Design Of Low Complexity Non-Binary LDPC Code

In digital communication system, channel coding is an efficient way to ensure the communication quality and to correct the transmission mistakes caused by the channel noise. Among the channel codes, LDPC(Low Density Parity Check) code has gained more and more attention due to its capacity approaching decoding performance and the potential of fast encoding and decoding. Compared to the binary LDPC code,non-binary LDPC code could have sparser parity check matrix and better decoding performance, especially for not very long block length. In the mean time, the decoding(computational) complexity of the non-binary LDPC code is higher than that of the binary LDPC code. In this dissertation, we show how to optimize the computational complexity of the non-binary LDPC code for different purposes or different applications. The main work is given as follows.1. EXIT(Extrinsic Information Transfer) chart is a performance evaluation tool for the LDPC decoder. For an LDPC code, there exist a one-to-one correspondence between its degree distributions and its EXIT chart(for a fixed channel condition). Based on the different definitions of the EXIT chart, we propose two complexity optimization algorithms by using Gallager’s formula(EXIT chart based the message error probability) and recursion of the extrinsic information function(EXIT chart based on the mutual information), respectively. Both algorithms are proposed to to find the optimal degree distributions which result in the reduction of the number of decoding iterations. Experimental studies show that after the optimization the decoding complexity of the non-binary LDPC code could be largely reduced.2. We utilize the binary vector and matrix representations of the finite field and introduce the equivalent binary LDPC code for the non-binary LDPC code. Then based on coefficients selection, we design cooperative decoders for non-binary LDPC code. A cooperative decoder is composed of two component decoders. If a cooperative decoder is composed of the binary BP decoder and the non-binary BP decoder and the degree distributions/decoder parameters are optimized, the decoding complexity is further reduced. We also proposed a hybrid soft-decision decoder by introducing matrix inverse operations. This decoder can be utilized to replace the non-binary component decoder in a cooperative decoder too. In addition, within the cooperative decoding process, a bit is decoded in different parity check equations sets in different component decoders. As a result, the cooperative decoders are capable of dealing with both random noise and burst noise. Moreover, the performance threshold of a cooperative decoder could also be lower than that of its component decoders for certain non-binary LDPC codes.3. We present a generalized binary representation(GBR) for the non-binary LDPC codes. Superior to the binary equivalent LDPC code, this representation can largely avoid the bit-level cycles while allowing the degree distributions to be more freely optimized. This method can be also utilized to design binary LDPC codes with optimized decoding performance. As an alternative of the non-binary decoder, we also design a(bit-level) hybrid parallel decoding process for the generalized binary representation. By utilizing this process, the performance of the GBR can closely approach the performance of its(performance-optimized)mother non-binary LDPC code under non-binary BP decoder(over binary input Gaussian channel).