Singlescan minsum algorithms for fast decoding of ldpc codes. Quasi cyclic low density parity check decoder using minsum algorithm for ieee 802. Errorcorrection code, lowdensity paritycheck code, ldpc decoder, minsum algorithm, normalized minsum algorithm 1. 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. Pdf optimized minsum decoding algorithm for ldpc codes. In this paper, an efficient implementation of the adaptive offset minsum aoms algorithm for decoding ldpc codes using the singlestep method is proposed. The generalized operation of ldpc is that variable node. Embodiments relate to a decoder 500 for iteratively decoding an ldpc encoded code word. Conventionally, each iteration in decoding process contains two steps, the horizontal step and the vertical step. Pdf optimized minsum decoding algorithm for low density. An optimized minsum algorithm for ldpc code is proposed in this paper. Design, simulation and hardware implementation of low density.
A lowcomplexity minsum decoding algorithm for ldpc codes. 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. An adaptivenormalizedoffset minsum anaoms algorithm for decoding lowdensity paritycheck ldpc codes is proposed. 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. Lowdensity paritycheck ldpc decoder is one such technique. In this paper the performance of minsum ldpc algorithm is analyzed. A modified min sum decoding algorithm based on lmmse for ldpc.
Simplified 2dimensional scaled minsum algorithm for ldpc. Low density parity check ldpc codes, is a linear block code having the decoding performance closer to shannons limit. Low complexity implementation of ldpc decoder using min. However, severe performance degradation might occur when it is realized in hardware due to the finite precision effect, especially in twobit precision. Novel modified minsum decoding algorithm for lowdensity. An improved ldpc decoding algorithm based on minsum algorithm. Index termsldpc codes, graph codes, minsum decoding. In this paper, we present a fast minsum algorithm for decoding ldpc codes over gfq.
Andreas leven, laurent schmalen, in optical fiber telecommunications sixth edition, 20. Research approach the proposed minsum algorithm is implemented using verilog hdl at questasim 10. Lowdensity paritycheckldpcdecoder using low complexity. There is also a \ min sum or maximumlikelihood sequence detection mlsd version of the sum product algorithm. An adaptivenormalizedoffset min sum anaoms algorithm for decoding lowdensity paritycheck ldpc codes is proposed. Unlike the normalizedoffset min sum nmsoms algorithm, the. An area efficient ldpc decoder using a reduced complexity. 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. Simplified variablescaled min sum ldpc decoder for. It is used to calculate the average probability density function pdf of messages. Reducedcomplexity minsum algorithm for decoding ldpc. An improvement is presented to the offset min sum decoding algorithm for lowdensity parity check codes. The estimated parameters a, b can be calculated easily used the methods as in this paper. The minsum algorithm msa for decoding lowdensity paritycheck ldpc.
The optimization factor is obtained before decoding program, and the same factor is multiplied twice in one. It can also achieve a nearoptimal performance in many cases at decoding ldpc codes, very close to the sumproduct algorithm. Decoding algorithm an overview sciencedirect topics. For this purpose, the paper points out the modified minsum decoding algorithmmmsa. Based on minsum algorithm, a novel modified minsum decoding algorithm for ldpc codes is proposed. Simplified variablescaled min sum ldpc decoder for irregular. Introduction low density parity check ldpc codes can. These algorithms can be described either in a graph structure commonly denoted as tanner graph, or given directly in a form suitable for implementation. Ber performance analysis of ldpc codes for minsum decoding algorithm rinku n.
A new modified min sum decoding algorithm based on lmmse estimate criterion for ldpc codes is presented in this paper. Unlike the normalizedoffset minsum nmsoms algorithm, the. When applied to a trellis, the minsum algorithm gives the same result as the viterbi algorithm. Minsum decoding of irregular ldpc codes with adaptive scaling. In this thesis, sumproduct algorithm and maxproduct algorithm are used. The decoder 500 further includes a processor 506 to select, from a. In this algorithm unlike other decoding methods, an optimization factor has been introduced in both check node and bit node of the minsum algorithm. With regular low density parity check codes ldpc, a fixed scaling of the llr yields. The codes were modulated using binary phase shift keying bpsk.
