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2015
In this paper we propose an efcient vectorized low den-sity parity check (LDPC) decoding scheme based on the min-sum algorithm and the horizontal scheduling method. Also, the well known forward-backward algorithm, used in the check-node messages update, is improved. Results are presented for 32 and 16 bits logarithm like-lihood ratio messages representation on a high performance and modern xed point DSP. The single instruction multiple data (SIMD) feature was explored in the 16 bits case. Both regular and irregular codes are considered. 1.
2004
Abstract An efficient decoding schedule for low-density parity-check (LDPC) codes that outperforms the conventional approach, in terms of both complexity and performance, is presented. Conventionally, in each iteration, all symbol nodes and, subsequently, all the check nodes, send messages to their neighbors (" flooding schedule"). In contrast, in the proposed method, the updating of nodes is performed according to a serial schedule which propagates the information twice as fast.
In this paper, a reduced-complexity, scalable implementation of LDPC decoder is presented. The decoder architecture in this paper is an improved version of . The new architecture makes the implementation of multiple code rates, multiple block sizes and multiple standards LDPC decoder very straightforward. As an example, we implemented a parameterized decoder that supports the LDPC code in IEEE 802.16e standard, which requires code rates of 1/2, 2/3 and 3/4, with block sizes varying from 576 to 2304. The decoder is synthesized with Texas Instruments' 90 nm ASIC process technology, with a target operation frequency of 100 MHz, 15 decoding iterations, the maximum data rate is up to 256 Mbps.
We propose a bit-serial LDPC decoding scheme to reduce interconnect complexity in fully-parallel low-density parity-check decoders. Bit-serial decoding also facilitates efficient implementation of wordlength-programmable LDPC decoding which is essential for gear shift decoding. To simplify the implementation of bit-serial decoding we propose a new approximation to the check update function in the min-sum decoding algorithm. The new check update rule computes only the absolute minimum and applies a correction to outgoing messages if required. We present a 650-Mbps bit-serial (480, 355) RS-based LDPC decoder implemented on a single Altera Stratix EP1S80 FPGA device. To our knowledge, this is the fastest FPGA-based LDPC decoder reported in the literature.
International Journal of Computing and Digital Systemss
This paper presents Verilog implementation of Low-Density Parity-Check (LDPC) decoders using Sum-Product and Min-Sum algorithms which will take more area as compared to other decoding algorithms. In this paper, area efficient LDPC decoder depending upon abridged complexity Minsum algorithm is presented. It reduces the permutational complexity with limiting the extrinsic information bit length to 4 bits and it modifies the check and variable node processing operation. Compilation at an algorithmic level explains that the proposed decoder attain good error performance as compared to a Sum Product Algorithm based decoder, and consequently handles the problem of immense error performance deprivation of a LDPC decoder. A Min Sum Based LDPC decoder with a matrix length (1000, 500) has been implemented in a MATLAB with a 10-1 BER and the design is implemented in HDL Verilog. The complete top level module was done by structural modeling style and simulated with SPARTAN FPGA Family. The percentage saving in area is about 33% of slices and provides a throughput of 1.46Gbps.
2006
A high throughput pipelined LDPC decoder that supports multiple code rates and codeword sizes is proposed. In or- der to increase memory throughput, irregular block struc- tured parity-check matrices are designed with the constrai nt of equally distributed odd and even nonzero block-columns in each horizontal layer for the pre-determined set of code rates. The designed decoder achieves a data
IEEE Transactions on Communications, 2009
In this letter, an improved bit-flipping decoding algorithm for high-rate finite-geometry low-density parity-check (FG-LDPC) codes is proposed. Both improvement in performance and reduction in decoding delay are observed by flipping multiple bits in each iteration. Our studies show that the proposed algorithm achieves an appealing tradeoff between performance and complexity for FG-LDPC codes.
In this paper the performance of Min-Sum LDPC algorithm is analyzed. A parallel software implementation of low density parity check decoding algorithm is proposed, a modified version of Min-Sum algorithm (MSA) has been used for the decoding. Specifically, Open Multi-Processing (OpenMP) for parallelizing software on a multi-core processor. We process information on H-matrices using OpenMP pragmas on a multi-core processor and execute decoding algorithms in parallel using MATLAB EXecutable (MEX) function in MATLAB. We evaluated the performance of the proposed implementation with respect to single-core processor execution and verified that the proposed parallel execution reduces the execution time and yields better results compared to single-core processor execution.
