Set Of Codewords Research Articles

Diversity analysis, code design, and tight error rate lower bound for binary joint network-channel coding

Joint network-channel codes (JNCC) can improve the performance of communication in wireless networks, by combining, at the physical layer, the channel codes and the network code as an overall error-correcting code. JNCC is increasingly proposed as an alternative to a standard layered construction, such as the OSI-model. The main performance metrics for JNCCs are scalability to larger networks and error rate. The diversity order is one of the most important parameters determining the error rate. The literature on JNCC is growing, but a rigorous diversity analysis is lacking, mainly because of the many degrees of freedom in wireless networks, which makes it very hard to prove general statements on the diversity order. In this article, we consider a network with slowly varying fading point-to-point links, where all sources also act as relay and additional non-source relays may be present. We propose a general structure for JNCCs to be applied in such network. In the relay phase, each relay transmits a linear transform of a set of source codewords. Our main contributions are the proposition of an upper and lower bound on the diversity order, a scalable code design and a new lower bound on the word error rate to assess the performance of the network code. The lower bound on the diversity order is only valid for JNCCs where the relays transform only two source codewords. We then validate this analysis with an example which compares the JNCC performance to that of a standard layered construction. Our numerical results suggest that as networks grow, it is difficult to perform significantly better than a standard layered construction, both on a fundamental level, expressed by the outage probability, as on a practical level, expressed by the word error rate.

Video concept detection by audio-visual grouplets

We investigate general concept classification in unconstrained videos by joint audio-visual analysis. An audio-visual grouplet (AVG) representation is proposed based on analyzing the statistical temporal audio-visual interactions. Each AVG contains a set of audio and visual codewords that are grouped together according to their strong temporal correlations in videos, and the AVG carries unique audio-visual cues to represent the video content. By using the entire AVGs as building elements, video concepts can be more robustly classified than using traditional vocabularies with discrete audio or visual codewords. Specifically, we conduct coarse-level foreground/background separation in both audio and visual channels, and discover four types of AVGs by exploring mixed-and-matched temporal audio-visual correlations among the following factors: visual foreground, visual background, audio foreground, and audio background. All of these types of AVGs provide discriminative audio-visual patterns for classifying various semantic concepts. To effectively use the AVGs for improved concept classification, a distance metric learning algorithm is further developed. Based on the AVG structure, the algorithm uses an iterative quadratic programming formulation to learn the optimal distances between data points according to the large-margin nearest-neighbor setting. Various types of grouplet-based distances can be computed using individual AVGs, and through our distance metric learning algorithm these grouplet-based distances can be aggregated for final classification. We extensively evaluate our method over the large-scale Columbia consumer video set. Experiments demonstrate that the AVG-based audio-visual representation can achieve consistent and significant performance improvements compared wth other state-of-the-art approaches.

A novel gray image representation using overlapping rectangular NAM and extended shading approach

In this paper, inspired by the idea of overlapping rectangular region coding of binary images, we extend the SDS design, which is based on overlapping representation from binary images to gray images based on the non-symmetry and anti-packing model (NAM). A novel gray image representation is proposed by using the overlapping rectangular NAM (RNAM) and the extended Gouraud shading approach, which is called ORNAM representation. Also, we present an ORNAM representation algorithm of gray images. The encoding and the decoding of the proposed algorithm can be performed in O(n logn) time and O(n) time, respectively, where n denotes the number of pixels in a gray image. The wrong decoding problem of the hybrid matrix R for the overlapping RNAM representation of gray images is solved by using the horizontal, vertical, and isolated matrices, i.e., H, V and I, respectively, which are used to identify the vertex types. Also, we put forward four criteria of anti-packing homogeneous blocks. In addition, by redefining a codeword set for the three vertices symbols, we also propose a new coordinate data compression procedure for coding the coordinates of all non-zone elements in the three matrices H, V and I. By taking some idiomatic standard gray images in the field of image processing as typical test objects, and by comparing our proposed ORNAM representation with the conventional S-Tree Coding (STC) representation, the experimental results in this paper show that the former has higher compression ratio and less number of homogeneous blocks than the latter whereas maintaining a satisfactory image quality, and therefore it is a better method to represent gray images.

