scholarly journals Error Exponents of LDPC Codes under Low-Complexity Decoding

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 253
Author(s):  
Pavel Rybin ◽  
Kirill Andreev ◽  
Victor Zyablov
Keyword(s):  
Linear Codes ◽  
Ldpc Codes ◽  
Low Complexity ◽  
Parity Check ◽  
Error Exponent ◽  
Error Exponents ◽  
Decoding Algorithms ◽  
Symmetric Channel ◽  
Low Density Parity Check ◽  
Specific Construction

This paper deals with the specific construction of binary low-density parity-check (LDPC) codes. We derive lower bounds on the error exponents for these codes transmitted over the memoryless binary symmetric channel (BSC) for both the well-known maximum-likelihood (ML) and proposed low-complexity decoding algorithms. We prove the existence of such LDPC codes that the probability of erroneous decoding decreases exponentially with the growth of the code length while keeping coding rates below the corresponding channel capacity. We also show that an obtained error exponent lower bound under ML decoding almost coincide with the error exponents of good linear codes.

scholarly journals Design of Quasi-Cyclic Low Density Parity Check Decoder Using Optimized Min-Sum Algorithm

2018 ◽  
Vol 7 (03) ◽  
pp. 23781-23784
Author(s):  
Rajarshini Mishra
Keyword(s):  
Variance Estimation ◽  
Cyclic Codes ◽  
Ldpc Codes ◽  
Ldpc Code ◽  
Low Complexity ◽  
Low Density ◽  
Parity Check ◽  
Decoding Algorithm ◽  
Low Density Parity Check ◽  
Xilinx Fpga

Low-density parity-check (LDPC) 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. Quasi-cyclic low-density parity-check (QC-LDPC) codes are an important subclass of LDPC codes that are known as one of the most effective error controlling methods. Quasi cyclic codes are known to possess some degree of regularity. Many important communication standards such as DVB-S2 and 802.16e use these codes. The proposed Optimized Min-Sum decoding algorithm performs very close to the Sum-Product decoding while preserving the main features of the Min-Sum decoding, that is low complexity and independence with respect to noise variance estimation errors.Proposed decoder is well matched for VLSI implementation and will be implemented on Xilinx FPGA family

scholarly journals Matching Pursuit Algorithm for Decoding of Binary LDPC Codes

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Jianzhong Guo ◽  
Cong Cao ◽  
Dehui Shi ◽  
Jing Chen ◽  
Shuai Zhang ◽  
...  
Keyword(s):  
Error Probability ◽  
High Efficiency ◽  
Matching Pursuit ◽  
Ldpc Codes ◽  
Inner Product ◽  
Parity Check ◽  
Decoding Algorithms ◽  
Low Density Parity Check ◽  
Matching Pursuit Algorithm ◽  
Simulation Results

This paper presents a novel hard decision decoding algorithm for low-density parity-check (LDPC) codes, in which the stand matching pursuit (MP) is adapted for error pattern recovery from syndrome over GF(2). In this algorithm, the operation of inner product can be converted into XOR and accumulation, which makes the matching pursuit work with a high efficiency. In addition, the maximum iteration is theoretically explored in relation to sparsity and error probability according to the sparse theory. To evaluate the proposed algorithm, two MP-based decoding algorithms are simulated and compared over an AWGN channel, i.e., generic MP (GMP) and syndrome MP (SMP). Simulation results show that the GMP algorithm outperforms the SMP by 0.8 dB at BER = 10 − 5 .

scholarly journals The Decoding Algorithms For Error-Correcting Product Codes Based On Project Geometry Low-Density Parity-Check Codes

2020 ◽  
Vol 12 (3) ◽  
pp. 399-406
Author(s):  
Lev E. Nazarov ◽  
Keyword(s):  
Turbo Codes ◽  
Ldpc Codes ◽  
Parity Check ◽  
Decoding Algorithm ◽  
Signal Noise ◽  
Product Codes ◽  
Decoding Algorithms ◽  
Low Density Parity Check ◽  
Code Constructions ◽  
Parity Check Codes

The focus of this paper is directed towards the investigation of the characteristics of symbol-by-symbol iterative decoding algorithms for error-correcting block product-codes (block turbo-codes) which enable to reliable information transfer at relatively low received signal/noise and provide high power efficiency. Specific feature of investigated product codes is construction with usage of low-density parity-check codes (LDPC) and these code constructions are in the class of LDPC too. According to this fact the considered code constructions have symbol-by-symbol decoding algorithms developed for total class LDPC codes, namely BP (belief propagation) and its modification MIN_SUM_BP. The BP decoding algorithm is iterative and for implementation the signal/noise is required, for implementation of MIN_SUM_BP decoding algorithm the signal/noise is not required. The resulted characteristics of product codes constructed with usage of LDPC based on project geometry (length of code words, information volume, code rate, error performances) are presented in this paper. These component LDPC codes are cyclic and have encoding and decoding algorithms with low complexity implementation. The computer simulations for encoding and iterative symbol-by-symbol decoding algorithms for the number of turbo-codes with different code rate and information volumes are performed. The results of computer simulations have shown that MIN_SUM_BP decoding algorithm is more effective than BP decoding algorithm for channel with additive white gaussian noise concerning error-performances.

Modified Bit-Flipping Decoding of Low-Density Parity-Check Codes

2013 ◽  
Vol 710 ◽  
pp. 723-726
Author(s):  
Yuan Hua Liu ◽  
Mei Ling Zhang
Keyword(s):  
High Throughput ◽  
Error Probability ◽  
Ldpc Codes ◽  
Low Complexity ◽  
Low Density ◽  
Parity Check ◽  
Excellent Performance ◽  
Low Density Parity Check ◽  
Lower Complexity ◽  
Parity Check Codes

A novel bit-flipping (BF) algorithm with low complexity for high-throughput decoding of low-density parity-check (LDPC) codes is presented. At each iteration, a novel threshold pattern is used to determine the code bits whether to be flipped or not, and the flipping error probability is effectively decreased. Compared with the weighted BF algorithm and its modifications, the modified BF algorithm has significantly lower complexity and decoding time. Through simulations the proposed BF algorithm is shown to achieve excellent performance and fast convergence speed while maintaining significantly low complexity thus facilitating high-throughput decoding.

scholarly journals Low-complexity decoding of LDPC codes using reduced-set WBF-based algorithms

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Sadjad Haddadi ◽  
Mahmoud Farhang ◽  
Mostafa Derakhtian
Keyword(s):  
Computational Complexity ◽  
Error Rate ◽  
Ldpc Codes ◽  
Low Complexity ◽  
Low Density ◽  
Parity Check ◽  
Decoding Complexity ◽  
Iterative Decoders ◽  
Low Density Parity Check ◽  
The Difference

Abstract We propose a method to substantially reduce the computational complexity of iterative decoders of low-density parity-check (LDPC) codes which are based on the weighted bit-flipping (WBF) algorithm. In this method, the WBF-based decoders are modified so that the flipping function is calculated only over a reduced set of variable nodes. An explicit expression for the achieved complexity gain is provided and it is shown that for a code of block length N, the decoding complexity is reduced from O(N2) to O(N). Moreover, we derive an upper bound for the difference in the frame error rate of the reduced-set decoders and the original WBF-based decoders, and it is shown that the error performances of the two decoders are essentially the same.

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