Entanglement-assisted Reed–Solomon codes over qudits: theory and architecture

This paper presents a comprehensive analysis and implementation of various error correction coding methods, focusing on Reed-Solomon (RS) codes and Liberation codes in RAID6 systems. RS codes are emphasized for their robust error correction capabilities, making them ideal for high-reliability environments such as enterprise data centers and mission-critical systems, where the ability to correct multiple errors or data losses is crucial. In contrast, Liberation codes are noted for their superior encoding efficiency and lower computational complexity, making them well-suited for high-performance systems with stringent speed requirements. Through experimental comparisons, this study also evaluates Cauchy Reed-Solomon (CRS) codes, EVENODD codes, and Blaum-Roth (BR) codes, identifying the strengths and weaknesses of each method in various scenarios. The findings underscore the importance of selecting the appropriate coding technique based on system-specific requirements, as different use cases benefit from different error correction schemes in terms of performance and data reliability. Additionally, this research highlights the potential of these coding methods in broader distributed storage applications and discusses the trade-offs between them. Future research directions are suggested, particularly in optimizing existing codes and expanding their application in more complex and distributed storage environments.

In the field of military wireless communication, digital signals will generate bit errors due to various interferences in the process of channel transmission. In order to improve the communication quality and ensure the correctness and reliability of the communication, the method of error control is usually used for error correction. Error control often adopts the technology of error correction code, which improves the reliability of information transmission by adding redundant information to the effective information code stream. RS code is a typical error correction code with strong error correction ability, which can correct both random errors and burst errors. On this basis, this paper studies the basic rules of RS code construction, designs a new type of codec system circuit for RS (35,27) code, and finally uses hardware description language to design the encoder and decoder, implementation and simulation verification. It has been verified that the RS encoding, and decoding system is stable and reliable, has excellent performance, strong error correction ability, strong scalability, and has a broad application space.

In this chapter, we describe different forward error correction (FEC) schemes currently in use or suitable for use in optical communication systems. We start with the description of standard block codes. The state-of-the-art in optical communication systems standardized by the ITU employ concatenated Bose–Chaudhuri–Hocquenghem (BCH)/RS codes [1, 2]. The RS(255,239), in particular, has been used in a broad range of long-haul communication systems [1, 2], and it is commonly considered as the first-generation of FEC [3, 4]. The elementary FEC schemes (BCH, RS, or convolutional codes) may be combined to design more powerful FEC schemes, e.g., RS(255,239) + RS(255,233). Several classes of concatenation codes are listed in ITU-T G975.1. Different concatenation schemes, such as the concatenation of two RS codes or the concatenation of RS and convolutional codes, are commonly considered as second generation of FEC [3, 4].

Forward error correction (FEC) is a key capability in modern satellite communications that provide the system designer with the needed flexibility to comply with the different applications' requirements. Reed-Solomon (RS) codes are well known for their ability to optimize between the system power, bandwidth, data rate, and the quality of service. This paper introduces an efficient decoding scheme for decoding the RS codes adhering to the Consultative Committee for Space Data Systems (CCSDS) standards based on Justesen's construction of concatenation. To maintain the standard output size, the proposed scheme first encodes every m - 1 bits using the single-parity-check (SPC) code, while the RS code encodes K SPC codewords into N symbols that are of the same size as CCSDS standard. Decoding on the inner SPC code is based on maximum-likelihood decoding Kaneko algorithm, while for the proposed coding scheme, the reduced test-pattern Chase algorithm is adapted for decoding the outer RS code. The simulation results show the coding gains of 1.4 and 7 dB compared with the algebraic decoding of RS codes over the AWGN and Rayleigh fading channels, respectively. Moreover, the adopted reduced test-pattern Chase algorithm for decoding the RS code achieves an overall complexity reduction of 40% compared with the conventional Chase decoding algorithm.

