We have developed a high performance and programmable LDPC decoder VLSI for decoding structured LDPC codes. In this paper, the architecture of the decoder and the structured parity check matrices are described along with the quantization method. We adopt floating point (FP) quantization method in check node processors so as to shrink down the complexity of look up tables (LUTs) of the Gallager function, and avoid performance degradation. Finally, simulation results show that the FP quantization method achieves high performance for wide range of code rates
We have developed a high performance and programmable LDPC decoder VLSI for decoding structured LDPC codes. In this paper, the architecture of the decoder and the structured parity check matrices are described along with the quantization method. We adopt floating point (FP) quantization method in check node processors so as to shrink down the complexity of look up tables (LUTs) of the Gallager function, and avoid performance degradation. Finally, simulation results show that the FP quantization method achieves high performance for wide range of code rates
In the past few years, Gallager's low-density parity-check (LDPC) codes received a lot of attention and many efforts have been devoted to analyzing and improving their error-correcting performance. However, little consideration has been given to the LDPC decoder VLSI implementation. The straightforward fully parallel decoder architecture usually incurs too high complexity for many practical purposes and should be transformed to a partly parallel realization. Unfortunately, due to the randomness of LDPC codes, it is nearly impossible to develop an effective transformation for an arbitrarily given LDPC code. We propose a joint code and decoder design approach to construct a class of (3, k)-regular LDPC codes which exactly fit a partly parallel decoder implementation and have a very good performance. Moreover, for such LDPC codes, we propose a systematic, efficient encoding scheme by effectively exploiting the sparseness of its parity check matrix.
Low-density parity-check (LDPC) codes have been shown to have good error correcting performance approaching Shannon’s limit. Good error correcting performance enables efficient and reliable communication. However, a LDPC code decoding algorithm needs to be executed efficiently to meet cost, time, power and bandwidth requirements of target applications. The constructed codes should also meet error rate performance requirements of those applications. Since their rediscovery, there has been much research work on LDPC code construction and implementation. LDPC codes can be designed over a wide space with parameters such as girth, rate and length. There is no unique method of constructing LDPC codes. Existing construction methods are limited in some way in producing good error correcting performing and easily implementable codes for a given rate and length. There is a need to develop methods of constructing codes over a wide range of rates and lengths with good performance and ease of hardware implementability. LDPC code hardware design and implementation depend on the structure of target LDPC code and is also as varied as LDPC matrix designs and constructions. There are several factors to be considered including decoding algorithm computations,processing nodes interconnection network, number of processing nodes, amount of memory, number of quantization bits and decoding delay. All of these issues can be handled in several different ways. \nThis thesis is about construction of LDPC codes and their hardware implementation. LDPC code construction and implementation issues mentioned above are too many to be addressed in one thesis. The main contribution of this thesis is the development of LDPC code construction methods for some classes of structured LDPC codes and techniques for reducing decoding time. We introduce two main methods for constructing structured codes. In the first method, column-weight two LDPC codes are derived from distance graphs. A wide range of girths, rates and lengths are obtained compared to existing methods. The performance and implementation complexity of obtained codes depends on the structure of their corresponding distance graphs. In the second method, a search algorithm based on bit-filing and progressive-edge growth algorithms is introduced for constructing quasi-cyclic LDPC codes. The algorithm can be used to form a distance or Tanner graph of a code. This method could also obtain codes over a wide range of parameters. Cycles of length four are avoided by observing the row-column constraint. \nRow-column connections observing this condition are searched sequentially or randomly. Although the girth conditions are not sufficient beyond six, larger girths codes were easily obtained especially at low rates. The advantage of this algorithm compared to other methods is its flexibility. It could be used to construct codes for a given rate and length with girths of at least six for any sub-matrix configuration or rearrangement. The code size is also easily varied by increasing or decreasing sub-matrix size. Codes obtained using a sequential search criteria show poor performance at low girths (6 and 8) while random searches result in good performing codes. \nQuasi-cyclic codes could be implemented in a variety of decoder architectures. One of the many options is the choice of processing nodes interconnect. We show how quasi-cyclic codes processing could be scheduled through a multistage network. Although