Peter Farkas

Applications of Complete Complementary Codes and Propositions for Future Research Areas of these Codes

Abstract Complete complementary codes represent special group of codes with unique properties, which were not detected for any other codes. These codes found a wide application in several science areas with the broadest application possibilities in telecommunications. This review paper analyses the applications of these codes proposed so far and aims to propose not sufficiently explored and new areas for further research endeavors.

Hybrid ARQ error control for broadcast or multicast in wireless networks

In this paper, new error control techniques are introduced for wireless networks with broadcasting or multicasting the information from one source to many sinks. They are compared with the standard selective repeat ARQ strategy. Reed-Solomon code is exploited in these techniques. Simulation results are presented, which show that the quantity of data to be retransmitted can be significantly decreased using these new methods.

One hybrid ARQ for broadcasting or multicasting in wireless erasure channel

In this paper, we introduce a new hybrid ARQ technique for broadcasting or multicasting in erasure channel. The system is tested according to the objective criteria—quantity of information sent by the source, loses, and number of negative acknowledgments (NACKs) sent by the receiver nodes (end nodes). We compare our proposed method with automatic repeat request (ARQ), hybrid ARQ II (HARQ II), and also with a forward error correction (FEC) transmission technique based on Reed Solomon code (RS). The main focus of the presented HARQ is to reduce the quantity of redundant information sent by the source as well as the number of NACKs sent by the receivers, maintaining the condition that all the information is being recovered successfully by the receivers.

Localized algorithm for border nodes detection in WSNs

The routing possesses a serious challenge in ad-hoc wireless sensor networks. In this paper, we focus on so-called self-organizing coordinate systems, which are perceived as the current state of the art in this area. More specifically, we focus on providing of a solid starting point by a detection of nodes located on a networks border. Our intention is to limit the number of nodes involved in this process in order to decrease their energy consumption. Thus, every node requires only locally available data to detect whether it is located on the networks border. We achieved this by fragmenting the network into smaller segments called packs. Then, an analysis of their mutual relations allows to identifying nodes on the networks border. We study three significantly different scenarios, offering various applications in the routing process. Moreover, a slight modification of the algorithm allows to find the center node of the network.

Fast Parallel Weighted Bit Flipping decoding algorithm for LDPC codes

In this paper a fast version of the Parallel Weighted Bit Flipping LDPC decoding algorithm (PWBF) is presented. The idea, which allowed decreasing the computational complexity of the PWBF method, is based on the observation that in dependency on signal to noise ratio, many of the received bits in the codeword of LDPC code could be without error. The augmented algorithm makes tests based on syndromes and symbol involvement in parity checks, which are given by the factor graph corresponding to the chosen LDPC code in order to define so called guaranteed bits. These guaranteed bits do not participate in the decoding calculations further. Simulation results are presented, which show that there is not visible any significant performance deterioration by application of this method and that the approximate speed up of the decoding for the tested codes is about 25% on the selected hardware in comparison with the known PWBF.

Ambiguity function of two-dimensional orthogonal complete complementary codes

This paper presents a possible utilization of Two-Dimensional Complete Complentary Codes (2D OCCC) in radar technologies. The aim is to evaluate the ambiguity function and cross-ambiguity function of phase modulated signals based on the second family of 2D OCCC. Signal is generated by modulation technique known as Orthogonal Frequency Division Multiplexing (OFDM). Complementarity of the codes is achieved by idealized scenario in which independent transmission of the corresponding sequence is utilized. The final ambiguity function is computed as the sum of partial ambiguity functions of each element. Results of the numerical computation are presented and evaluated. It is shown that the ambiguity function yields zero values for every time shift and every Doppler shift outside the duration of the first chip. The only drawback is a presence of zero lattice values along the Doppler shift axis. It is also shown that the observed Peak-to-Sidelobe Ratio (PSR) rapidly increases with the rising order of 2D OCCC.

Hard decision decoding of single parity turbo product code with N-level quantization

In this paper we propose an iterative hard decision decoding algorithm with N-level quantization for multidimensional turbo product codes composed of single parity codes. The paper introduces the idea of adjusting original iterative HIHO decoding algorithm to keep the same decoder complexity, but approaching SISO decoder performance. Performance for single parity product codes and various quantization levels in an additive white Gaussian noise channel for different single parity turbo codes is presented.

Construction of Error Control Run Length Limited Codes Exploiting Some Parity Matrix Properties

Abstract Error control codes (ECC) as well as translation codes (TC) are used today in many different systems such as computer storages, communications systems and consumer electronic devices. ECC introduce redundancy into the encoded digital sequence in order to decrease the number of errors at output of its decoder [1]. TC introduce redundancy, in order to translate any digital sequence at the input of TC encoder to such output sequence, which fulfills constrains deduced from practical requirements. It is possible to construct codes, which have both of these properties, so called Transcontrol codes or their subclass error control run length limited (ECRLL) codes. In this manuscript a new approach to construction of EC-RLL codes is presented. The new construction is based on some parity check matrix properties of a linear binary block code from which the new EC-RLL code is obtained.

An algorithm for central point estimation in WSNs

Wireless sensor networks possess many challenges. One of the most significant is routing. In this paper, we focus on so-called Self-organizing Coordinate Systems, which are perceived as the current state of the art. Protocols included in this class are intended to create a virtual coordinate system within the network, applying principles of geographical routing. We aim to find a solid starting point for virtual coordinate assignment in a random network with no location data available. In our previous work, we presented a localized algorithm which is able to derive basic location information from the nodes connectivity. In this paper, we extend this algorithm to estimate the networks central point.

On run-length limited error control codes constructed from binary product codes

Abstract In this paper it is presented that run-length limited error control codes could be constructed from any two or more- dimensional binary product codes as long as at least one of the one-dimensional binary component codes is or can be converted to a run-length limited error control code. The advantages of this construction are as follows: It does not require any additional redundancy except that which is already contained in the original error control code and that the encoding and decoding procedure used for the underlying error control code do not to be changed