Iterative decoding that is adopted by near capacity limit error-correcting codes,improves the correcting capability of coding system greatly.This paper presents the design of encoding and decoding system of hamming codes with iterative decoding,and the theoretical analysis of iterative decoding process of hamming codes using modern encoding and decoding theory such as factor graph and sum-product algorithm.Simulation results show that there is 3 db coding gain between iterative decoding and classical decoding in hamming codes when the BER(bit error rate) is 10~(-3) under some times of iterative decoding and AWGN channel.At the same time,the BER performances between iterative decoding and the best enumerate decoding are equal,but the complexity of iterative decoding descends evidently,which is of importantly actual value for the hamming codes to be used in practical systems.
Iterative decoding that is adopted by near capacity limit error-correcting codes,improves the correcting capability of coding system greatly.This paper presents the design of encoding and decoding system of hamming codes with iterative decoding,and the theoretical analysis of iterative decoding process of hamming codes using modern encoding and decoding theory such as factor graph and sum-product algorithm.Simulation results show that there is 3 db coding gain between iterative decoding and classical decoding in hamming codes when the BER(bit error rate) is 10~(-3) under some times of iterative decoding and AWGN channel.At the same time,the BER performances between iterative decoding and the best enumerate decoding are equal,but the complexity of iterative decoding descends evidently,which is of importantly actual value for the hamming codes to be used in practical systems.
Abstract:Contraposing the distance between the theoretic correcting capacity and the actual correcting capacity of TPC, on the base of studying the encoding and constructing methods of the TPC, this paper analysed the theoretic correcting capacity and the actual correcting capacity of TPC，and indicated that if the two component codes had error-correcting capacity t, the TPC had error-correcting capacity (t+1)2+t. An improved iterative decoding algorithm which could be used after usual decoding algorithms to improve the decoding performance was brought forward，and it can correct some errors which usual decoding algorithms could detect but could not correct. The simulation result showed that the improved iterative decoding algorithm could lower the BER, especially when the SNR was low.
Considering the difference between the theoretic correcting capacity and the actual correcting capacity of TPC,on the base of studying the encoding and constructing methods of the TPC,the theoretic correcting capacity and the actual correcting capacity of TPC were analyzed,and the result showed that if the two component codes has the error-correcting capacity of t,the TPC has the error-correcting capacity of(t+1)2+t.An improved iterative decoding algorithm which could be used after usual decoding algorithms to improve the decoding performance was put forward,and it can correct some errors which usual decoding algorithms could detect but could not correct.The simulation result showed that the improved iterative decoding algorithm could lower the BER,especially when the SNR was low.
Since IoT requires low power transmission and ultra-small devices, a strong error correction codes with simple encoders are needed. Hamming code is considered as an useful simple error correction code. Hamming code with hard decision has a low complexity scheme, but its error correction capability is degraded. Therefore, in this paper, we consider a low complexity decoding method to improve error correction property with applying Sum-product algorithm. Sum-product decoding is a kind of brief propagation (BP) decoding, and can efficiently determine the posterior probability. In addition, using messages in the LLR domain, decoding operation will be much easier. However, it is not an exact MAP decoding because the Tanner graph of the Hamming code has the loops of length 4, and its decoding performance is not predictable. Therefore, we verified the effectiveness of the proposed scheme by computer simulation.
Low-Density Parity-Check code (LDPC) is a kind of linear block error-correcting codes.Sum-product algorithm is an iterative decoding algorithms commonly used in LDPC code decoding.This paper studies into the LDPC code message passing iterative decoding algorithm under the binary symmetric channel (BSC) and simulates the bit error probability,then simulates the convergence of check nodes' and variable nodes' probability density in the iterative process using the method of density evolution.The result show that under a given channel threshold,LDPC code has a good correction performance.
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.
In the field of Error Correcting Coding (ECC), the concept of ''stopping set'' recently became a hot topic. A stopping set for a parity-check matrix is the set of bits which would cause the iterative decoding progress in Binary Erasure Channel (BEC) to ''stop'' when it is erased. It has already been proved in several papers that the decoding performance under iterative decoding algorithm of any linear block code in BEC is determined by their stopping set performance, in particular, their size and number. And it is commonly assumed by the coding researchers that those codes which have better stopping set performance would also perform better in other channels. In this thesis, the decoding performance of linear block codes, in particular, Hamming Codes, the original LDPC code proposed by Gallager and FG-LDPC codes is studied in Binary Symmetric Channel (BSC) and Additive White Gaussian Noise (AWGN) channel. Three iterative decoding algorithms, respectively Bit-Flipping algorithm, Weighted Bit-Flipping algorithm and Sum Product Algorithm are used. To emphasize the influence of stopping set property, the parity-check matrix for each code is modified by adding linearly dependent rows to the original parity-check matrix, or removing rows from it. These modifications are made in order to change the stopping set property of the codes. The performance of the modified parity-check matrices is thus analyzed, by comparing them to the original ones, using both theoretical analysis and simulation. The results show that the stopping set performance of linear block codes is not a crucial factor to their performances on other channels as it is in BEC. Sometimes the linear block codes of a better stopping set property do perform better in other channels, but sometimes the performance barely changes or even degrades. More precisely, the decoding performance of a certain parity-check matrix is determined by the type of codes, the type of channel and the decoding algorithm, rather than its stopping set property.