Research On Performance Evaluation Of Generalized LDPC Codes Over The Binary Erasure Channel

As the extension of low density parity check(LDPC)code,error correcting codes other than single parity check(SPC)codes can play the role of check nodes in generalized LDPC(GLDPC)code.GLDPC code is a kind of iteratively decodable code which is Shannon-limit-approaching and shows excellent performance both in waterfall region and error floor region of the bit error rate chart,which enhance its candidate status in the potential applications of channel coding.Considering the low decoding complexity of Hamming code,the strategy of mixing SPC code with Hamming code is proposed to construct check nodes for GLDPC code.The theoretical asymptotic performance and actual decoding performance over the binary erasure channel(BEC)are analyzed and obtained.Firstly,we use extrinsic information transfer(EXIT)chart to obtain the asymptotic performance of hybrid GLDPC codes.EXIT chart is an effective method assessing the convergence behavior and tracking the message passing process between the node processors for LDPC codes.According to the dual property of EXIT chart,the EXIT functions of compound component codes for GLDPC code over the BEC are derived.With the aid of improved hill climbing algorithm,we can achieve the decoding threshold and the corresponding degree distribution by adjusting the proportion of Hamming codes over the BEC for GLDPC code with fixed coding rate of 1/2.Numerical results show that,the GLDPC code outperforms LDPC codes with respect to asymptotic performance over the BEC.It reaches Shannon limit within 0.034.Secondly,we construct a GLDPC code with optimal degree distribution mentioned above using progressive edge growth(PEG)algorithm.Under the help of PEG,the construction begins with the base matrix which has optimal degree distribution of variable nodes.Then,a fraction of the(15,14)SPC codes are replaced by(15,11)Hamming codes to act as the component codes of check nodes.By row expansion through the parity-check matrix of Hamming code,we can obtain the 1/2-rate(10000,5000)GLDPC code.Simulation results show that the code performs only 0.118 away from Shannon limit at the BER of 10'5 over the BEC.Finally,in order to speed the decoding convergence of GLDPC code,based on the standard message-passing(SMP)schedule algorithm for LDPC code,we modify the message-passing depth and regulate the update order of check nodes dynamically in each iteration process according to the characteristics of component codes of(10000,5000)GLDPC code.Four different kinds of schedule algorithms have been proposed in this thesis,i.e.,order-2 message-passing(02MP)schedule,order-4 message-passing(04MP)schedule,classified check-nodes message-passing(CCMP)schedule,and sorted check-nodes message-passing(SCMP)schedule.In comparison with SMP schedule,04-SCMP schedule algorithm is able to reduce the average number of iteration times by 3/4,and decrease the bit error rate by two orders of magnitude.