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.

Assessment of Galileo E6B Data Demodulation Performance at High Latitudes: A Norwegian Vessel Case Study

The Galileo High Accuracy Service (HAS) is currently in its testing phase, in which actual corrections are transmitted along with standard dummy messages. The dissemination of Precise Point Positioning (PPP) corrections is performed using an innovative scheme based on a Reed–Solomon code, which allows the reconstruction of the original navigation message from a subset of received pages. This approach introduces robustness to the reception process and aims at reducing the Time-To-Retrieve Data (TTRD); that is, the time to retrieve the HAS message. This study investigated the HAS demodulation performance considering Galileo signals collected at high latitudes. In particular, a Galileo E6-capable receiver was mounted on a vessel sailing from Bergen to Kirkenes, Norway, and reaching up to 71 degrees North. The trajectory of the vessel was at the border of the Galileo HAS service area and high-latitudes impact reception conditions, potentially leading to poor satellite geometries. Three months of data from January to March 2021 were analyzed, considering several metrics including Bit Error Rate (BER), Page Error Rate (PER), and TTRD. The analysis shows that the Reed–Solomon scheme adopted for data dissemination is also effective at high-latitudes, with daily PER below one percent and mean TTRD in the order of eight seconds when three satellites are broadcasting valid HAS corrections. Lower values of the TTRD are achieved with an increased number of satellites. These values are significantly lower than the update rate of the corrections broadcast by the Galileo HAS.

On Ordinary Words of Standard Reed–Solomon Codes over Finite Fields

Reed–Solomon codes are widely used to establish a reliable channel to transmit information in digital communication which has a strong error correction capability and a variety of efficient decoding algorithm. Usually we use the maximum likelihood decoding (MLD) algorithm in the decoding process of Reed–Solomon codes. MLD algorithm relies on determining the error distance of received word. Dür, Guruswami, Wan, Li, Hong, Wu, Yue and Zhu et al. got some results on the error distance. For the Reed–Solomon code [Formula: see text], the received word [Formula: see text] is called an ordinary word of [Formula: see text] if the error distance [Formula: see text] with [Formula: see text] being the Lagrange interpolation polynomial of [Formula: see text]. We introduce a new method of studying the ordinary words. In fact, we make use of the result obtained by Y.C. Xu and S.F. Hong on the decomposition of certain polynomials over the finite field to determine all the ordinary words of the standard Reed–Solomon codes over the finite field of [Formula: see text] elements. This completely answers an open problem raised by Li and Wan in [On the subset sum problem over finite fields, Finite Fields Appl. 14 (2008) 911–929].

Blind Recognition of Parameters of Reed Solomon Code from Intercepted Erroneous Codewords

Error correcting codes are designed for reliable transmission of digital information over a noisy channel. Several papers have been published on blind identification of binary FEC codes but papers reported on the identification of non-binary error correcting codes are less. Due to its strong error correction capability, RS (Reed-Solomon) code is being used widely. So technique for blind recognition of RS code is required to analyse intercepted signal as well as for intelligent communication. This paper presents a technique for extraction of parameters of Reed-Solomon code from intercepted demodulated bitstream. The proposed algorithm is very simple and hence it is very practical for hardware implementation. Our approach has been verified using MATLAB simulation.

Implementation of Reed Solomon Code Over GF(9) and 9-Ary Symmetric Channel

Reed-Solomon and related codes have recently become very important for erasure correction in large disk arrays used in data centers. In this paper, we will implement a 3-error correcting Reed-Solomon encoder and decoder over the field GF(9) generated by the primitive polynomial D^2 + D + 2 over GF(3) and the decoding is carried out by the Berlekamp. We simulate the encoder and decoder using Monte-Carlo simulations over the 9-ary symmetric channel that outputs the correct symbol with probability (1-p), and outputs one of the other 8 possible incorrect symbols with probability p/8. Then, we compare the simulated probability of symbol error P(E) of out code with the union upper bound.

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.

Information Leakages in Code-based Masking: A Unified Quantification Approach

This paper presents a unified approach to quantifying the information leakages in the most general code-based masking schemes. Specifically, by utilizing a uniform representation, we highlight first that all code-based masking schemes’ side-channel resistance can be quantified by an all-in-one framework consisting of two easy-tocompute parameters (the dual distance and the number of conditioned codewords) from a coding-theoretic perspective. In particular, we use signal-to-noise ratio (SNR) and mutual information (MI) as two complementary metrics, where a closed-form expression of SNR and an approximation of MI are proposed by connecting both metrics to the two coding-theoretic parameters. Secondly, considering the connection between Reed-Solomon code and SSS (Shamir’s Secret Sharing) scheme, the SSS-based masking is viewed as a particular case of generalized code-based masking. Hence as a straightforward application, we evaluate the impact of public points on the side-channel security of SSS-based masking schemes, namely the polynomial masking, and enhance the SSS-based masking by choosing optimal public points for it. Interestingly, we show that given a specific security order, more shares in SSS-based masking leak more information on secrets in an information-theoretic sense. Finally, our approach provides a systematic method for optimizing the side-channel resistance of every code-based masking. More precisely, this approach enables us to select optimal linear codes (parameters) for the generalized code-based masking by choosing appropriate codes according to the two coding-theoretic parameters. Summing up, we provide a best-practice guideline for the application of code-based masking to protect cryptographic implementations.

Performance of a parallel Hamming coding in short-frame OFDM sensor's network

In this paper, we focus on the most relevant Error Correcting Codes (ECCs): the Hamming code and the Reed-Solomon code in order to meet the trade-off between the low implementation complexity and the high error correction capacity in a short-frame OFDM communication system. Moreover, we discuss and validate via simulations this trade-off between complexity (Hamming is the easiest to code) and error correction capability (Reed-Solomon being the most effective). Therefore, we have to either improve the correction capacity of the Hamming code, or decrease the complexity cost for the Reed-Solomon code. Based on this analysis, we propose a new design of parallel Hamming coding. On the one hand, we validate this new model of parallel Hamming coding with numerical results using MATLAB-Simulink tools and BERTool Application which makes easier the Bit Error Rate (BER) performance simulations. On the other hand, we implement the design of this new model on an FPGA mock-up and we show that this solution of a parallel Hamming encoder/decoder uses a few resources (LUTs) and has a higher capability of correcting when compared to the simple Hamming code.