A Study on LDPC-CC with Rational Parity-Check Metrices and Related Decoding Algorithms

• Main Authors: Lai, Chih-Chieh, 賴志傑
• Other Authors: Wang, Chung-Hsuan
• Format: Others
• Language: en_US
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/62847277741472901379

碩士 === 國立交通大學 === 電信工程系所 === 97 === Low-density parity-check convolutional codes (LDPC-CC) are convolutional codes with low-density of ones in the scalar form of parity-check matrices. They have good features that do not exist in LDPC block codes such as they can be encoded with arbitrary length by simple shift registers, and can be decode by only one decoder. On the other hand, a decoder for LDPC block code can only decode codewords with xed length. Besides, the decoder pops out the decoded outputs continuously, and makes LDPC-CC more adequate to real time operating systems than LDPC block codes. In this thesis, we discuss the decoding algorithms for LDPC-CC in two perspectives. First, we propose a new perspective for decoding LDPC-CC with rational parity-check matrices. Second, we present an improved bit-fipping decoding algorithm for LDPC-CC. Recently, good performance LDPC-CC are constructed from quasi-cyclic LDPC (QCLDPC) codes. There are zeros, monomial or binomial in the parity-check matrices of those LDPC-CC. In this thesis, we discuss the possibility that LDPC-CC with rational paritycheck matrices can still have good bit error rate (BER) performance. We propose a new perspective of constructing Tanner graph to represent the rational in parity-check matrix. There are no cycles of length 4, and the iterative message passing algorithm can be free from high dependence in the examples. The simulation results show that the BER performance is better than that of previous perspective for decoding LDPC-CC with rational parity-check matrices about 1 dB improvement and 1 dB away from maximum likelihood (ML) decoding results in the cases of LDPC-CC with small memory. In the cases of LDPC-CC with large memory, our simulation results show about 0.7 dB improvement. We also generate rational parity-check matrices equivalent to the monomial parity-check matrices constructed from QC-LDPC. The simulation results show that there are no dierence between two BER peformance. In addition to the decoding for LDPC-CC with rational parity-check matrices, we also discuss the hard decision decoding for LDPC-CC. In many applications such as the communication in flash memory, the power consumption and the volume of the system are the most important concern, and a simplied decoding algorithm for LDPC codes is needed. Bit-flipping algorithms are good choices because they provide decoded results very quickly by utilizing hard decisions of received sequence. There is much research on modied bit-flipping algorithms for dierent type of LDPC block codes but few discussion about LDPC-CC. Unluckily, the bit-flipping algorithm for LDPC block codes are not well suitable for decoding LDPC-CC due to the nature of the decoders for LDPC-CC. Therefore, we propose a modified bit- ipping algorithm for decoding LDPC-CC in this thesis. The simulation results show that the BER performance is better than previous work about 2 dB improvement in many cases.