On the condition of no increasing in the decoding complexity, it makes the errorcorrecting performance improved by adding the appropriate scaling factor based on the min sum algorithm msa, and it is very suitable for hardware implementation. In 7, an adaptive offset minsum aoms algorithm is presented, which lets the offset factor adaptively change for the better performance. Implementation of channel coder for ldpc low density. A parallel software implementation of low density parity check decoding algorithm is proposed, a modified version of minsum algorithm msa has been used for the decoding. The algorithm used for decoding ldpc is the minsum algorithm. Each column of l subsequently regenerates message word m. It is used to calculate the average probability density function pdf of messages. Among a variety of decoding algorithms, the wellknown. When the minsum decoding algorithm is implemented using a hybrid ldpc decoder hardware, its ber performance can be improved by using layered decoding technique in which message updates are not done only after finishing the whole parity check matrix but also after finishing each layer of the parity check matrix 6, 7. Progressive edge growth peg algorithm is used for generating ldpc codes 8. Selfcorrected minsum decoding performs very close to the sumproduct decoding, while preserving the main features of the minsum decoding, that is low complexity and independence with respect to noise variance estimation errors. Welldesigned irregular ldpc codes demonstrate better performance than regular ones 6.
Low density parity check ldpc codes, is a linear block code having the decoding performance closer to shannons limit. Decoding algorithms with strong practical value not only have good decoding performance, but also have the computation complexity as low as possible. The proposed algorithm introduces a more efficient adjustment for checknode update. For this purpose, the paper points out the modified minsum decoding algorithmmmsa. Finally, in section iv, an fpga implementation of a bitserial 480, 355 fullyparallel ldpc decoder is presented.
Abstractminsum decoding ms is an alternative to belief propagation decoding. The design is based on the layered offsetminsum algorithm and is runtimeprogrammable to process different code matrices including all rates and block lengths speci. An improved self adaptive minsum decoding algorithm for. Quantized minsum decoders with low error floor for ldpc codes. Pdf optimized minsum decoding algorithm for low density. The estimated parameters a, b can be calculated easily used the methods as in this paper.
Trellisbased extended minsum algorithm for nonbinary. Quasi cyclic low density parity check decoder using minsum algorithm for ieee 802. It can also achieve a nearoptimal performance in many cases at decoding ldpc codes, very close to the sumproduct algorithm. The algorithm is simulated and the results show that the. Pdf in this paper a modified offset minsum decoding algorithm for lowdensity parity check codes is presented. In this paper, we present an improvement and a new implementation of a simplified decoding algorithm for nonbinary low density paritycheck codes nbldpc in galois fields gfq. The decoder reduces the interconnect complexity by restricting the extrinsic message length to 2 bits and also simplifies the check node operation. Quasi cyclic low density parity check decoder using min. Pdf a modified offset minsum decoding algorithm for ldpc codes. A modified selfcorrected minsum ldpc decoding algorithm. Introduction low density parity check ldpc codes can. For this, various decoding algorithms were introduced of which min sum algorithm is the most efficient method. Introduction lowdensity paritycheck ldpc codes were. A modified min sum decoding algorithm based on lmmse for.
Svs minsum algorithm can outperform minsum algorithm by 0. Research approach the proposed minsum algorithm is implemented using verilog hdl at questasim 10. Unlike the normalizedoffset minsum nmsoms algorithm, the. Different works have been done on min sum decoding to improve its performance to get closer to sum product algorithm performance like normalized min sum decoding algorithm, adaptive min sum decoding algorithm, selfcorrected min sum decoding algorithm etc. Layered offset minsum decoding for low density parity check.
The generalized operation of ldpc is that variable node. A massively parallel implementation of qcldpc decoder on gpu guohui wang, michael wu, yang sun, and joseph r. Index terms ldpc,hard decision decoding, soft decision decoding, minsum algorithm. High throughput low latency ldpc decoding on gpu for. The minsum algorithm msa for decoding lowdensity paritycheck ldpc.
