Error-Correction in Flash Memories via Codes in the Ulam Metric

We consider rank modulation codes for flash memories that allow for handling arbitrary charge-drop errors. Unlike classical rank modulation codes used for correcting errors that manifest themselves as swaps of two adjacently ranked elements, the proposed \emph{translocation rank codes} account for more general forms of errors that arise in storage systems. Translocations represent a natural extension of the notion of adjacent transpositions and as such may be analyzed using related concepts in combinatorics and rank modulation coding. Our results include derivation of the asymptotic capacity of translocation rank codes, construction techniques for asymptotically good codes, as well as simple decoding methods for one class of constructed codes. As part of our exposition, we also highlight the close connections between the new code family and permutations with short common subsequences, deletion and insertion error-correcting codes for permutations, and permutation codes in the Hamming distance

M-ary Coded Mouldation Assisted Genetic Algorithm Based Multiuser Detection for CDMA Systems

In this contribution we propose a novel M-ary Coded Modulation assisted Genetic Algorithm based Multiuser Detection (CM-GA-MUD) scheme for synchronous CDMA systems. The performance of the proposed scheme was investigated using Quadrature-Phase-Shift-Keying (QPSK), 8-level PSK (8PSK) and 16-level Quadrature Amplitude Modulation (16QAM) when communicating over AWGN and narrowband Rayleigh fading channels. When compared with the optimum MUD scheme, the GAMUD subsystem is capable of reducing the computational complexity significantly. On the other hand, the CM subsystem is capable of obtaining considerable coding gains despite being fed with sub-optimal information provided by the GA-MUD output

Answer-set programming as a new approach to event-sequence testing

In many applications, faults are triggered by events that occur in a particular order. Based on the assumption that most bugs are caused by the interaction of a low number of events, Kuhn et al. recently introduced sequence covering arrays (SCAs) as suitable designs for event sequence testing. In practice, directly applying SCAs for testing is often impaired by additional constraints, and SCAs have to be adapted to fit application-specific needs. Modifying precomputed SCAs to account for problem variations can be problematic, if not impossible, and developing dedicated algorithms is costly. In this paper, we propose answer-set programming (ASP), a well-known knowledge-representation formalism from the area of artificial intelligence based on logic programming, as a declarative paradigm for computing SCAs. Our approach allows to concisely state complex coverage criteria in an elaboration tolerant way, i.e., small variations of a problem specification require only small modifications of the ASP representation

Testing of random matrices

Let $n$ be a positive integer and $X = [x_{ij}]_{1 \leq i, j \leq n}$ be an $n \times n$\linebreak \noindent sized matrix of independent random variables having joint uniform distribution \hbox{Pr} {x_{ij} = k \hbox{for} 1 \leq k \leq n} = \frac{1}{n} \quad (1 \leq i, j \leq n) \koz. A realization $\mathcal{M} = [m_{ij}]$ of $X$ is called \textit{good}, if its each row and each column contains a permutation of the numbers $1, 2,..., n$. We present and analyse four typical algorithms which decide whether a given realization is good

On the phase transitions of graph coloring and independent sets

We study combinatorial indicators related to the characteristic phase transitions associated with coloring a graph optimally and finding a maximum independent set. In particular, we investigate the role of the acyclic orientations of the graph in the hardness of finding the graph's chromatic number and independence number. We provide empirical evidence that, along a sequence of increasingly denser random graphs, the fraction of acyclic orientations that are `shortest' peaks when the chromatic number increases, and that such maxima tend to coincide with locally easiest instances of the problem. Similar evidence is provided concerning the `widest' acyclic orientations and the independence number

Interleaving schemes for multidimensional cluster errors

We present two-dimensional and three-dimensional interleaving techniques for correcting two- and three-dimensional bursts (or clusters) of errors, where a cluster of errors is characterized by its area or volume. Correction of multidimensional error clusters is required in holographic storage, an emerging application of considerable importance. Our main contribution is the construction of efficient two-dimensional and three-dimensional interleaving schemes. The proposed schemes are based on t-interleaved arrays of integers, defined by the property that every connected component of area or volume t consists of distinct integers. In the two-dimensional case, our constructions are optimal: they have the lowest possible interleaving degree. That is, the resulting t-interleaved arrays contain the smallest possible number of distinct integers, hence minimizing the number of codewords required in an interleaving scheme. In general, we observe that the interleaving problem can be interpreted as a graph-coloring problem, and introduce the useful special class of lattice interleavers. We employ a result of Minkowski, dating back to 1904, to establish both upper and lower bounds on the interleaving degree of lattice interleavers in three dimensions. For the case t≡0 mod 6, the upper and lower bounds coincide, and the Minkowski lattice directly yields an optimal lattice interleaver. For t≠0 mod 6, we construct efficient lattice interleavers using approximations of the Minkowski lattice

Optimization of bit interleaved coded modulation using genetic algorithms

Modern wireless communication systems must be optimized with respect to both bandwidth efficiency and energy efficiency. A common approach to achieve these goals is to use multi-level modulation such as quadrature-amplitude modulation (QAM) for bandwidth efficiency and an error-control code for energy efficiency. In benign additive white Gaussian noise (AWGN) channels, Ungerboeck proposed trellis-coded modulation (TCM), which combines modulation and coding into a joint operation. However, in fading channels, it is important to maximize diversity. As shown by Zehavi, diversity is maximized by performing coding and modulation separately and interleaving bits that are passed from the encoder to the modulator. Such systems are termed BICM for bit-interleaved coded modulation. Later, Li and Ritcey proposed a method for improving the performance of BICM systems by iteratively passing information between the demodulator and decoder. Such systems are termed BICM-ID , for BICM with Iterative Decoding. The bit error rate (BER) curve of a typical BICM-ID system is characterized by a steeply sloping waterfall region followed by an error floor with a gradual slope.;This thesis is focused on optimizing BICM-ID systems in the error floor region. The problem of minimizing the error bound is formulated as an instance of the Quadratic Assignment Problem (QAP) and solved using a genetic algorithm. First, an optimization is performed by fixing the modulation and varying the bit-to-symbol mapping. This approach provides the lowest possible error floor for a BICM-ID system using standard QAM and phase-shift keying (PSK) modulations. Next, the optimization is performed by varying not only the bit-to-symbol mapping, but also the location of the signal points within the two-dimensional constellation. This provides an error floor that is lower than that achieved with the best QAM and PSK systems, although at the cost of a delayed waterfall region