Application Research Of Compressed Sensing Theory In LDPC Channel Coding

In the past few decades, communication systems channel coding has been a hotresearch topic, by seeking an appropriate rule, add oversight codes to transmittinginformation in accordance with this rule, thus forming a new transmissioncodeword. At the receiving end of the communication system, content informationtransmitted for further channel decoding, as to remove redundant information data.This is mainly in order to transmit information by error rate as small as possible,thereby enhancing the reliability of the communication system. So far, LDPC codesis the one of the codes closest to the Shannon limit, have a good decodingperformance, how to use a variety of ways to improve the performance of LDPCcodes, the closer to the Shannon limit, and to overcome the deficiencies of existingchannel coding, to reduce the complexity of the application and the hardwareconsumption, is great significance to improve the efficient transmission ofinformation. While a new idea in another mathematical field to provide a newdirection for us, which is compressed sensing (Compressive Sensing, CS).Compressed sensing theory can be seen as a thinking which use of signalsparsity or compressibility to measurement signals, the number of measured valuesis far less than the number of samples directly, but we can still get the signalapproximation reconstruction. The biggest advantage of this idea is to save systemresources and reduce consumption of the actual hardware. a very important researchdirection for LDPC coding is how to remove a lot of redundant information, extractthe exact original information, and according to the compressed sensing theory, wecan recover the original signal based on a small amount of observations, which has agreat advantages of reducing redundant information of channel coding andextracting the original information.This article describes the research status of compressed sensing and LDPCchannel coding, including an overview of channel coding, compressed sensing andLDPC-coded basic theory. Compressed sensing mathematical model has beenelaborated, also as a variety of compressed sensing recovery algorithms, and we take signal simulation for the one-dimensional and two-dimensional signal. We describethe characteristics and classification of the LDPC codes，illustrate LDPC encodingprocess and decoding process, and a check matrix structure. All of these is thebasics in theory for future study.Based on LDPC codes and compressed sensing, first of all, in this paper, theidea of compressed sensing is applied to the field of LDPC channel coding, a LDPCcoding system framework is proposed based on compressed sensing. In thetransmission process of LDPC codes, due to coding, noise, interference and otherfactors, a lot of redundant information has been generated in LDPC codes, accordingcompressed sensing feature, we use CS algorithm to take appropriate transformationto transmit information, to extract a small amount of redundant information whichcontains the original signal, these redundant information is added to the LDPC codedecoding process as the external information, to assist correction the channeldecoding process,in this way the LDPC coded BER has been reduced. On thisbasis, we take a series of analysis and research. In addition, we also study theimpact on the system for a variety of CS algorithm, by a number of contrast we cansee, the system time by BP algorithm is similar to OMP algorithm，while thecomputation time used StOMP algorithm is much less than the OMP and BP, whichis that we can achieve the effect of reducing the system operation time by improvingthe different CS reconstruction algorithm. On this basis, we also optimize the CSalgorithm in the system, we propose many methods to optimize the observationmatrix, including parity check matrix and Gaussian matrix linear superposition, QRdecomposition and the quasi unit matrix, and these methods are discussed andanalyzed for impact on system performance.Secondly, on the basis of the overall coding system, we discussed the extrinsicinformation extraction method, namely the use the concept and nature of Gaussiankernel in image segmentation processing field to process information, throughsimulation experiments show that residual redundancy of information extracted bythe use of this process can remove the noise effectively, with more of the originalinformation, using such information as the extrinsic information, a transmissionerror in the received sequence can be effectively corrected, the system bit error ratehas dropped, effectively improve decoding performance. We then through further testing, to change a Gaussian kernel function optimized important parametervalue, and the results were analyzed, experiments show that, in this system,different values of the parameters, but also affect the system performance, in acertain range, parameter greater system BER is lower. By adjusting theappropriate parameters, coding gain has improved of about1.5db or so. Inaddition, for different CS reconstruction algorithms, in error rate performance,StOMP algorithm although only slightly better than BP and OMP algorithm, butwhen applied to large-scale calculations, StOMP computing speed is obviouslyfaster.In order to further improve anti-interference performance, according toamplification coefficients and parameters, we propose amendments to theapproximate Gaussian kernel model of the extracted information outside, and itsrange carried out a detailed analysis to understand the intrinsic value of the modellaw, identify extreme values of the parameter values, and by the line simulation.Experiments show that by improving the model to improve coding gain of about2dbor so. To make the system more practical, we also propose a new LDPC-CS-LDPCdecoding model, this model is more compact, suitable for practical applications,and for the signal length, transmission speed, running time, sparsity, observationmatrix and different of CS algorithms,we conduct in-depth research of BER, FERand run-time of the model.In addition, we also optimize compressed sensing observation matrix. Wemake SVD thoughts and compressed sensing observation matrix integration,observation matrix optimization method is proposed based on the SVD, through aseries of simulations, we can see that for one-dimensional signal, using a Gaussianrandom matrix as the observation matrix, the resulting error has large volatility,about0.1of magnitude. While the corresponding use SVD matrix as the observationmatrix, the resulting error is small fluctuations, about0.001of magnitude,which ishigher than the Gaussian matrix of two orders of magnitude. For thetwo-dimensional signal, we can see that using Gaussian random matrix as themeasurement matrix, the error of the peak signal to noise ratio PSNRisabout101dB. Using Gaussian random SVD matrix as the measurement matrix,PSNRis about102dB., which is around a number of high-level than the Gaussian matrix. That is, SVD Gaussian random matrix as the measurement matrixdemonstrated excellent anti-jamming performance. In the fixed noise conditions,after optimization of SVD transform matrix, this measurement matrix comparedwith Gaussian random, the PSNR for reconstruction can improve about3dB. And,after several measurements, using SVD optimized matrix remodeling PSNR valueonly show small fluctuations, compared with a Gaussian matrix, better stability.Meanwhile, this optimization method can be generalized to random measurementmatrix. On this basis, the paper also madea thorough exploration, we construct theidea of LDPC check matrix to introduce compressed sensing theory, throughMackay construction method of LDPC codes, we construct a new matrix as thecompressed sensing measurement matrix for data sampling observation. Andsimulation verification. Through a series of simulations, it can be seen thatcompared to conventional Gaussian random, LDPC parity check matrix H as a newobservation matrix has many advantages to small individual elements of matrix,save storage space and to restore the projection calculation simpler, reducecomputational complexity degree, especially for noisy images have betterreconstruction results. This paper also presents a new observation matrix,Toeplitz-SVD matrix, this matrix take advantage of Gaussian matrices and Toeplitzmatrix fused together, several simulation experiments show that, using this matrixas the compressed sensing observation matrix, can achieve better quality ofrecovery, and Toeplitz-SVD observation matrix for noisy images and other recoveryalgorithms, but also universally applicable.