Index termsldpc codes, graph codes, minsum decoding. Errorcorrection code, lowdensity paritycheck code, ldpc decoder, minsum algorithm, normalized min sum algorithm 1. Pdf in this paper a modified offset minsum decoding algorithm for low density parity check codes is presented. Singlescan minsum algorithms for fast decoding of ldpc codes. The most common decoding algorithm for ldpc codes is the sumproduct decoding algorithm and its simplified versions. Ber performance analysis of ldpc codes for minsum decoding algorithm rinku n. In this paper the performance of minsum ldpc algorithm is analyzed. The min sum algorithm msa for decoding lowdensity paritycheck ldpc code is an approximation algorithm that can greatly reduce the computational complexity of the belief propagation algorithm bpa. In the proposed algorithm, new modifications are incorporated in both the check node and variable node update process to support the irregular ldpc codes. An area efficient ldpc decoder using a reduced complexity. Low complexity implementation of ldpc decoder using minsum. Performance analysis of minsum ldpc decoding algorithm s. In this paper, we present an improvement and a new implementation of a simplified decoding algorithm for nonbinary low density paritycheck codes nb ldpc in galois fields gfq.
The base algorithm that we use is the extended minsum ems algorithm, which has been widely studied in the recent literature, and has been shown to. A modified min sum decoding algorithm based on lmmse for ldpc. Wiberg 6 developed the minsum algorithm as a generalization of the viterbi algorithm. Andreas leven, laurent schmalen, in optical fiber telecommunications sixth edition, 20. Singlescan minsum algorithms for fast decoding of ldpc. The codes were modulated using binary phase shift keying bpsk. Simplified variablescaled min sum ldpc decoder for irregular. Wiberg 6 developed the min sum algorithm as a generalization of the viterbi algorithm. The ldpc decoder is using the analog output from the channel after conversion to binary. Ldpc minimum sum algorithm decoder with weight 3, 6. Simulation results for two ldpc codes show the proposed decoding algorithm with only 4bit quantization closely matches the performance of floatingpoint normalizedoffset min sum and sum product. Adaptive offset minsum algorithm using a singlestep for. One of the most important algorithms that satisfy this goal is the minsum algorithm, minsum is introduced in 11 as a simplification of llrspa by using minimum.
For example, when ber is 105, our algorithm can achieve 0. In this algorithm unlike other decoding methods, an optimization factor has been introduced in both check node and bit node of the minsum algorithm. Quantized minsum decoders with low error floor for ldpc. The degradation factor of bp to ms is found and optimized based on jacobian logarithm and hardware. An improved ldpc decoding algorithm based on minsum algorithm. Xu x, wu x, zhang x national asic system engineering center, southeast university, nanjing, 210096 abstract. Abstractmany implementations for decoding ldpc codes are based on the normalizedoffset minsum algorithm due to its satisfactory. In this thesis, sumproduct algorithm and maxproduct algorithm are used. Simplified 2dimensional scaled minsum algorithm for ldpc decoder 1924 j electr eng technol. A massively parallel implementation of qcldpc decoder on. Adaptive offset minsum algorithm using a singlestep for decoding ldpc codes xiaoju lin, gansuren baasantseren, sungsoo kim school of electrical engineering college of electrical and computer engineering chungbuk national university, republic of korea email. The min sum algorithm is also proposed in 7 as an approximation to the belief propagation bp algorithm 8, 9. When applied to a trellis, the min sum algorithm gives the same result as the viterbi algorithm. In msa, the quantized intrinsic message, also known as loglikelihood ratio llr and the extrinsic messages between variable and.
The offset minsum decoding rule may be according to equation 8 or 9, for example. Optimized minsum decoding algorithm for low density. In 10, a dual mode adaptive uniform quantization scheme was proposed to better approximate the logtanh function used in sumproduct algorithm spa. Scaled minsum algorithm for ldpc decoding the sumproduct algorithm spa algorithm is usually used to decode ldpc codes, in which belief messages are passed and processed between check nodes and variable nodes. Ber performance analysis of ldpc codes for minsum decoding algorithm ijsrdvol. The minsum algorithm is also proposed in 7 as an approximation to the belief propagation bp algorithm 8, 9. Min sum decoding algorithm is an approximation for sum of products algorithm to decode ldpc codes and does not have the complexity associated with nonlinear functions used in bp2. In this algorithm unlike other decoding methods, an optimization factor has been introduced in both check node and bit. The minsum algorithm msa for decoding lowdensity paritycheck ldpc code is an approximation algorithm that can greatly reduce the computational complexity. A modified minsum algorithm for quantized ldpc decoders. The minsum algorithm as an approximation of the sumproduct algorithm spa for decoding of ldpc codes has much lower computational complexity, but slightly worse performance than the spa. Nonbinary ldpc is the class of binary ldpc, which works on the higher order galois field. A lowcomplexity minsum decoding algorithm for ldpc codes. The proposed algorithm modifies the variable node message in the iteration process by averaging the new message and previous message if their signs are different.
