NLP) codes. The decoder is shown to be a bounded-distance (BD) information decoder that is the nonlinear equivalent of the BD decoder employed for linear codes. A list-based maximum-likelihood decoder is also discussed.

Performance Bounds for Maximum Likelihood Detection of Single Carrier FDMA

Single Carrier FDMA (SC-FDMA) plays an important role in modern wireless communications as an alternative to OFDM mainly since it exhibits low peak-to-average power ratio. Accordingly, SC-FDMA is employed as the uplink scheme for the 3GPP long term evolution (LTE). In the presence of multipath, the SC-FDMA signal may arrive at the receiver perturbed by inter-symbol-interference, which renders the single-tap frequency-domain equalization suboptimal. Optimum maximum likelihood detection for SC-FDMA is often prohibitively complex, and hence useful mostly as a performance bound for suboptimal detection schemes. In this work, the optimum-detector performance is analyzed in detail; the analysis can be easily applied to any SC frequency-domain equalization scheme. Closed form bounds on the achievable bit error rate are provided for low and high SNR regimes in correlated and uncorrelated Rayleigh fading channels. The bounds reveal that the diversity order at high SNR is significantly smaller than in the low SNR regime. Moreover, error rate flaring behavior is demonstrated under optimum detection of SC-FDMA. The analytical results are verified by simulations.