2007
Low-Density Parity-Check Codes: Construction and Implementation by Gabofetswe A. Malema 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. This 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
Procedia Computer Science, 2016
This paper proposes a low complexity low-density parity check decoder (LDPC) design. The design mainly accomplishes a message passing algorithm and systolic high throughput architecture. The typical mathematical calculations are based on the observation that nodes with high log likelihood ratio provide almost same information in every iteration and can be considered as stationary, we propose an algorithm in which the parity check matrix H is updated to a reduced complexity form every time a stationary node is encountered which results in lesser number of numerical computations in subsequent iterations. In this paper, we contemplately focuses on computational complexity and the decoder design significantly benefits from the high throughput point of view and the various improvisations introduced at various levels of abstraction in the decoder design. Threshold Controlled Min Sum Algorithm implements the LDPC decoder design for a code compliant with wired and wireless applications. A high performance LDPC decoder has been designed that achieves a throughput of 0.890 Gbps. The whole design of LDPC Decoder is designed, simulated and synthesized using Xilinx ISE 13.1 EDA Tool.
IEEE Transactions on Communications, 2005
In this paper, we develop a new low-complexity algorithm to decode low-density parity-check (LDPC) codes. The developments are oriented specifically toward low-cost, yet effective, decoding of (high-rate) finite-geometry (FG) LDPC codes. The decoding procedure updates iteratively the hard-decision received vector in search of a valid codeword in the vector space. Only one bit is changed in each iteration, and the bit-selection criterion combines the number of failed checks and the reliability of the received bits. Prior knowledge of the signal amplitude and noise power is not required. An optional mechanism to avoid infinite loops in the search is also proposed. Our studies show that the algorithm achieves an appealing tradeoff between performance and complexity for FG-LDPC codes.
IEEE Communications Letters, 2016
This letter presents a heuristic technique for simplifying the parity-check node operation in a Relaxed Min-Sum iterative decoder. The proposed decoder eliminates the secondminimum computation in check nodes, which allows broadcasting the same output to all neighboring variable nodes to alleviate routing problem in VLSI implementations of Low-Density Parity Check (LDPC) decoders. The second-minimum, when required, is emulated by adding an offset to the first-minimum. The proposed relaxed decoder also uses a relaxation factor equal to 0.5 to simplify variable nodes. Simulation results for two LDPC codes show the proposed decoding algorithm with only 4-bit quantization closely matches the performance of floatingpoint Normalized/Offset Min-Sum and Sum-Product decoders in the waterfall region.
The Journal of Korean Institute of Communications and Information Sciences, 2005
In this paper, we propose a new sequential message-passing decoding algorithm of low-density parity-check (LDPC) codes by partitioning check nodes. This new decoding algorithm shows better bit error rate(BER) performance than that of the conventional message-passing decoding algorithm, especially for small number of iterations. Analytical results tell us that as the number of partitioned subsets of check nodes increases, the BER performance becomes better. We also derive the recursive equations for mean values of messages at variable nodes by using density evolution with Gaussian approximation. Simulation results also confirm the analytical results.
2007
Abstract Conventionally, in each low-density parity-check (LDPC) decoding iteration all the variable nodes and subsequently all the check nodes send messages to their neighbors (flooding schedule). An alternative, more efficient, approach is to update the nodes' messages serially (serial schedule). A theoretical analysis of serial message passing decoding schedules is presented. In particular, the evolution of the computation tree under serial scheduling is analyzed.
Journal of Lightwave Technology, 2000
We describe simple iterative decoders for low-density parity check codes based on Euclidean geometries, suitable for practical VLSI implementation in applications requiring very fast decoders. The decoders are based on shuffled and replica-shuffled versions of iterative bit-flipping and quantized weighted bit-flipping schemes. The proposed decoders converge faster and provide better ultimate performance than standard bit-flipping decoders. We present simulations that illustrate the performance versus complexity trade-offs for thes decoders. We can show in some cases through importance sampling that no significant error-floor exists.