these net-works have more delay than other modes of communication, they offer more flexibility at a reasonable cost. Banyan and Benes networks are suggested as the most suitable networks. \nDecoding delay is also one of several issues considered in decoder design and implementation. In this thesis, we overlap check and variable node computations to reduce decoding time. Three techniques are discussed, two of which are introduced in this thesis. The techniques are code matrix permutation, matrix space restriction and sub-matrix row-column scheduling. Matrix permutation rearranges the parity-check matrix such that rows and columns that do not have connections in common are separated. This techniques can be applied to any matrix. Its effectiveness largely depends on the structure of the code. We show that its success also depends on the size of row and column weights. Matrix space restriction is another technique that can be applied to any code and has fixed reduction in time or amount of overlap. Its success depends on the amount of restriction and may be traded with performance loss. The third technique already suggested in literature relies on the internal cyclic structure of sub-matrices to achieve overlapping. The technique is limited to LDPC code matrices in which the number of sub-matrices is equal to row and column weights. We show that it can be applied to other codes with a lager number of sub-matrices than code weights. However, in this case maximum overlap is not guaranteed. We calculate the lower bound on the amount of overlapping. Overlapping could be applied to any sub-matrix configuration of quasi-cyclic codes by arbitrarily choosing \nthe starting rows for processing. Overlapping decoding time depends on inter-iteration waiting times. We show that there are upper bounds on waiting times which depend on the code weights. Waiting times could be further reduced by restricting shifts in identity sub-matrices or using smaller sub-matrices. This overlapping technique can reduce the decoding time by up to 50% compared to conventional message and computation scheduling. \nTechniques of matrix permutation and space restriction results in decoder architectures that are flexible in LDPC code design in terms of code weights and size. This is due to the fact that with these techniques, rows and columns are processed in sequential order to achieve overlapping. However, in the existing technique, all sub-matrices have to be processed in parallel to achieve overlapping. Parallel processing of all code sub-matrices requires the architecture to have the number of processing units at least equal to the number sub-matrices. Processing units and memory space should therefore be distributed among the sub-matrices according to the sub-matrices arrangement. This leads to high complexity or inflexibility in the decoder architecture. We propose a simple, programmable and high throughput decoder architecture based on matrix permutation and space restriction techniques.
Low-Density Parity-Check (LDPC) codes have recaptured the attention of the scientific community a few years after Turbo codes were invented in the early nineties. Originally proposed in the 1960s at MIT by R. Gallager, LDPC codes represent powerful error correcting codes that allow working very close to the Shannon limit and achieve excellent Bit Error Rate (BER) due to computationally intensive algorithms on the decoder side of the system. Advances in microelectronics introduced small process technologies that allowed developing complex designs incorporating a high number of transistors in Very Large Scale Integration (VLSI) systems. Recently, these processes have been used to develop architectures able of performing LDPC decoding in real-time and delivering considerably high throughputs. Mainly for these reasons and naturally because the patent has expired, they have been adopted by modern communication standards which triggered their popularity, showing how actual they are. Due to the increase of transistor density in VLSI systems, and also to the fact that recently processing speed has risen faster than bandwidth, power and memory walls have created a new paradigm in computer architectures: rather than just increasing the frequency of operation supported by smaller process designs, the introduction of multiple cores on a single chip has become the new trend to provide augmented computational power. This thesis proposes new approaches for these computationally intensive algorithms, by performing parallel LDPC decoding based on ubiquitous multi-core architectures and achieves efficient throughputs that compare well with dedicated VLSI systems. We extensively address the challenges faced in the investigation and development of these programmable solutions, with focus mainly given on flexibility and scalability of the proposed algorithms, throughput and BER performance, and general efficiency of the programmable solutions here presented, that also achieve results more than an order of magnitude superior to those obtained with conventional CPUs. Furthermore, the investigation herein described follows a methodology that analyzes in detail the computational complexity of these decoding algorithms in order to propose strategies to accelerate their processingwhich, if conveniently transposed to other areas of computer science, can demonstrate that in this new multi-core era we may be in the presence of valid alternatives to non-reprogrammable dedicated VLSI hardware that requires non-recurring engineering.
