Error Control Mechanism Based on Reed-Solomon Code for Wireless Networks

The reliability of information transmission has a significant influence on network performance, so it has attracted extensive attention from researchers. Many error control mechanisms have been designed and proposed in order to improve the reliability of transmission. However, during transmission in wireless networks, high bit error rate and burst errors often occur, which poses great challenges in the design of error control mechanisms. The existing mechanisms suffer from a problem of either poor error correction ability or waste of network resources. The primary aim of this study is to develop an error control mechanism based on Reed-Solomon (RS) codes, which encodes packets using RS codes, and a re-encoding algorithm is designed for reducing the coded packet length. The proposed error control mechanism can not only reduce the number of redundant bits in the transmission process but also improve the error correction ability as much as possible when burst errors occur. Therefore, both the error correction ability and the network utility are considered in this work. The proposed mechanism was verified by experiments using the NS2 simulator. The experimental results verified the error control ability and throughput performance of the proposed mechanism.

MIMO-Filtered OFDM System Improvement Using Modified Concatenated RS/LDPC Codes

In mobile communication systems, there are errors that will be generated in the digital signal due to fading and interference. Consequently, different techniques are used to improve the system's reliability and enhance the signal's robustness. Channel coding techniques are used to enhance the system reliability of 5G wireless communication systems . In the upcoming wireless technologies, LDPC codes are still introduced as an alternative to turbo codes. However, the error floor phenomenon is one of the biggest demerits of using LDPC code in the different communication systems that need low error rates. This paper uses RS codes with LDPC codes in a concatenated code to solve this demerit of LDPC codes. Meanwhile, a modified concatenated RS/LDPC codes are created using outer RS codes with inner LDPC codes then appended by interleaver, unlike the conventional concatenated codes that use the interleaver between both codes. Thereafter, the modified concatenated RS/LDPC codes were suggested to enhance BER performance for the f-OFDM system. The results showed that using the proposed concatenated code outperformed using single and familiar concatenated RS/LDPC code in terms of improving BER performance. Meanwhile, the proposed system achieved lower OOBE values than the conventional OFDM system. Therefore, the resulted system can be introduced as a competitor candidate for 5G wireless communication systems due to these features

Analysis of the Performance of Coded and Uncoded Mixed RF and Multihop Coherent OFDM-FSO Systems for 5G-CRAN Applications

The performance of coded and uncoded mixed single-hop RF links and multihop FSO link systems for the 5G centralized radio access network (C-RAN) is investigated in this paper using a coherent detection technique. A generalized Nakagami-m fading channel is chosen for the RF link, and the Gamma-Gamma distribution channel is chosen for the FSO link. The RF and FSO links use M-Quadrature Amplitude Modulated Orthogonal Frequency Division Multiplexing (M-QAM OFDM) modulation for the coherent detection scheme. The Meijer-G function is used to calculate outage probability (OP) and average symbol error rate (ASER) for analyzing the performance of coded and uncoded systems. Reed Solomon (RS) and Bose-Chaudhuri-Hocquenghem (BCH) codes are used in the coded system. In relays, the decode and forward (DF) method is used. For analysis, the effects of atmospheric turbulence, atmospheric loss, and pointing error are considered. The results show that the coding technique improves the system's performance. When compared to BCH codes, RS codes improve system performance more. A Monte-Carlo simulation is used to validate the analytical results.

Error Control Mechanism Based on Reed-Solomon Code for Wireless Networks

The reliability of information transmission has a significant influence on network performance, so it has attracted extensive attention from researchers. Many error control mechanisms have been designed and proposed in order to improve the reliability of transmission. However, during transmission in wireless networks, high bit error rate and burst errors often occur, which poses great challenges in the design of error control mechanisms. The existing mechanisms suffer from a problem of either poor error correction ability or waste of network resources. The primary aim of this study is to develop an error control mechanism based on Reed-Solomon (RS) codes, which encodes packets using RS codes, and a re-encoding algorithm is designed for reducing the coded packet length. The proposed error control mechanism can not only reduce the number of redundant bits in the transmission process but also improve the error correction ability as much as possible when burst errors occur. Therefore, both the error correction ability and the network utility are considered in this work. The proposed mechanism was verified through theoretic analysis and by experiments using the NS2 simulator. The experimental results verified the error control ability and throughput performance of the proposed mechanism.

Jointly Optimized Design of Distributed RS Codes by Proper Selection in Relay

This paper proposes a distributed RS coding scheme which is comprised of two different ReedSolomon (RS) codes over fast Rayleigh fading channel. Practically in any distributed coding scheme, an appropriate encoding strategy at the relay plays a vital role in achieving an optimized code at the destination. Therefore, the authors have proposed an efficient approach for proper selection of information at the relay based on subspace approach. Using this approach as the proper benchmark, another more practical selection approach with low complexity is also proposed. Monte Carlo simulations demonstrate that the distributed RS coding scheme under the two approaches can achieve nearly the same bit error rate (BER) performance. Furthermore, to jointly decode the source and relay codes at the destination, two different decoding algorithms named as naive and smart algorithms are proposed. The simulation results reveal that the advantage of smart algorithm as compared to naive one. The proposed distributed RS coding scheme with smart algorithm outperforms its non-cooperative scheme by a gain of 2.4-3.2 dB under identical conditions. Moreover, the proposed distributed RS coding scheme outperforms multiple existing distributed coding schemes, making it an excellent candidate for the future distributed coding wireless communications.

