FPGA implementation of Reed Solomon codec for 40Gbps Forward Error Correction in optical networks

Reed-Solomon error correcting codes (RS codes) are widely used in communication and data storage systems to recover data from possible errors that occur during data transfer. A growing application of RS codes is Forward Error Correction (FEC) in the Optical Network (OTN G.709), which uses RS(255,239) to support the OTU-3 (43.018 Gbps) standard. There have been considerable efforts in the area of RS architecture for ASIC implementation. However, there appears to be little reported work on efficient RS codec (encoder and decoder) for Field Programmable Gate Arrays (FPGAs), which has increasing interests in industry. This thesis investigates the implementation and design methodology of the RS(255,239) codec on FPGAs. A portable VHDL code is developed and synthesized for Xilinx\u27s Virtex4 and Altera\u27s StratixII. The FPGA architectures are analyzed and the required design methodologies are adopted to efficiently utilize the available resources. Unfortunately, due to the fixed size of FPGA devices, the RS decoder is not only constrained by the required timing of the system, but also by the size of the targeted device. This research will facilitate the decision-making process for selecting a reconfigurable device for a RS decoder, implementing the Berlekamp-Massey Algorithm

Architectures for soft-decision decoding of non-binary codes

En esta tesis se estudia el dise¿no de decodificadores no-binarios para la correcci'on de errores en sistemas de comunicaci'on modernos de alta velocidad. El objetivo es proponer soluciones de baja complejidad para los algoritmos de decodificaci'on basados en los c'odigos de comprobaci'on de paridad de baja densidad no-binarios (NB-LDPC) y en los c'odigos Reed-Solomon, con la finalidad de implementar arquitecturas hardware eficientes. En la primera parte de la tesis se analizan los cuellos de botella existentes en los algoritmos y en las arquitecturas de decodificadores NB-LDPC y se proponen soluciones de baja complejidad y de alta velocidad basadas en el volteo de s'¿mbolos. En primer lugar, se estudian las soluciones basadas en actualizaci'on por inundaci 'on con el objetivo de obtener la mayor velocidad posible sin tener en cuenta la ganancia de codificaci'on. Se proponen dos decodificadores diferentes basados en clipping y t'ecnicas de bloqueo, sin embargo, la frecuencia m'axima est'a limitada debido a un exceso de cableado. Por este motivo, se exploran algunos m'etodos para reducir los problemas de rutado en c'odigos NB-LDPC. Como soluci'on se propone una arquitectura basada en difusi'on parcial para algoritmos de volteo de s'¿mbolos que mitiga la congesti'on por rutado. Como las soluciones de actualizaci 'on por inundaci'on de mayor velocidad son sub-'optimas desde el punto de vista de capacidad de correci'on, decidimos dise¿nar soluciones para la actualizaci'on serie, con el objetivo de alcanzar una mayor velocidad manteniendo la ganancia de codificaci'on de los algoritmos originales de volteo de s'¿mbolo. Se presentan dos algoritmos y arquitecturas de actualizaci'on serie, reduciendo el 'area y aumentando de la velocidad m'axima alcanzable. Por 'ultimo, se generalizan los algoritmos de volteo de s'¿mbolo y se muestra como algunos casos particulares puede lograr una ganancia de codificaci'on cercana a los algoritmos Min-sum y Min-max con una menor complejidad. Tambi'en se propone una arquitectura eficiente, que muestra que el 'area se reduce a la mitad en comparaci'on con una soluci'on de mapeo directo. En la segunda parte de la tesis, se comparan algoritmos de decodificaci'on Reed- Solomon basados en decisi'on blanda, concluyendo que el algoritmo de baja complejidad Chase (LCC) es la soluci'on m'as eficiente si la alta velocidad es el objetivo principal. Sin embargo, los esquemas LCC se basan en la interpolaci'on, que introduce algunas limitaciones hardware debido a su complejidad. Con el fin de reducir la complejidad sin modificar la capacidad de correcci'on, se propone un esquema de decisi'on blanda para LCC basado en algoritmos de decisi'on dura. Por 'ultimo se dise¿na una arquitectura eficiente para este nuevo esquemaGarcía Herrero, FM. (2013). Architectures for soft-decision decoding of non-binary codes [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/33753TESISPremiad

Polynomials in Error Detection and Correction in Data Communication System

The chapter gives an overview of the various types of errors encountered in a communication system. It discusses the various error detection and error correction codes. The role of polynomials in error detection and error correction is discussed in detail with the architecture for practical implementation of the codes in a communication channel