In recent years, the amount of digital data which is stored and transmitted for private and public usage has increased considerably. To allow a save transmission and storage of data despite of error-prone transmission media, error correcting codes are used. A large variety of codes has been developed, and in the past decade low-density parity-check (LDPC) codes which have an excellent error correction performance became more and more popular. Today, low-density parity-check codes have been adopted for several standards, and efficient decoder hardware architectures are known for the chosen structured codes. However, the existing decoder designs lack flexibility as only few structured codes can be decoded with one decoder chip. In consequence, different codes require a redesign of the decoder, and few solutions exist for decoding of codes which are not quasi-cyclic or which are unstructured. In this thesis, three different approaches are presented for the implementation of fully programmable LDPC decoders which can decode arbitrary LDPC codes. As a design study, the first programmable decoder which uses a heuristic mapping algorithm is realized on a field-programmable gate array (FPGA), and error correction curves are measured to verify the correct functionality. The main contribution of this thesis lies in the development of the second and the third architecture and an appropriate mapping algorithm. The proposed fully programmable decoder architectures use one-phase message passing and layered decoding and can decode arbitrary LDPC codes using an optimum mapping and scheduling algorithm. The presented programmable architectures are in fact generalized decoder architectures from which the known decoder architectures for structured LDPC codes can be derived.
After the introduction of iterative coding, Low Density Parity Check (LDPC) codes have received a lot of attention due to their remarkable near Shannon-limit performance and practical decoder implementation. However, when employing an LDPC code for various applications, multiple issues do arise at the simulation, algorithm and implementation levels. The first issue is the performance evaluation of the iterative LDPC decoder in the very low Bit Error Rate (BER) regions. So far, no analytical tool has been developed to evaluate the performance of LDPC codes. Unfortunately standard Monte Carlo (MC) simulations cannot be used for performance estimation in these low BER regions due to prohibitive execution times. The second issue is the efficiency of the decoding algorithm. Due to the presence of short cycles in the bipartite graph, sum-product decoding algorithms lead to considerable performance loss for short block-length LDPC codes and produce error floors for longer codes. In addition, the iterative processing and estimation of soft probabilistic values with these algorithms result in very high computational complexity, which in turn impedes the adoption of LDPC codes for power constrained systems. Another prime objective is to design a high throughput decoder architecture which is capable of supporting multiple rates and variable code lengths within minimal area.
This work aims to address and provide solutions to the above problems. As a solution to the performance estimation problem of LDPC codes, a highly efficient and novel fast BER simulation technique is developed. At the algorithm level, a performance improvement and error floor avoidance method is introduced, and a computationally efficient algorithm is developed for the sum-product decoding of LDPC codes. And finally, at the architecture level, a high throughput multi-rate variable code length implementation is presented which, when implemented, efficiently minimizes device resources while alleviating the routing complexity of the decoder.
With the superior error correction capability, low-density parity-check (LDPC) codes have initiated wide scale interests in wireless communication and storage fields. In the past, various structures of single code-rate LDPC decoders have been reported. However, to cover a wide range of service requirements and diverse interference conditions in wireless applications, LDPC decoders that can operate at both high and low code rates are desirable. In this paper, a 9k code length multi-rate LDPC decoder architecture is presented and implemented on a Xilinx FPGA device. Using pin selection, three operating modes, namely, the irregular 1/2 code, the regular 5/8 code and the regular 7/8 code, are supported. Furthermore, to suppress the error floor level, a characterization on the conditions for short cycles in a LDPC code matrix expanded from a small base matrix is presented, and a cycle elimination algorithm is developed to detect and break such short cycles. The effectiveness of the cycle elimination algorithm has been verified by both simulation and hardware measurements, which show that the error floor is suppressed to a much lower level without incurring any performance penalty. The implemented decoder is tested in an experimental LDPC-OFDM system and achieves the superior measured performance of block error rate below 10/sup -7/ at SNR 1.8 dB.