Research On Improvement Of Encoding And Decoding Algorithms Of Near-Shannon-Limit Error Correcting Codes

In 1993,after the birth of Turbo codes,scholars began to design and research various types of near-Shannon-limit error correcting codes.Low-Density Parity-Check(LDPC)codes were rediscovered in 1996.LDPC codes have near-Shannon-limit error performance and low decoding complexity,and can be implemented in parallel.Currently,LDPC codes are adopted in many standards,such as 5G,DVB-S2,etc.However,LDPC codes are limited in some applications due to their fixed code rate.Therefore,the concept of digital fountains has emerged.In 2002,the first practical digital fountain codes were presented.The fountain codes have no fixed code rate and have low encoding and decoding complexity,and are especially suitable for reliable broadcast communications and multi-source download.Raptor codes are currently the best fountain codes.LDPC codes and Raptor codes have many commonalities in code structure and decoding algorithms,and the pre-coder of Raptor codes usually adopts LDPC codes,which makes many research results of LDPC codes provide useful reference for the improvement of Raptor codes.Therefore,this dissertation researches on the encoding and decoding algorithms of LDPC codes and Raptor codes.The main contributions are as follows:(1)A resetting and switching weighted bit-flipping algorithm is proposed for LDPC codes in low power applications.The algorithm combines two existing weighted bit-flipping decoding algorithms,and adds two mechanisms,including the reset of hard decision and the cyclic switching of algorithms,which effectively eliminates the "loop effects" in decoding.Compared with the existing weighted bit-flipping algorithms,the new algorithm significantly improves the bit error performance without significantly increasing the computational complexity.(2)For LDPC codes in high-speed communications applications,an update scheduling of variable nodes based on second-level degrees is proposed,which can be applied to layered decoding algorithms in belief propagation.The proposed update scheduling enables the layered decoding algorithms to utilize more aggregate information at each iteration,thereby resulting in faster convergence speeds than existing algorithms.(3)For encoding algorithms of Raptor codes,an encoding algorithm based on short cycle elimination of joint matrix of Raptor codes is proposed by using the cascading property of Raptor codes and applying the short cycle elimination mechanism of LDPC codes between the inner code and the outer code of Raptor codes.The algorithm can selectively perform themechanism of short cycle elimination according to the degrees of the output symbols of LT codes,thereby preserving a certain coding randomness.The simulation results show that the algorithm can effectively improve the bit error performance of Raptor codes.(4)An optimized encoding algorithm is proposed for Raptor codes with irregular codes as the pre-coder.The algorithm can encode the LT codes according to the column weight of the parity check matrix of the LDPC pre-coder,so that the sum of degrees on both sides of the intermediate nodes of Raptor codes are more balanced,thereby improving coding gain.At the same time,the algorithm does not increase the computational complexity basically,and the hardware implementation is simple.