Decomposition of Modular Codes for Computing Test Sets and Graver Basis

In order to obtain the set of codewords of minimal support for codes defined over \({\mathbb{Z}_q}\), one can compute a Graver basis of the ideal associated to such codes. The main aim of this article is to reduce the complexity of the algorithm obtained by the authors in a previous work taking advantage of the powerful decomposition theory for linear codes provided by the decomposition theory of representable matroids over finite fields. In this way we identify the codes that can be written as “gluing” of codes of shorter length. If this decomposition verifies certain properties then computing the set of codewords of minimal support in each code appearing in the decomposition is equivalent to computing the set of codewords of minimal support for the original code. Moreover, these computations are independent of each other, thus they can be carried out in parallel for each component, thereby not only obtaining a reduction of the complexity of the algorithm but also decreasing the time needed to process it.

Simultaneous Codeword Optimization (SimCO) for Dictionary Update and Learning

We consider the data-driven dictionary learning problem. The goal is to seek an over-complete dictionary from which every training signal can be best approximated by a linear combination of only a few codewords. This task is often achieved by iteratively executing two operations: sparse coding and dictionary update. In the literature, there are two benchmark mechanisms to update a dictionary. The first approach, such as the MOD algorithm, is characterized by searching for the optimal codewords while fixing the sparse coefficients. In the second approach, represented by the K-SVD method, one codeword and the related sparse coefficients are simultaneously updated while all other codewords and coefficients remain unchanged. We propose a novel framework that generalizes the aforementioned two methods. The unique feature of our approach is that one can update an arbitrary set of codewords and the corresponding sparse coefficients simultaneously: when sparse coefficients are fixed, the underlying optimization problem is similar to that in the MOD algorithm; when only one codeword is selected for update, it can be proved that the proposed algorithm is equivalent to the K-SVD method; and more importantly, our method allows us to update all codewords and all sparse coefficients simultaneously, hence the term simultaneous codeword optimization (SimCO). Under the proposed framework, we design two algorithms, namely, primitive and regularized SimCO. We implement these two algorithms based on a simple gradient descent mechanism. Simulations are provided to demonstrate the performance of the proposed algorithms, as compared with two baseline algorithms MOD and K-SVD. Results show that regularized SimCO is particularly appealing in terms of both learning performance and running speed.

On $(r,\leq 2)$-locating-dominating codes in the infinite king grid

Assume that $G=(V,E)$ is an undirected graph with vertex set $V$ and edge set $E$.The ball $B_r(v)$ denotes the vertices within graphical distance $r$ from $v$.Let $I_r(F)=\bigcup$$v\in F$$(B_r(v) \cap C)$ be a set of codewords in the neighbourhoods of vertices $v\in F$.A subset $C\subseteq V$ is called an $(r,\leq l)$-locating-dominating code of type A if sets $I_r(F_1)$ and $I_r(F_2)$are distinct for all subsets $F_1,F_2\subseteq V$ where $F_1\ne F_2$, $F_1\cap C= F_2 \cap C$ and $|F_1|,|F_2| \leq l$.A subset $C\subseteq V$ is an $(r,\leq l)$-locating-dominating code of type B if the sets $I_r(F)$ are distinct for all subsets$F\subseteq V\setminus C$ with at most $l$ vertices. We study $(r,\leq l)$-locating-dominating codes in the infinite king gridwhen $r\geq 1$ and $l=2$. The infinite king grid is the graph with vertex set $\mathbb Z^2$ and edge set$\{\{(x_1,y_1),(x_2,y_2)\}||x_1-x_2|\leq 1, |y_1-y_2|\leq 1, (x_1,y_1)\ne(x_2,y_2)\}.$

