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This paper introduces a new family of rank metric codes: the Low Rank Parity Check Codes (LRPC) for which we propose an efficient probabilistic LRPC decoding algorithm concatenated with convolutional code associated with an interleaver. The main idea of decoding LRPC codes is based on calculations of vector spaces over a finite field F(q). This family of codes can be seen as the equivalent of classical...
This paper proposes an interpolation based progressive algebraic Chase decoding (PACD) algorithm for Reed-Solomon (RS) codes. Based on the received information, 2η (η > 0) interpolation test-vectors are constructed. They are ordered using a reliability function, assessing their potential of yielding the intended message. The decoding is performed progressively granting priority to decode the test-vectors...
This work proposes a construction for high-rate generalized concatenated (GC) codes. The proposed codes are well suited for error correction in flash memories for high reliability data storage. The GC codes are constructed from inner nested binary Bose-Chaudhuri-Hocquenghem (BCH) codes and outer Reed-Solomon (RS) codes. For the inner codes we propose extended BCH codes, where we apply single parity-check...
This paper presents the usage of the Reed Solomon Codes as the Forward Error Correction (FEC) unit of the Hybrid Automatic Repeat Request (ARQ) methods. Parametric and flexible FPGA implementation details of such Erasure-Only RS decoders with high symbol lengths (e.g. GF(232)) have been presented. The design is based on the GF(2m) multiplier logic core operating at a single clock cycle, where the...
Galois Field arithmetic forms the basis of Reed-Solomon erasure coding techniques to protect storage or communication systems from failures. Most recent implementations of Galois Field arithmetic rely on 128-bit vector instructions, such as Intel's Streaming SIMD Extensions, which allows us to perform fast Galois Field computations. However, these implementations are not optimized for multi-threaded...
A secure and efficient key agreement method is required by Wireless Body Area Network, especially for intersensor/controller communication. The communicating parties share similar channel information at physical layer that the others cannot grasp. The physical layer information-based key generation and agreement will only pass check symbols from one side to the other side of the communication channel...
Error correcting codes are used for detection and correction of errors in digital communication system. Reed Solomon (RS) codes are part of channel coding and are based on appending of redundancy to the information message to withstand the effect of noise, interference and fading. With the development of smaller process technology, systems are becoming more sensitive to radiation. If not considered,...
Error detection and correction techniques are used to accomplish reliable data transmission through a communication channel. Redundant Residue Number System (RRNS) is a type of number system in which the arithmetic operations are carry free, so errors do not propagate from one residue to other. This paper analyses the performance of burst error correction algorithm using RRNS code and is compared...
Cloud storage is an important service of cloud computing where the data owners store their data in cloud servers so that users can access the data from cloud servers anywhere irrespective of their device and location such as thin clients with limited memory capabilities, CPU and limited bandwidth. The owners can also reduce the maintenance and burden of cloud storage. However this cloud storage is...
This paper addresses to design an R-S (Reed-Solomon) encoder and R-S decoder and verify its functionality on FPGA. An RTL (register transfer logic) code was developed for an R-S encoder that takes a 32-bit input data and produces a 48-bit output. The logic synthesis and optimization of the code was carried out using Quartus II tool. Also, an R-S decoder was developed that decodes the transmitted data.
Locally correctable codes are error-correcting codes that allow a single bit of the codeword to be recovered by looking up a small subset of the coordinates of the received word. In this work, we generalize the concept of traditional locally correcting to locally correcting multiple bits, and present a family of codes which allow multiple bits to be recovered with probability approaching 1 by visiting...
Recently, erasure codes such as Reed-Solomon (RS) code and Cauchy Reed-Solomon (CRS) code have been widely used in distributed file system to reduce the large storage overhead incurred by replication scheme. Now, there is a new erasure code called Binary Reed-Solomon (BRS) code that can achieve better performance than that of RS code, CRS code and is available to be deployed in distributed file system...
Locally correctable codes are error-correcting codes with efficient decoding schemes, which can recover any bit of a codeword by visiting a small number of locations of the codeword. Recently Kopparty et. al. [1] and Guo et. al. [2] presented multiplicity codes and lifted Reed-Solomon codes, respectively, which are two families of high-rate locally correctable codes. In this paper, we generalize the...
In this paper, a novel reversible data hiding by using Reed-Solomon (RS) code is proposed for efficient transmission in encryption image. To increase the recovery of data from encrypted image, RS codes are used to encode messages, and then the code words can be embedded into encrypted image according to encryption key. After receiving embedding the code words, the receiver firstly decrypts the encrypted...
The article discusses the use of error-correcting codes and methods of their decoding and also analysis of the use of different depths of interleaving for modeling concatenated codes.
Large Scale distributed storage systems play a vital role in maintaining data across storage locations globally. These systems use replication as the default mechanism for providing fault-tolerance. Recently, erasure codes are being used as a viable alternative to replication, since they provide the same fault-tolerance for reduced storage overhead. However, their performance is unclear in a geographically...
The partial-inverse approach is further developed to decoding interleaved Reed-Solomon codes and subfield-evaluation codes beyond half the minimum distance. The resulting decoding algorithm is new, and its decoding capability is shown to be state-of-the-art.
In this paper, an iterative soft-decision decoding algorithm is proposed for Reed-Solomon (RS) codes. The proposed decoding algorithm combines the concepts of adapting the parity-check matrix and informed dynamic scheduling. Before each iteration, the parity-check matrix is re-arranged according to the reliability of the codeword bits, meaning that the influence of the least reliable variable nodes...
Gabidulin codes can be seen as the rank-metric equivalent of Reed-Solomon codes. It was recently proven, using subspace polynomials, that Gabidulin codes cannot be list decoded beyond the so-called Johnson radius. In another result, cyclic subspace codes were constructed by inspecting the connection between subspaces and their subspace polynomials. In this paper, these subspace codes are used to prove...
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