Error correction by Reed–Solomon codes using its automorphisms

The article explores the syndrome invariants of АГ-group of automorphisms of Reed–Solomon codes (RS-codes) that are a joint group of affine and cyclic permutations. The found real invariants are a set of norms of N Г-orbits that make up one or another АГ-orbit. The norms of Г-orbits are vectors with 2 1 Cδ− coordinates from the Galois field, that are determined by all kinds of pairs of components of the error syndromes. In this form, the invariants of the АГ-orbits were cumbersome and difficult to use. Therefore, their replacement by conditional partial invariants is proposed. These quasi-invariants are called norm-projections. Norm-projection uniquely identifies its АГ-orbit and therefore serves as an adequate way for formulating the error correction method by RS-codes based on АГ-orbits. The power of the АГ-orbits is estimated by the value of N2, equal to the square of the length of the RS-code. The search for error vectors in transmitted messages by a new method is reduced to parsing the АГ‑orbits, but actually their norm-projections, with the subsequent search for these errors within a particular АГ-orbit. Therefore, the proposed method works almost N2 times faster than traditional syndrome methods, operating on the basic of the “syndrome – error” principle, that boils down to parsing the entire set of error vectors until a specific vector is found.

TRANSMISSION OF SHORT MESSAGES IN SATELLITE COMMUNICATION SYSTEMS WITH PERMUTATION MODULATION AND REED-SOLOMON CODES

В статье выполнено исследование возможности создания энергетически эффективных систем связи, предназначенных для передачи коротких сообщений длиной 50...1000 бит по каналу связи, в которых применяются ансамбли сигналов с перестановочной модуляцией, а также коды Рида-Соломона. Полученные результаты показали, что рассмотренные системы связи при вероятности ошибки декодирования принятого сообщения, равной Pdec=10-6 , имеют существенный энергетический выигрыш (примерно 2,6 дБ) по сравнению с системами, в которых используются сигналы с модуляцией 2-PSK, коды с малой плотностью проверок на четность (LDPC), турбокоды и др. Кроме того, показано, что системы связи, в которых для передачи коротких сообщений применяются ансамбли сигналов, оптимальных по Шеннону, энергетически эффективнее по сравнению с системами, в которых для этого используются традиционные методы модуляции и помехоустойчивые коды. Применение оптимальных по Шеннону ансамблей позволяет существенно сократить длительность сигналов при передаче такого же количества бит, которое может быть передано по каналу связи традиционными методами. The article investigates the possibility of creating energy-efficient communication systems designed to transmit short messages 50...1000 bits long via a communication channel in which signal ensembles with permutation modulation (PM) are used, as well as Reed-Solomon (RS) codes. The results obtained showed that the considered communication systems with a probability of decoding error of the received message equal to Pdec=10-6 have a significant energy gain (approximately 2.6 dB), in comparison with systems that use signals with 2-PSK and LDPC codes, turbo codes, etc. It is shown that communication systems using Shannon-optimal signal ensembles for short message transmission are more energy efficient than systems using traditional modulation methods and noise-resistant codes. The use of Shannon-optimal ensembles can significantly reduce the duration of signals when transmitting the same number of bits that can be transmitted over the communication channel by traditional methods.

A Topological View of Reed–Solomon Codes

We studied a particular class of well known error-correcting codes known as Reed–Solomon codes. We constructed RS codes as algebraic-geometric codes from the normal rational curve. This approach allowed us to study some algebraic representations of RS codes through the study of the general linear group GL(n,q). We characterized the coefficients that appear in the decompostion of an irreducible representation of the special linear group in terms of Gromov–Witten invariants of the Hilbert scheme of points in the plane. In addition, we classified all the algebraic codes defined over the normal rational curve, thereby providing an algorithm to compute a set of generators of the ideal associated with any algebraic code constructed on the rational normal curve (NRC) over an extension Fqn of Fq.

PB: A Product-Bitmatrix Construction to Reduce the Complexity of XOR Operations of PM-MSR and PM-MBR Codes over GF 2 w

Edge computing, as an emerging computing paradigm, aims to reduce network bandwidth transmission overhead while storing and processing data on edge nodes. However, the storage strategies required for edge nodes are different from those for existing data centers. Erasure code (EC) strategies have been applied in some decentralized storage systems to ensure the privacy and security of data storage. Product-matrix (PM) regenerating codes (RGCs) as a state-of-the-art EC family are designed to minimize the repair bandwidth overhead or minimize the storage overhead. Nevertheless, the high complexity of the PM framework contains more finite-domain multiplication operations than classical ECs, which heavily consumes computational resources at the edge nodes. In this paper, a theoretical derivation of each step of the PM minimum storage regeneration (PM-MSR) and PM minimum bandwidth regeneration (PM-MBR) codes is performed and the XOR complexity over finite fields is analyzed. On this basis, a new construct called product bitmatrix (PB) is designed to reduce the complexity of XOR operations in the PM framework, and two heuristics are used to further reduce the XOR numbers of the PB-MSR and PB-MBR codes, respectively. The evaluation results show that the PB construction significantly reduces the XOR number compared to the PM-MSR, PM-MBR, Reed–Solomon (RS), and Cauchy RS codes while retaining optimal performance and reliability.