Model of Overlapping Messages with Degenerate Coding

Superposition of signals in DNA molecule is a sufficiently general principle of information coding. The necessary re-quirement for such superposition is the degeneracy of the code, which allows placing different messages on the same DNA fragment. Code words that are equivalent in the informational sense (i.e., synonyms) form synonymous group and the entire set of code words is partitioned into synonymous groups. This paper is dedicated to constructing and analyzing the model of synonymous coding. We evaluate some characteristics of synonymous coding as applied to code words of length two although many definitions may be extended for words of arbitrary length.

Asynchronous code-division random access using convex optimization

Many applications in cellular systems and sensor networks involve a random subset of a large number of users asynchronously reporting activity to a base station. This paper examines the problem of multiuser detection (MUD) in random access channels for such applications. Traditional orthogonal signaling ignores the random nature of user activity in this problem and limits the total number of users to be on the order of the number of signal space dimensions. Contention-based schemes, on the other hand, suffer from delays caused by colliding transmissions and the hidden node problem. In contrast, this paper presents a novel pairing of an asynchronous non-orthogonal code-division random access scheme with a convex optimization-based MUD algorithm that overcomes the issues associated with orthogonal signaling and contention-based methods. Two key distinguishing features of the proposed MUD algorithm are that it does not require knowledge of the delay or channel state information of every user and it has polynomial-time computational complexity. The main analytical contribution of this paper is the relationship between the performance of the proposed MUD algorithm in the presence of arbitrary or random delays and two simple metrics of the set of user codewords. The study of these metrics is then focused on two specific sets of codewords, random binary codewords and specially constructed algebraic codewords, for asynchronous random access. The ensuing analysis confirms that the proposed scheme together with either of these two codeword sets significantly outperforms the orthogonal signaling-based random access in terms of the total number of users in the system.

Fast decoding of the (23, 12, 7) Golay code with four‐error‐correcting capability

ABSTRACTIn this paper, a fast and efficient decoding algorithm for correcting the (23, 12, 7) Golay code up to four errors is presented. The aim of this paper is to develop a fast syndrome‐group search method for finding the candidate codewords by utilizing the property that the syndromes of the weight‐4 error patterns are identical to that of the weight‐3 error pattern. When the set of the candidate codewords is constructed, the most likely one is determined by assessing the corresponding correlation metrics. The well‐known Chase‐II decoder, which needs to perform the hard‐decision decoder multiple times, acts as a comparison basis. Simulation results over the additive white Gaussian noise channel show that the decoding complexity of the proposed method is averagely reduced by at least 86% in terms of the decoding time. Furthermore, the successful decoding percentage of the new decoder in the case of four errors is always superior to Chase‐II decoder. At the signal‐to‐noise ratio of 0 dB, the proposed algorithm still can correct up to 97.40% weight‐4 error patterns. The overall bit error rate performance of the proposed decoder is close to that of Chase‐II decoder. It implies that the new decoder is beneficial to the practical implementation. Copyright © 2011 John Wiley & Sons, Ltd.

On MIMO Detection Under Non-Gaussian Target Scattering

In this paper, we consider a multiple-input-multiple-output (MIMO) detection problem with <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> widely spaced transmit antennas and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> widely spaced receive antennas, and we study the problem of designing the signal waveforms transmitted by each source node under non-Gaussian target scattering and temporally correlated Gaussian clutter. Two figures of merit are investigated for space-time code (STC) optimization under a semidefinite rank constraint: 1) the lower Chernoff bound (LCB) to the detection probability for fixed probability of false alarm, and 2) the mutual information (MI) between the observations available at the receive nodes and the “channel response” generated by a point-like target, assumed present tout court. Both receive and transmit power constraints are discussed. If the scattering distribution possesses some suitably defined properties of unitary invariance (see Section II-B), both MI-optimal and LCB-optimal STCs have a simple canonical structure: the same set of (clutter dependant) temporal codewords are employed at the transmit nodes, the only difference among the many solutions being the amount of power radiated by each antenna. Such a spatial power allocation critically depends upon the adopted figure of merit, the specified power constraint, and the underlying scattering model. Sufficient conditions to determine the optimal power allocation for all design criteria are provided. Asymptotic power distributions are also derived in the limit of vanishingly small and increasingly large signal-to-clutter ratios, proving that assuming Gaussian scattering at the design stage is a robust choice. A case study of relevant practical interest is examined in depth so as to compare the proposed design criteria and to assess the impact of signal non-Gaussianity on the system performances.

