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Desenvolvimento em linguagem de descrição de hardware de codificador e decodificador Reed-Solomon
Get PDFDissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia Elétrica, Florianópolis, 2014.Atualmente, diversos sistemas de comunicação demandam grandes volumes de tráfego de dados para consumo quase instantâneo. Estes dados devem ser entregues aos usuários tal qual foram gerados: sem erros. Por isso, técnicas de controle e correção de erros estão intrinsecamente ligadas aos sistemas que realizam trocas de dados, sejam sistemas de armazenamento, os quais estão sujeitos a falhas durante a leitura, ou sistemas de comunicação, que estão sujeitos às adversidades do meio (radiação, interferência eletromagnética, desvanecimento, entre outros). Neste cenário, os códigos Reed-Solomon representam uma solução viável para inúmeras aplicações, bem como pesquisas acadêmicas, mesmo tanto tempo após sua invenção. Este trabalho realiza um estudo da teoria que embasa os códigos Reed-Solomon, assim como implementa as técnicas do estado-da-arte dos módulos que compõem tanto o codificador quanto o decodificador, as quais são prototipadas em hardware reconfigurável.<br
FNT-based reed-solomon erasure codes
Get PDFThis paper presents a new construction of Maximum-Distance Separable (MDS) Reed-Solomon erasure codes based on Fermat Number Transform (FNT). Thanks to FNT, these codes support practical coding and decoding algorithms with complexity O(n log n), where n is the number of symbols of a codeword. An open-source implementation shows that the encoding speed can reach 150Mbps for codes of length up to several 10,000s of symbols. These codes can be used as the basic component of the Information Dispersal Algorithm (IDA) system used in a several P2P systems
Reed-solomon forward error correction (FEC) schemes, RFC 5510
Get PDFThis document describes a Fully-Specified Forward Error Correction (FEC) Scheme for the Reed-Solomon FEC codes over GF(2^^m), where m is in {2..16}, and its application to the reliable delivery of data objects on the packet erasure channel (i.e., a communication path where packets are either received without any corruption or discarded during transmission). This document also describes a Fully-Specified FEC Scheme for the special case of Reed-Solomon codes over GF(2^^8) when there is no encoding symbol group. Finally, in the context of the Under-Specified Small Block Systematic FEC Scheme (FEC Encoding ID 129), this document assigns an FEC Instance ID to the special case of Reed-Solomon codes over GF(2^^8).
Reed-Solomon codes belong to the class of Maximum Distance Separable (MDS) codes, i.e., they enable a receiver to recover the k source symbols from any set of k received symbols. The schemes described here are compatible with the implementation from Luigi Rizzo
Reed-Solomon Codes (Codici di Reed-Solomon)
Get PDFThis work offers a general overview on Reed-Solomon codes as a subclass of cyclic codes and BCH codes, using a mathematical approach to describe their practical aspects. After briefly exposing Galois Fields theory, a systematic encoding strategy through generator polynomial and a decoder based on Berlekamp-Massey and Forney algorithm are presented. A Matlab implementation of an encoder and a decoder can be found in this workope
Amplify-and-Forward Relaying Aided Reed-Solomon Coded Hybrid-ARQ Relying on Realistic Channel Estimation
Get PDFChannel estimation (CE) plays an important role in determining the achievable performance of coherently detected communications systems. In this paper, the impact of imperfect CE on Reed-Solomon coded Hybrid Automatic-Repeat-Request (ReS/H-ARQ) systems is investigated for transmission over correlated Rayleigh fading channels. The proposed scheme invokes Amplify-and-Forward relaying, where the benefits of multiple cooperative stations are also quantified. Both the corresponding bit error probability and goodput are characterized. The system parameters are adjusted for maximizing the attainable system performance. An optimum pilot power allocation scheme is proposed, which reduces the required bit-energy by 4 dB for the (255/223) Reed-Solomon code defined over the Galois field GF (256) without reducing the goodput