Acoustics, Speech, and Signal …, 2004
We present a high performance implementation of a belief propagation decoder for decoding low-density parity-check (LDPC) codes on a fixed point digital sig-nal processor. A simplified decoding algorithm was used and a stopping criteria for the iterative decoder was ...
IEEE Transactions on Circuits and Systems I: Regular Papers, 2010
A low-complexity message-passing algorithm, called Split-Row Threshold, is used to implement low-density parity-check (LDPC) decoders with reduced layout routing congestion. Five LDPC decoders that are compatible with the 10GBASE-T standard are implemented using MinSum Normalized and MinSum Split-Row Threshold algorithms. All decoders are built using a standard cell design flow and include all steps through the generation of GDS II layout. An = 16 decoder achieves improvements in area, throughput, and energy efficiency of 4.1 times, 3.3 times, and 4.8 times, respectively, compared to a MinSum Normalized implementation. Postlayout results show that a fully parallel = 16 decoder in 65-nm CMOS operates at 195 MHz at 1.3 V with an average throughput of 92.8 Gbits/s with early termination enabled. Low-power operation at 0.7 V gives a worst case throughput of 6.5 Gbits/s-just above the 10GBASE-T requirement-and an estimated average power of 62 mW, resulting in 9.5 pJ/bit. At 0.7 V with early termination enabled, the throughput is 16.6 Gbits/s, and the energy is 3.7 pJ/bit, which is 5.8 lower than the previously reported lowest energy per bit. The decoder area is 4.84 mm 2 with a final postlayout area utilization of 97%. Index Terms-Full parallel, high throughput, low-density parity check (LDPC), low power, message passing, min sum, nanometer, 10GBASE-T, 65-nm CMOS, 802.3an. I. INTRODUCTION S TARTING in the 1990s, much work was done to enhance error-correction codes to where communication over noisy channels was possible near the Shannon limit. Defined by sparse random graphs and using probability-based message-passing algorithms, low-density parity-check (LDPC) codes [1] became popular for their error-correction and near-channel-capacity performances. At first, neglected since its discovery [2], advances in VLSI have given LDPC a recent revival [3]-[6]. LDPC has relatively low error floors, as well as better error performance with large code lengths, and as a result, they have been adopted as the forward error-correction method for many recent standards, such as digital video broadcasting via satellite (DVB-S2) [7], the WiMAX standard for microwave communications (802.16e) [8], the G.hn/G.9960 standard for wired home networking [9], and the 10GBASE-T standard for 10-Gbit Ethernet (802.3an) [10]. While there has been much Manuscript
2006
Abstract Serial decoding schedules for low-density parity-check (LDPC) codes are described and analyzed. Conventionally, in each iteration all the variable nodes and subsequently all the check nodes send messages to their neighbors (¿ flooding schedule¿). In contrast, in the considered methods, the updating of the nodes is implemented according to a serial schedule. The evolution of the decoding algorithm¿ s computation tree under serial scheduling is analyzed.
IEEE Transactions on Communications, 2000
In this paper, we analyze the sequential messagepassing decoding algorithm of low-density parity-check (LDPC) codes by partitioning check nodes. This decoding algorithm shows better bit error rate (BER) performance than the conventional message-passing decoding algorithm, especially for the small number of iterations. Analytical results indicate that as the number of partitioned subsets of check nodes increases, the BER performance is improved. We also derive the recursive equations for mean values of messages at check and variable nodes by using density evolution with a Gaussian approximation. From these equations, the mean values are obtained at each iteration of the sequential decoding algorithm and the corresponding BER values are calculated. They show that the sequential decoding algorithm converges faster than the conventional one. Finally, the analytical results are confirmed by the simulation results.
… Symposium on Turbo-Codes & Related …, 2003
We explore in this paper some issues concerning the parallel hardware implementation of LDPC codes. We propose a LDPC matrix construction that is well suited to parallel decoding, that we called Hardware-Constrained LDPC codes (HC-LDPC). Although this construction is highly constrained, we show by simulations that there is no loss of performance compared to a pseudo-random parity matrix.
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