A Family of Asymptotically Good Binary Fingerprinting Codes

A fingerprinting code is a set of codewords that are embedded in each copy of a digital object with the purpose of making each copy unique. If the fingerprinting code is c-secure with error, then the decoding of a pirate word created by a coalition of at most c dishonest users, will expose at least one of the guilty parties with probability 1-ϵ. The Boneh-Shaw fingerprinting codes are n-secure codes with ϵB error, where n also denotes the number of authorized users. Unfortunately, the length the Boneh-Shaw codes should be of order O(n3 log(n/ϵB)), which is prohibitive for practical applications. In this paper, we prove that the Boneh-Shaw codes are (c<; n)-secure for lengths of order O(nc2 log(n/ϵB)). Moreover, in this paper it is also shown how to use these codes to construct binary fingerprinting codes of length L=O(c6 log(c/ϵ) log n), with probability of error ϵ<;ϵB and an identification algorithm of complexity poly(log n)=poly(L). These results improve in some aspects the best known schemes and with a much more simple construction.

Complexity results for identifying codes in planar graphs

AbstractLet G be a simple, undirected, connected graph with vertex set V(G) and 𝒞⊆V(G) be a set of vertices whose elements are called codewords. For v∈V(G) and r1, let us denote by Ir𝒞(v) the set of codewords c∈𝒞 such that d(v, c)r, where the distance d(v, c) is defined as the length of a shortest path between v and c. More generally, for A⊆V(G), we define , which is the set of codewords whose minimum distance to an element of A is at most r. If r and l are positive integers, 𝒞 is said to be an (r, l)‐identifying code if one has Ir𝒞(A)≠Ir𝒞(A′) whenever A and A′ are distinct subsets of V(G) with at most l elements. We consider the problem of finding the minimum size of an (r, l)‐identifying code in a given graph. It is already known that this problem is NP‐hard in the class of all graphs when l=1 and r1. We show that it is also NP‐hard in the class of planar graphs with maximum degree at most three for all (r, l) with r1 and l∈{1, 2}. This shows, in particular, that the problem of computing the minimum size of an (r, 2)‐identifying code in a given graph is NP‐hard.

Secret sharing schemes from binary linear codes

In principle, every linear code can be used to construct a secret sharing scheme. However, in general, determining the access structure of the scheme is very hard. On the other hand, finding error correcting codes that produce secret sharing schemes with efficient access structures is also difficult. In this paper, we study a set of minimal codewords for certain classes of binary linear codes, and then determine the access structure of secret sharing schemes based on these codes. Furthermore, we prove that the secret sharing schemes obtained are democratic in the sense that every participant is involved in the same number of minimal access sets.

Knuth's Balanced Codes Revisited

In 1986, Don Knuth published a very simple algorithm for constructing sets of bipolar codewords with equal numbers of ?1?s and ?-1?s, called balanced codes. Knuth's algorithm is well suited for use with large codewords. The redundancy of Knuth's balanced codes is a factor of two larger than that of a code comprising the full set of balanced codewords. In this paper, we will present results of our attempts to improve the performance of Knuth's balanced codes.