Konstruksi Kode Reed-Solomon sebagai Kode Siklik dengan Polinomial Generator
Get PDFSuatu kode pengoreksi kesalahan adalah himpunan vektor kode yang dirancang untuk mendeteksi dan mengoreksi kesalahan bit di dalam untaian yang diterima atau diakses. Kode siklik adalah salah satu kelas dari kode pengoreksi kesalahan. Kode siklik mempunyai subkelas yang disebut sebagai kode BCH yang mempunyai bentuk khusus yang disebut Kode Reed-Solomon. Kode Reed-Solomon mempunyai kemampuan mengoreksi kesalahan yang tinggi. Pada tulisan ini kode Reed-Solomon dibatasi bekerja pada lapangan hingga (Galois Field) GF(2^m), untuk m bilangan bulat.. Lebih tepatnya, kode Reed-Solomon yang merupakan ideal prima dari GF(2^m)/???x^n-1??? dalam tulisan ini dikonstruksi dengan menggunakan sebuah polinom generator g(x)???GF(2^m)/???x^n-1???. Agar bisa mengoreksi t kesalahan bit dan merentang kode Reed-Solomon dengan panjang n=2^m-1, dimensi k=n-2t, jarak minimum d_min=n-k+1 dan memuat q^k vektor kode, polinom generator harus memiliki derajat 2t
Inapproximability of the Shortest Vector Problem by means of Reed-Solomon codes
No full textopenLo Shortest Vector Problem (SVP) è il problema di individuare l'elemento più corto di un reticolo. La sua complessità è alla base della sicurezza di numerosi sistemi di criptazione moderni.
In questo lavoro dimostriamo che la variante decisionale e approssimata dello SVP è NP-difficile per riduzioni randomizzate utilizzano reticoli localmente densi costruiti attraverso codici Reed-Solomon
A Reed-Solomon Coded DS-CDMA System Using Noncoherent M-ary Orthogonal Modulation over Multipath Fading Channels
No full textThe performance of Reed–Solomon (RS) coded direct-sequence code division multiple-access (DS-CDMA) systems using noncoherent M-ary orthogonal modulation is investigated over multipath Rayleigh fading channels. Diversity reception techniques with equal gain combining (EGC) or selection combining (SC) are invoked and the related performance is evaluated for both uncoded and coded DS-CDMA systems. "Errors-and-erasures" decoding is considered, where the erasures are based on Viterbi’s so-called ratio threshold test (RTT). The probability density functions (PDF) of the ratio associated with the RTT conditioned on both the correct detection and erroneous detection of the M-ary signals are derived. These PDFs are then used for computing the codeword decoding error probability of the RS coded DS-CDMA system using "errors-and-erasures" decoding. Furthermore, the performance of the "errors-and-erasures" decoding technique employing the RTT is compared to that of "error-correction-only" decoding refraining from using side-information over multipath Rayleigh fading channels. As expected, the numerical results show that when using "errors-and-erasures" decoding, RS codes of a given code rate can achieve a higher coding gain than without erasure information. Index Terms—Direct sequence code division multiple-access, error-correction-only decoding, errors-and-erasures decoding, noncoherent -ary orthogonal signaling, ratio threshold test, Reed–Solomon codes
Ternary Reed-Solomon codes
No full textIncludes bibliographical references (page 34)Ternary Reed-Solomon codes and a technique for encoding and\ud
decoding these special codes have been investigated. The algebraic\ud
theory of finite fields is used to discuss cyclic codes and thus\ud
introduce Bose-Chaudhuri-Hocquenghem codes, a special case of which is\ud
the Reed-Solomon code. An algorithm for decoding Reed-Solomon codes is\ud
given. Also, several specific examples are worked out to help\ud
illustrate these codes
Ternary Reed-Solomon codes
Get PDFTernary Reed-Solomon codes and a technique for encoding and decoding these special codes have been investigated. The algebraic theory of finite fields is used to discuss cyclic codes and thus introduce Bose-Chaudhuri-Hocquenghem codes, a special case of which is the Reed-Solomon code. An algorithm for decoding Reed-Solomon codes is given. Also, several specific examples are worked out to help illustrate these codes.California State University, Northridge. Department of Engineering.Includes bibliographical references (page 34
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