Performance analysis of minsum ldpc decoding algorithm. Abstractminsum decoding ms is an alternative to belief propagation decoding. A reconstructioncomputationquantization rcq approach. It exchanges softinformation iteratively between vn and cn. In this paper, a modified offset min sum decoding algorithm for lowdensity parity check codes is presented. In section ii, different ldpc decoding algorithms are discussed, and section iii explains our proposed optimized min sum algorithm. In 10, a dual mode adaptive uniform quantization scheme was proposed to better approximate the logtanh function used in sumproduct algorithm spa. Deriving the normalized minsum algorithm from cooperative. Ldpc codes can be decoded by the gallagers iterative beliefpropagation bp or sum of products algorithm sp 1. Pdf in this paper a modified offset minsum decoding algorithm for lowdensity parity check codes is presented. 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. It is obvious that multiplying the two minima by these scaling factors is quite complicated in aspect of hardware implementation. Simplified 2dimensional scaled minsum algorithm for ldpc decoder 1924 j electr eng technol.
Of the many that exist, the two most common ldpc decoding algorithms are the sumproduct algorithm spa 24 and the minsum algorithm msa 25. Progressive edge growth peg algorithm is used for generating ldpc codes 8. 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. Minmax decoding for non binary ldpc codes valentin savin, cealeti, minatec, grenoble, france, valentin.
The degradation factor of bp to ms is found and optimized based on jacobian logarithm and hardware. The design is based on the layered offsetminsum algorithm and is runtimeprogrammable to process different code matrices including all rates and block lengths speci. In the check node and variable node update process of the proposed algorithm, an improved. 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. Wiberg 6 developed the min sum algorithm as a generalization of the viterbi algorithm. Pdf performance analysis of minsum ldpc decoding algorithm. 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.
In this paper, an improved self adaptive minsum decoding algorithm for flexible lowdensity paritycheck ldpc code is proposed. Trellisbased extended minsum algorithm for nonbinary. An improved ldpc decoding algorithm based on min sum algorithm. Quantized minsum decoders with low error floor for ldpc codes.
There is also a \minsum or maximumlikelihood sequence detection mlsd version of the sumproduct algorithm. A massively parallel implementation of qcldpc decoder on gpu guohui wang, michael wu, yang sun, and joseph r. Simulation results for two ldpc codes show the proposed decoding algorithm with only 4bit quantization closely matches the performance of floatingpoint normalizedoffset min. 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.
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. A modified normalized min sum decoding algorithm for. 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. Nonbinary ldpc is the class of binary ldpc, which works on the higher order galois field. 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. 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. On the condition of no increasing in the decoding complexity, it makes the errorcorrecting performance improved by adding the appropriate scaling factor based. Finally, in section iv, an fpga implementation of a bitserial 480, 355 fullyparallel ldpc decoder is presented.
Optimized minsum decoding algorithm for low density parity. 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. Errorcorrection code, lowdensity paritycheck code, ldpc decoder, minsum algorithm, normalized min sum algorithm 1. A modified min sum decoding algorithm based on lmmse for. 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. Fast minsum algorithms for decoding of ldpc over gf q. The two main message passing algorithms conclude sumproduct algorithm or belief propagation algorithm or probability propagation algorithm and maxproduct algorithm or minsum algorithm. An improvement is presented to the offset minsum decoding algorithm for lowdensity parity check codes. For this, various decoding algorithms were introduced of which min sum algorithm is the most efficient method. 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.
Abstractmany implementations for decoding ldpc codes are based on the normalizedoffset minsum algorithm due to its satisfactory. Introduction lowdensity paritycheck ldpc codes were. The proposed algorithm introduces a more efficient adjustment for checknode update. Another improvement to the standard minsum algorithm, is to reduce the reliability values lk mn computed in 1 by a positive value. In the proposed algorithm, new modifications are incorporated in both the check node and variable node update process to support the irregular ldpc codes. 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. Design, simulation and hardware implementation of low. For example, when ber is 105, our algorithm can achieve 0. Welldesigned irregular ldpc codes demonstrate better performance than regular ones 6. 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. 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. 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. Ldpc minimum sum algorithm decoder with weight 3, 6. Implementation of channel coder for ldpc low density.