All digital television broadcast schemes require some form of forward error correction. Trellis coded modulation and Reed-Solomon (RS) codes are two of the most commonly used error correction strategies. While RS codes have been used for a fairly long time in various applications and are well understood, use of trellis coded modulation has been restricted mostly to telephone modems. We explain the principles of trellis coded modulation and how trellis codes can be chosen as part of the error correction strategy for digital television broadcasting. A variety of coding and interleaving schemes that can be used to obtain the desired performance for compressed TV signal transmission is discussed. The nature of the terrestrial channel and the system performance requirements for a high definition television (HDTV) system are described, including a coding strategy called concatenated coding. >

In this paper, a blind reconstruction method of Bose-Chaudhuri-Hocquenghem (BCH) and Reed-Solomon (RS) codes is proposed, which aims to reconstruct the generator polynomials of BCH and RS codes from the intercepted noisy bitstream in non-cooperative environments. The previous blind reconstruction methods try to select correct (or noiseless) codewords or extract code information from the received bitstream. However, they need to have sufficiently correct codewords for successful reconstruction. Therefore, the existing methods are highly dependent on the channel conditions because a sufficient number of correct codewords should be available for achieving good reconstruction performance. To overcome such high dependency on channel conditions, the proposed blind reconstruction method performs error correction of single-error codewords through the proposed single-error correction method (SCM). Then, both the correct codewords and the corrected single-error codewords are utilized for blind reconstruction. Specifically, the correct codewords are selected based on the algebraic property of BCH and RS codes that codeword polynomials have consecutive roots. At the same time, the codewords presumably with a single error are selected and corrected based on the fact that the most of BCH and RS codeword polynomials with either a single error or double errors do not have consecutive roots. Based on this fact, SCM is devise, which selects and corrects the codewords with a single error with high probability. Finally, it is verified that the proposed blind reconstruction method shows much better reconstruction performance by using only one-tenth of the received codewords compared to the existing best methods even under harsh channel conditions.

The structure of a Digital Cellular Packet Data (CDPD) network is briefly explained with the aid of a general block diagram. The Air-Interface represents the most error-prone portion of the CDPD network. To protect user's data, CDPD employs Reed-Solomon (RS) code. RS codes and their single burst error correcting capabilities are described. A parameter that measures how efficiently the random error correcting capability of an RS code is used to correct single burst of errors is introduced. Tables of single burst error correcting capabilities of RS codes constructed over GF(64) and GF(256) are given. It is shown that in order to provide signal robustness against 2.2 millisecond of mean fade-duration-time, a (63, 47) RS code is required. The modulation scheme used in CDPD networks is required to be both bandwidth and power efficient. It is shown that GMSK with BT=0.5 satisfies all the CDPD network requirements.

A fast decoding algorithm for double error correcting Reed Solomon (RS) codes is presented. A new approach to the RS code decoding is introduced to eliminate the Chien search, to reduce substantially the root search time and hence to increase the decoding speed. It is interesting that the error locating time almost constant as the number of bits per symbol is increased. The algorithm finds suitable for microprocessor-based as well as VLSI implementations. Various RS codes are considered. Complexity, memory space and decoding time are all minimized as compared to the normal Chien search approach.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In recent years, conveying information using molecules via diffusion has attracted significant interest in micro and nanoscale applications. Yet, very little research have been conducted on the performance analysis of large-scale molecular communication (MC) systems with swarm of interfering receivers. In this type of MC system, the collective signal strength at a desired receiver can be impaired by the interference caused by other MC transmitters. The paper presents the first tractable analytical framework for the collective signal strength at a partially absorbing receiver due to a desired transmitter under the impact of a swarm of interfering transmitters in a three-dimensional (3D) large-scale MC system using stochastic geometry. We propose Reed Solomon (RS) coding as an error correction technique to combat the effects of interference caused by the multiple transmitters and the delayed molecules from the previous bits. We derive analytical expressions for the bit error probability (BEP) to evaluate the level of reliability that can be achieved by the proposed scheme. The results obtained using Monte Carlo simulations, matched extactly with the anlytical results, justifying the accuracy of the derivations. Results reveal that the RS codes are capable of providing an acceptable level of improvement in terms of BEP. Furthermore, by carefully selecting the code length, n, and the message length, k, of the RS(n, k) code, we can fine tune the BEP improvement to match the system requirements.