Testing Whether a Set of Code Words Satisfies a Given Set of Constraints

This paper investigates the problem of testing whether a set of code words satisfies certain biologically motivated Hamming distance constraints. The paper provides three efficient techniques to verify the code words, namely, the Enumeration, Table Lookup, and Encoding methods, with applications to the design of DNA words. The Enumeration method enumerates all combinations of positions in a word, so that all the words in a set can be compared simultaneously and the testing process is improved. The Table Lookup method constructs a data table and divide each word into sub-words to reduce the time complexity of the testing process. The Encoding method which is similar to Table Lookup method uses a linked list to store necessary information in addition. The proposed methods run in O(n) ~ O(log log n) times faster than the naive method when e=O(log n), where n is the number of code words in a set and e is the length of a word.

Very Efficient Balanced Codes

The prior art construction of sets of balanced codewords by Knuth is attractive for its simplicity and absence of look-up tables, but the redundancy of the balanced codes generated by Knuth's algorithm falls a factor of two short with respect to the minimum required. We present a new construction, which is simple, does not use look-up tables, and is less redundant than Knuth's construction. In the new construction, the user word is modified in the same way as in Knuth's construction, that is by inverting a segment of user symbols. The prefix that indicates which segment has been inverted, however, is encoded in a different, more efficient, way.

Learning natural scene categories by selective multi-scale feature extraction

Natural scene categorization from images represents a very useful task for automatic image analysis systems. In the literature, several methods have been proposed facing this issue with excellent results. Typically, features of several types are clustered so as to generate a vocabulary able to describe in a multi-faceted way the considered image collection. This vocabulary is formed by a discrete set of visual codewords whose co-occurrence and/or composition allows to classify the scene category. A common drawback of these methods is that features are usually extracted from the whole image, actually disregarding whether they derive properly from the natural scene to be classified or from foreground objects, possibly present in it, which are not peculiar for the scene. As quoted by perceptual studies, objects present in an image are not useful to natural scene categorization, indeed bringing an important source of clutter, in dependence of their size. In this paper, a novel, multi-scale, statistical approach for image representation aimed at scene categorization is presented. The method is able to select, at different levels, sets of features that represent exclusively the scene disregarding other non-characteristic, clutter, elements. The proposed procedure, based on a generative model, is then able to produce a robust representation scheme, useful for image classification. The obtained results are very convincing and prove the goodness of the approach even by just considering simple features like local color image histograms.

Cyclic DNA codes over the ring based on the deletion distance

Abstract We study the structure of cyclic DNA codes over the ring F 2 [ u ] / ( u 2 - 1 ) . We employ the deletion similarity distance on the set of codewords. A set of generators for this type of codes is found. We also study the CG -content of these type of codes and their deletion distance. Examples of cyclic DNA codes are constructed with their CG -content and their corresponding deletion distance.

Salient Remote Sensing Image Segmentation Based on Rate-Distortion Measure

The ill-defined nature of the segmentation problem makes the selection of the optimal image partition difficult. One can characterize image segmentation as an attempt to find the best possible representation of a data set using a certain number of ldquoobjects.rdquo This can be regarded as data information compression, resulting in the distortion of the original values. Data sets are well represented when the correct number of regions is chosen. The concept behind this approach is similar to the main problem of rate distortion theory: A finite set of code words is chosen to approximate the numbers or source symbols as well as possible. In our approach, the number of regions is equivalent to the number of code words. The mean of a region provides canonical representation of respective group members, and the distortion function is the mean-square error assuring a good evaluation method for image segmentation.

On the Usefulness of Fibonacci Compression Codes

Recent publications advocate the use of various variable length codes for which each codeword consists of an integral number of bytes in compression applications using large alphabets. This paper shows that another tradeoff with similar properties can be obtained by Fibonacci codes. These are fixed codeword sets, using binary representations of integers based on Fibonacci numbers of order m ≥ 2. Fibonacci codes have been used before, and this paper extends previous work presenting several novel features. In particular, the compression efficiency is analyzed and compared to that of dense codes, and various table-driven decoding routines are suggested.