An improvement is presented to the offset min sum decoding algorithm for lowdensity parity check codes. An improvement is presented to the offset minsum decoding algorithm for lowdensity parity check codes. The ldpc decoder comprises a decoding module which is configured to decode an ldpc encoded code word or ldpc frame according to an offset minsum decoding rule applying at least one offset value. Trellisbased extended minsum algorithm for nonbinary ldpc. Optimized minsum decoding algorithm for low density parity. On the condition of no increasing in the decoding complexity, it makes the errorcorrecting performance improved by adding the appropriate scaling factor based. Fast minsum algorithms for decoding of ldpc over gf q. Based on minsum algorithm, a novel modified minsum decoding algorithm for ldpc codes is proposed. Simplified variablescaled min sum ldpc decoder for. In 10, a dual mode adaptive uniform quantization scheme was proposed to better approximate the logtanh function used in sum product algorithm spa. Unlike the normalizedoffset min sum nmsoms algorithm, the.
A bitserial approximate minsum ldpc decoder and fpga. Design, simulation and hardware implementation of low density. It is obvious that multiplying the two minima by these scaling factors is quite complicated in aspect of hardware implementation. Adaptive scaling factors, ldpc decoding, combined variable and check node architecture. Viraktamath 1, girish attimarad 2 1department of ece, sdm college of engineering and technology, dharwad, india 2department of ece, dayanand sagar college of engineering, bangalore, india abstract in this paper the performance of minsum ldpc algorithm is analyzed. Design, simulation and hardware implementation of low. A modified normalized min sum decoding algorithm for. Lowdensity paritycheck ldpc decoder is one such technique. Conventionally, each iteration in decoding process contains two steps, the horizontal step and the vertical step. Pdf performance analysis of minsum ldpc decoding algorithm. An alternative approach obtaining a normalization factor in. Another improvement to the standard minsum algorithm, is to reduce the reliability values lk mn computed in 1 by a positive value. There is also a \minsum or maximumlikelihood sequence detection mlsd version of the sumproduct algorithm.
The decoder 500 further includes a processor 506 to select, from a. Pdf a modified offset minsum decoding algorithm for. In this paper, an efficient implementation of the adaptive offset minsum aoms algorithm for decoding ldpc codes using the singlestep method is proposed. Decoding algorithm an overview sciencedirect topics. Novel modified minsum decoding algorithm for lowdensity paritycheck codes 5 it is worth to mention that a reduced complexity spabased algorithm referred as rcspa 15 for decoding ldpc codes is proposed recently. Reducedcomplexity minsum algorithm for decoding ldpc. There is also a \ min sum or maximumlikelihood sequence detection mlsd version of the sum product algorithm.
Sumproduct algorithm for ldpc decoder the sumproduct algorithm spa is based on iterative. For this purpose, the paper points out the modified min sum decoding algorithm mmsa. In section ii, different ldpc decoding algorithms are discussed, and section iii explains our proposed optimized min sum algorithm. A reconstructioncomputationquantization rcq approach. Minsum decoding of irregular ldpc codes with adaptive scaling.
The software model of the sum product algorithm spa, min sum algorithm msa and the modified min sum of each algorithm is plotted using matlab. May 15, 20 trellisbased extended min sum algorithm for nonbinary ldpc codes and its hardware structure abstract. Simulation results show that the normalized minsum algorithm can improve the performance of the original minsum algorithm 1. Pdf the effects of clipping and quantization on the performance of the minsum algorithm for the decoding of lowdensity paritycheck ldpc codes at. The min sum algorithm as an approximation of the sum product algorithm spa for decoding of ldpc codes has much lower computational complexity, but slightly worse performance than the spa. The declercq and fossoriers algorithm speeds up the computation by reducing the. Of the many that exist, the two most common ldpc decoding algorithms are the sumproduct algorithm spa 24 and the minsum algorithm msa 25. Pdf optimized minsum decoding algorithm for ldpc codes. The two main message passing algorithms conclude sumproduct algorithm or belief propagation algorithm or probability propagation algorithm and maxproduct algorithm or minsum algorithm. Selfcorrected minsum decoding of ldpc codes by valentin savin 2008. Minmax decoding for non binary ldpc codes valentin savin, cealeti, minatec, grenoble, france, valentin. The base algorithm that we use is the extended minsum ems algorithm, which has been widely studied in the recent literature, and has been shown to approach the performance of the belief. When applied to a trellis, the minsum algorithm gives the same result as the viterbi algorithm. Ldpc codes can be decoded by the gallagers iterative beliefpropagation bp or sum of products algorithm sp 1.