Forward Error Correction code (FEC) is important for Wireless Communication and Cryptography applications to perform the Error Detection and Correction (EDC) mechanisms. FEC codes are classified into two types such as Convolutional code and Block code. Various FEC codes can be used in Wireless Communication likes Viterbi code, Reed Solomon code, Golay, BCH, Multidimensional parity, Hamming code and LDPC codes. In this paper, an analysis between Reed Solomon code, Bose, Chaudhuri, and Hocquenghem (BCH) code and LDPC codes are presented. A Low Density Parity Check (LDPC) code provides low area and high speed than all other codes. Simulation is carried out by ModelSim6.3C and Synthesis is carried out by Xilinx10.1.

5G uses various types of access networks and has a high frequency spectrum. At present, there are no mobile handsets that support all spectrum ranges due to limitations of hardware and the expenses involved in the process. This challenge can be addressed with the help of Software Defined Radio (SDR). Universal Software Radio Peripheral (USRP) is a range of software-defined radios and most USRPs connect to a host computer through a high-speed link, which the host-based software uses to control the USRP hardware and transmit/receive data. In general, error occurs during data transmission through different communication channel. These errors can be corrected using Forward Error Correction (FEC) techniques. In this paper, an error correction code named as Reed-Solomon (RS) code, which is suitable for correcting burst error is presented. Further, a Simulation module in LabVIEW for RS Codes using MSK modulation scheme through AWGN channel is presented and its Bit Error Rate (BER) performance for codes such as RS (32,16), RS (127,111) and RS (255,239) are evaluated.

In this paper, error resilient stereoscopic video streaming problem is addressed. Two different forward error correction (FEC) codes namely systematic LT and RS codes are utilized to protect the stereoscopic video data against transmission errors. Initially, the stereoscopic video is categorized in 3 layers with different priorities. Then, a packetization scheme is used to increase the efficiency of error protection. A comparative analysis of RS and LT codes are provided via simulations to observe the optimum packetization and UEP strategies.

Smart building is an effective solution to address the issue of energy consumption in today's cyber-physical systems (CPSs) connected world. As an important tool to collect information from a fleet of electric appliance that installed in the building scope, a wireless sensor network is widely employed for this purpose. In this paper, we propose to incorporate forward error correction into the media access control layer of IEEE 802.15.4 standard for packets transmission, as the originally used automatic repeat request mechanism is a timing and energy consumed process that should be avoided in a noisy wireless channel of a smart building environment. Based on the developed CPS simulation platform, the bits error rate and packets error rate of convolutional codes (CCs), Reed-Solomon (RS) codes, and their concatenated codes are intensively investigated, on condition of been applied to different packet length and code rates. We show that the CCs are superior to other codes in most cases. However, the RS and CCs concatenated codes are good candidates, and the RS codes with larger symbol length are preferred for a longer packet. In this regard, future research will concentrated on non-line-of-sight wireless channel, and take the pulse interference from other devices into account.

The Internet of Everything is the ultimate level form of the Internet of Things. The result of digitizing the objects in life is a huge amount of data that needs to be stored and transmitted. This paper will briefly introduce the IoT and the current status of data processing. Different coding methodologies, Reed Solomon (RS) codes, Low-Density Parity-Check (LDPC) codes, and Low Complexity Parity Check (LCPC) codes will also be explained in detail from their encoding and decoding aspect. Then different codes are specifically analyzed for their usage scenarios in IoT data transmission and storage based on their particular characteristics. In the experimental section, different codes are compared from different perspectives. The main comparisons are made in terms of memory usage, operation time, energy consumption per bit of encoding, and error correction performance. The results of the analysis are RS code is simple but lacks error correction, the LDPC code has good error correction but is more complex, LCPC code strikes a balance between power efficiency and performance.

Reed-Solomon (RS) code is one of the most important error controlling codes in digital communications. It is especially powerful for multiple error correction, thus suitable for random and burst error correction. In this paper, we propose a lookforward architecture that can reduce the number of cycles in the longer pipeline stage, thus resulting in a more efficient use of the pipelined structure. We implemented a (255,239) RS codec chip using the lookforward architecture. Both the code length and error correcting capability of the codec chip are programmable. This chip consists of 310,000 transistors in 61 mm/sup 2/ area with a 0.8 /spl mu/m SPDM CMOS technology.