An alternative approach obtaining a normalization factor in. The algorithm is simulated and the results show that the. Svs minsum algorithm can outperform minsum algorithm by 0. However, performance of binary ldpc code is degraded when the code word length is small. Each column of l subsequently regenerates message word m. 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. The declercq and fossoriers algorithm speeds up the computation by reducing the. The offset minsum decoding rule may be according to equation 8 or 9, for example. An optimized min sum algorithm for ldpc code is proposed in this paper. In msa, the quantized intrinsic message, also known as loglikelihood ratio llr and the extrinsic messages between variable and. In this algorithm unlike other decoding methods, an optimization factor has been introduced in both check node and bit. Quasi cyclic low density parity check decoder using min. A massively parallel implementation of qcldpc decoder on. Decoding algorithms with strong practical value not only have good decoding performance, but also have the computation complexity as low as possible.
May 15, 20 trellisbased extended min sum algorithm for nonbinary ldpc codes and its hardware structure abstract. When applied to a trellis, the min sum algorithm gives the same result as the viterbi algorithm. Wiberg 6 developed the minsum algorithm as a generalization of the viterbi algorithm. 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 nbldpc in galois fields gfq. In this paper the performance of min sum ldpc algorithm is analyzed. A configurable approximation min sum decoding algorithm for ldpc is proposed in this paper. A modified minsum algorithm for quantized ldpc decoders. A twobit precision decoding algorithm for ldpc codes over the binary symmetric channel abstract. Pdf a modified offset minsum decoding algorithm for ldpc codes.
Ber performance analysis of ldpc codes for minsum decoding algorithm ijsrdvol. 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. Pdf in this paper a modified offset minsum decoding algorithm for low density parity check codes is presented. Adaptive offset minsum algorithm to achieve the optimal performance. The minsum algorithm msa for decoding lowdensity paritycheck ldpc code is an approximation algorithm that can greatly reduce the computational complexity. Simulation results show that the normalized minsum algorithm can improve the performance of the original minsum algorithm 1. A twobit precision decoding algorithm for ldpc codes over. 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. The simulation results show that compared with other kinds of modified min sum algorithms, this algorithm possesses the following. The min sum algorithm is also proposed in 7 as an approximation to the belief propagation bp algorithm 8, 9.
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. 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 7, an adaptive offset minsum aoms algorithm is presented, which lets the offset factor adaptively change for the better performance. Adaptive scaling factors, ldpc decoding, combined variable and check node architecture. Xu x, wu x, zhang x national asic system engineering center, southeast university, nanjing, 210096 abstract. Pdf a modified offset minsum decoding algorithm for.
A bitserial approximate minsum ldpc decoder and fpga. Selfcorrected minsum decoding of ldpc codes by valentin savin 2008. An improved self adaptive minsum decoding algorithm for. Pdf the effects of clipping and quantization on the performance of the minsum algorithm for the decoding of lowdensity paritycheck ldpc codes at. Low density parity check ldpc code approaches shannonlimit performance for binary field and long code lengths. Singlescan minsum algorithms for fast decoding of ldpc. Fast minsum algorithms for decoding of ldpc over gfq. Optimized minsum decoding algorithm for low density. A minsum algorithm suitable for hardware implementation. Adaptive offset minsum algorithm using a singlestep for. Among a variety of decoding algorithms, the wellknown. For this purpose, the paper points out the modified min sum decoding algorithm mmsa.
In 10, a dual mode adaptive uniform quantization scheme was proposed to better approximate the logtanh function used in sum product algorithm spa. 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. The algorithm used for decoding ldpc is the minsum algorithm. Trellisbased extended minsum algorithm for nonbinary ldpc.
The most common decoding algorithm for ldpc codes is the sumproduct decoding algorithm and its simplified versions. To study ldpc codes ive started implementing a soft decision decoder using floating point operations only. A modified selfcorrected minsum ldpc decoding algorithm. The ldpc decoder is using the analog output from the channel after conversion to binary. An alternative approach obtaining a normalization factor. 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. Ldpc codes are used in many future analog vlsi implementation. Low complexity implementation of ldpc decoder using minsum. Simulation results show that the normalized min sum algorithm can improve the performance of the original min sum algorithm 1. The minsum algorithm is also proposed in 7 as an approximation to the belief propagation bp algorithm 8, 9. Quantized minsum decoders with low error floor for ldpc. Index terms ldpc,hard decision decoding, soft decision decoding, minsum algorithm. Layered offset minsum decoding for low density parity check. 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.
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