In this paper the performance of min sum ldpc algorithm is analyzed. The minsum algorithm msa for decoding lowdensity paritycheck ldpc code is an approximation algorithm that can greatly reduce the computational complexity of the belief propagation algorithm. In this paper, a modified offset min sum decoding algorithm for lowdensity parity check codes is presented. An improved ldpc decoding algorithm based on min sum algorithm. Simplified 2dimensional scaled minsum algorithm for ldpc. A configurable approximation min sum decoding algorithm for ldpc is proposed in this paper. In this paper, an improved self adaptive minsum decoding algorithm for flexible lowdensity paritycheck ldpc code is proposed. The min sum algorithm msa 1 is a simplified version of the sumproduct algorithm spa 2 that is commonly used for iterative mp decoding of ldpc codes. An optimized minsum algorithm for ldpc code is proposed in this paper.
However, severe performance degradation might occur when it is realized in hardware due to the finite precision effect, especially in twobit precision. It exchanges softinformation iteratively between vn and cn. The min lut decoder cannot perform well if the fraction of degree2 variable nodes is large, thus suitable ldpc codes for min lut decoders need careful optimization 7. Simulation results for two ldpc codes show the proposed decoding algorithm with only 4bit quantization closely matches the performance of floatingpoint normalizedoffset min. Simulation results show that the normalized min sum algorithm can improve the performance of the original min sum algorithm 1. A twobit precision decoding algorithm for ldpc codes over. An adaptivenormalizedoffset minsum anaoms algorithm for decoding lowdensity paritycheck ldpc codes is proposed. Novel modified minsum decoding algorithm for lowdensity. Low density parity check ldpc code approaches shannonlimit performance for binary field and long code lengths.
A new modified min sum decoding algorithm based on lmmse estimate criterion for ldpc codes is presented in this paper. To study ldpc codes ive started implementing a soft decision decoder using floating point operations only. The optimization factor is obtained before decoding program, and the same factor is multiplied twice in one. The decoder comprises a decoding module 502 to decode the ldpc encoded code word according to an offset minsum decoding rule applying at least one offset correction value. Low complexity implementation of ldpc decoder using min. An alternative approach obtaining a normalization factor. Our algorithm is different from the one presented by david declercq and marc fossorier in isit 05 only at the way of speeding up the horizontal scan in the minsum algorithm. An adaptivenormalizedoffset min sum anaoms algorithm for decoding lowdensity paritycheck ldpc codes is proposed. For better speed at almost the same decoding performance ive added support for saturating fixedpoint operations parallel decoding of multiple blocks using simd is available for all variations of the minsum algorithm. Errorcorrection code, lowdensity paritycheck code, ldpc decoder, minsum algorithm, normalized minsum algorithm 1. A minsum algorithm suitable for hardware implementation. 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. Adaptive offset minsum algorithm to achieve the optimal performance. However, performance of binary ldpc code is degraded when the code word length is small.
Performance analysis of minsum ldpc decoding algorithm. Lowdensity paritycheckldpcdecoder using low complexity. In the check node and variable node update process of the proposed algorithm, an improved. A twobit precision decoding algorithm for ldpc codes over the binary symmetric channel abstract. The simulation results show that compared with other kinds of modified min sum algorithms, this algorithm possesses the following. Ldpc codes are used in many future analog vlsi implementation.
Embodiments relate to a decoder 500 for iteratively decoding an ldpc encoded code word. The minsum algorithm msa is the modified version of the sumproduct algorithm spa, where the check node operation is simplified to significantly reduce the complexity of the algorithm. In this paper, we present a fast minsum algorithm for decoding ldpc codes over gfq. An optimized min sum algorithm for ldpc code is proposed in this paper. With regular low density parity check codes ldpc, a fixed scaling of the llr yields.
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