Research On The Construction And Decoding Methods Of Sparse Graph Codes

Due to their good iterative decoding performance,sparse-graph codes have attracted a great deal of attention.Many works showed that they can approach the Shannon capacity.This dissertation investigates the construction,analysis,decoding and related issues of several sparse-graph codes with widespread academic concern.Specifically,it includes the improvement and construction of binary and nonbinary Kite codes(a class of Rateless codes),Kite based incremental redundancy hybrid ARQ scheme,simplified decoding algorithm for nonbianry LDPC codes,and the construction,decoding,and analysis of a class of spatially coupled turbo code-braided convolutional codes.The main contributions are summarized as follows:To construct a universal Rateless code which performs well on the noisy channel over a wide range of code rates,two improvements on Kite codes are proposed.First,the precoding technique is applied into Kite code.That is,an accumulator is concatenated as an outer code with Kite codes.The resulted codes are a class of variable-rate codes,called precoded Kite codes.The EXIT chart tool is used to analyze and optimize the precoded Kite codes.Simulation results show that the precoded Kite code performs well from the low code rate to high code rate.They outperform Kite codes by up to 0.3 d B.The comparison between precoded Kite codes and Raptor codes shows that precoded Kite codes perform better than Raptor codes over a wide range of rates.Second,the new construction method is proposed to construct the nonbinary rate-compatible Kite codes.The high-order modulation performance of nonbinary rate-compatible Kite codes is also investigated.Besides,the performance of nonbinary rate-compatible Kite codes with fountain communications are analyzed.The simulation results show that the average achievable rate can approach the capacity.To design an incremental redundancy hybrid ARQ scheme based on Ratelss codes over noisy channels(fast-fading channels,or AWGN channels),the Kite based incremental redundancy hybrid ARQ scheme in the finite length regime is proposed.The optimal transmission schedule under the unlimited retransmission time is given.Besides,under the condition of the limited retransmission time,an algorithm that exploits current decoding reliability to determine the size of subsequent retransmissions is given.The mapping between the reliability,code rate,and BER are made to find the empirical function of reliability.Furthermore,two algorithms((early terminate algorithm and freezing node algorithm))are introduced to reduce the decoding complexity.Due to the fact that the high decoding complexity of nonbinary LDPC codes and bad performance of iterative joint detection decoding(IJDD)algorithm for the nonbinary LDPC codes with the low column weight,we first extended the IJDD algorithm to the case of q?|X |.Then we propose a reliability-based iterative joint detection-decoding(also termed improved IJDD)algorithm,which combines the accumulated reliability of symbols based on the one-step majority-logic decoding(MLGD)algorithm and a Chase-like local list decoding algorithm.The key idea of this algorithm is that each variable node feeds back two most reliable symbols to the associated check node based on one-step majority-logic decoding,which makes the needed reliability are remained to help make decision.Besides,the complexity comparison among the IJDD algorithm,the improved IJDD algorithm,and the FFT-QSPA is made.To reduce the high decoding latency of a class of spatially coupled turbo codes-braided convolutional codes,we present a novel low-latency sliding window decoding scheme based on iterative BCJR decoding for braided convolutional codes,a class of turbo-like codes with short constraint length component convolutional codes.With the help of passing the extrinsic informaiton between the component codes in different time instants in a decoding window,the target symbols are decoded correctly.To reduce decoding complexity,both uniform and nonuniform message passing schedules within the decoding window,along with early stopping rules,are proposed.The comparison of decoding complexity and performance between different schedules is made.We also perform a density evolution analysis of sliding window decoding over the binary erasure channel(BEC)to guide the selection of the window size and message passing schedule.In order to reduce the computational complexity,two early stopping rules(stopping rule based on CE and stopping rule based on the reliability)are proposed.Periodic puncturing is employed to obtain rate-compatible braided convolutional codes.