Simplified decoding techniques for linear block codes

Error correcting codes are combinatorial objects, designed to enable reliable transmission of digital data over noisy channels. They are ubiquitously used in communication, data storage etc. Error correction allows reconstruction of the original data from received word. The classical decoding algorithms are constrained to output just one codeword. However, in the late 50’s researchers proposed a relaxed error correction model for potentially large error rates known as list decoding. The research presented in this thesis focuses on reducing the computational effort and enhancing the efficiency of decoding algorithms for several codes from algorithmic as well as architectural standpoint. The codes in consideration are linear block codes closely related to Reed Solomon (RS) codes. A high speed low complexity algorithm and architecture are presented for encoding and decoding RS codes based on evaluation. The implementation results show that the hardware resources and the total execution time are significantly reduced as compared to the classical decoder. The evaluation based encoding and decoding schemes are modified and extended for shortened RS codes and software implementation shows substantial reduction in memory footprint at the expense of latency. Hermitian codes can be seen as concatenated RS codes and are much longer than RS codes over the same aphabet. A fast, novel and efficient VLSI architecture for Hermitian codes is proposed based on interpolation decoding. The proposed architecture is proven to have better than Kötter’s decoder for high rate codes. The thesis work also explores a method of constructing optimal codes by computing the subfield subcodes of Generalized Toric (GT) codes that is a natural extension of RS codes over several dimensions. The polynomial generators or evaluation polynomials for subfield-subcodes of GT codes are identified based on which dimension and bound for the minimum distance are computed. The algebraic structure for the polynomials evaluating to subfield is used to simplify the list decoding algorithm for BCH codes. Finally, an efficient and novel approach is proposed for exploiting powerful codes having complex decoding but simple encoding scheme (comparable to RS codes) for multihop wireless sensor network (WSN) applications

FPGA-based architectures for next generation communications networks

This engineering doctorate concerns the application of Field Programmable Gate Array (FPGA) technology to some of the challenges faced in the design of next generation communications networks. The growth and convergence of such networks has fuelled demand for higher bandwidth systems, and a requirement to support a diverse range of payloads across the network span. The research which follows focuses on the development of FPGA-based architectures for two important paradigms in contemporary networking - Forward Error Correction and Packet Classification. The work seeks to combine analysis of the underlying algorithms and mathematical techniques which drive these applications, with an informed approach to the design of efficient FPGA-based circuits

Desenvolvimento em linguagem de descrição de hardware de codificador e decodificador Reed-Solomon

Dissertação (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.2014-08-06T18:05:10

Reconfigurable architectures for the next generation of mobile device telecommunications systems

Mobile devices have become a dominant tool in our daily lives. Business and personal usage has escalated tremendously since the emergence of smartphones and tablets. The combination of powerful processing in mobile devices, such as smartphones and the Internet, have established a new era for communications systems. This has put further pressure on the performance and efficiency of telecommunications systems in delivering the aspirations of users. Mobile device users no longer want devices that merely perform phone calls and messaging. Rather, they look for further interactive applications such as video streaming, navigation and real time social interaction. Such applications require a new set of hardware and standards. The WiFi (IEEE 802.11) standard has been at the forefront of reliable and high-speed internet access telecommunications. This is due to its high signal quality (quality of service) and speed (throughput). However, its limited availability and short range highlights the need for further protocols, in particular when far away from access points or base stations. This led to the emergence of 3G followed by 4G and the upcoming 5G standard that, if fully realised, will provide another dimension in “anywhere, anytime internet connectivity.” On the other hand, the WiMAX (IEEE 802.16) standard promises to exceed the WiFi signal coverage range. The coverage range could be extended to kilometres at least with a better or similar WiFi signal level. This thesis considers a dynamically reconfigurable architecture that is capable of processing various modules within telecommunications systems. Forward error correction, coder and navigation modules are deployed in a unified low power communication platform. These modules have been selected since they are among those with the highest demand in terms of processing power, strict processing time or throughput. The modules are mainly realised within WiFi and WiMAX systems in addition to global positioning systems (GPS). The idea behind the selection of these modules is to investigate the possibility of designing an architecture capable of processing various systems and dynamically reconfiguring between them. The GPS system is a power-hungry application and, at the same time, it is not needed all of the time. Hence, one key idea presented in this thesis is to effectively exploit the dynamic reconfiguration capability so as to reconfigure the architecture (GPS) when it is not needed in order to process another needed application or function such as WiFi or WiMAX. This will allow lower energy consumption and the optimum usage of the hardware available on the device. This work investigates the major current coarse-grain reconfigurable architectures. A novel multi-rate convolution encoder is then designed and realised as a reconfigurable fabric. This demonstrates the ability to adapt the algorithms involved to meet various requirements. A throughput of between 200 and 800 Mbps has been achieved for the rates 1/2 to 7/8, which is a great achievement for the proposed novel architecture. A reconfigurable interleaver is designed as a standalone fabric and on a dynamically reconfigurable processor. High throughputs exceeding 90 Mbps are achieved for the various supported block sizes. The Reed Solomon coder is the next challenging system to be designed into a dynamically reconfigurable processor. A novel Galois Field multiplier is designed and integrated into the developed Reed Solomon reconfigurable processor. As a result of this work, throughputs of 200Mbps and 93Mbps respectively for RS encoding and decoding are achieved. A GPS correlation module is also investigated in this work. This is the main part of the GPS receiver responsible for continuously tracking GPS satellites and extracting messages from them. The challenging aspect of this part is its real-time nature and the associated critical time constraints. This work resulted in a novel dynamically reconfigurable multi-channel GPS correlator with up to 72 simultaneous channels. This work is a contribution towards a global unified processing platform that is capable of processing communication-related operations efficiently and dynamically with minimum energy consumption