Research On Low Density Parity Check Codes And Its Performance In Wireless Fading Channels

Along with the continuous development of mobile communication system, thechannel coding technology used by the system also changes frequently. It is anoticeable question that adopting which kind of channel coding scheme couldsatisfy the demand of high performance system in the future. The research indicatesthat, the mobile communication system should adopt more advanced channelcoding scheme in order to ensure enough performance with the extremely lowsignal-to-noise ratio (SNR).The low-density parity-check codes are one kind of sparse parity-check matrixbased linear block error-correcting codes which could highly approach the Shannonlimit with iterative decoding. The recent research result tells us that, with thedecoding algorithm of belief propagation (BP Algorithm), the optimized LDPCcodes have performances surpassing Turbo codes, which could be within only0.0045 dB of the Shannon limit. So far, LDPC codes are considered to be with thebest performance, and now the research about LDPC is one of the most amazinghighlights in the area of channel coding. And meanwhile, the application of LDPCcodes has also been raised in practice and lists as essential technology of the fourthgeneration mobile communication system (4G).At present the research about LDPC codes is mainly divided into two aspects:one is doing theoretical research on the performance of LDPC codes, containingthe methods of constructing good LDPC codes, research about fast decodingalgorithms, analysis of weight distribution of LDPC codes, derivation of capacityof performance and code rate etc.;the other is paying attention to the practicalapplication of LDPC codes, containing the application in the communicationsystems and magnetic recording systems, hardware realization etc.With the profound understanding and grasping of the elementary theory ofLDPC codes as basis, this thesis conducts thorough research on decodingalgorithms of LDPC codes and proposes some improvements, then discusses indetail the performance of LDPC codes in wireless fading channels. The maincontents of this article are given as follows.(1) The elementary theory and developing process of channel coding technologyare introduced, and the appearance, present situation and developing prospect ofLDPC codes are systematically summarized and discussed. This part is helpful toforming general cognition of LDPC codes and orients the main research directionand contents of this article.(2) Concisely introduces and discusses the encoding-decoding principles oflinear block codes and LDPC codes, and involves some important relative conceptssuch as parity-check matrix, factor graph, circle, iterative decoding, and probabilityof error and so on. In the world scope recognizing the LDPC codes again startedlater and in our country the research on LDPC codes is comparatively more limited,so it requires urgently that researchers should profoundly understand and grasp theelementary theory of LDPC codes to prepare for the deep level research.(3) Mainly pay attention to the comprehensive study and discussion about thedecoding algorithms of LDPC codes. Systematically study and compare the maindecoding algorithms of belief propagation (probability-domain BP & LLR-domainBP) and several kinds of popular simplified decoding algorithms such as BP-basedalgorithm, Normalized BP-based algorithm, Offset BP-based algorithm andAPP-based algorithm, and obtain the corresponding decoding performance results.Through three parts contents (elementary principle of density evolution,Gaussian approximation of density evolution and discrete density evolution),analyze and derive the message density evolution in the iterative decodingalgorithms, and discuss the threshold effect of channel parameters under the BPalgorithm. The density evolution theory can help to get the systematic analysis forthe convergence characteristic of decoding algorithm independent of channels, andit is one kind of very helpful tool for theory and practice.(4) In order to reduce the complexity of decoding and enhance the decodingperformance, based on the current LLR-domain BP algorithm, propose someimprovements and simplifications to the LDPC codes' decoding algorithms.With the "clipping" technology, modify the hyperbolic tangent functioncontained in the check nodes updating operation of LLR-BP algorithm so that theconfidence and correctness of LLR information between message nodes areenhanced, then the decoding decisions become more correct and decodingperformance is improved.Because the realization of hyperbolic tangent operation is difficult in practice, inorder to reduce the complexity of decoding computation and improve the decodingperformance, based on the modified hyperbolic tangent function, it does somesimplifications with the linear fitting method to the check nodes updatingoperations both in Tanh-rule based LLR-BP algorithm and in Gallager-approachbased LLR-BP algorithm, then improved decoding algorithms are proposed. Thetheoretical analysis and computer simulation results prove the superiority ofimproved decoding algorithms comparing with standard LLR-BP algorithm. Withthe improved algorithms, not only the decoding performance can be improved, butalso the complexity of decoding operations can be reduced and the decodingprocess can be simplified. This makes it easy for hardware realization.(5) Because the current research about LDPC codes mainly concentrates on BSCand AWGN channels but merely on wireless fading channels, so this thesisanalyzes and studies the decoding performance of LDPC codes in fading channels,especially rician channel. It gives the corresponding fading channels' models,proposes the improved BP algorithm of LDPC codes in fading channels, provesand derives the characteristics of symmetry and stability for decoding algorithms,and does systematical analysis with simulation results. The results show that, theLDPC codes have good performance of preventing fading inferences. According tothe construction of LDPC codes and the characteristic of decoding, the reasonresulting in this kind of situation is analyzed and studied, and the results finallyindicate that LDPC codes have excellent performance in both Gaussian channelsand fading channels. In the end, the Shannon limit of channel capacity for ricianfading channel is discussed and derived and satisfying result is obtained.(6) The main work of this thesis is concluded and meanwhile the questions andresearch directions which should be concentrated on in the next steps are proposed.