| Channel coding is one of the most important technologies to guarantee the reliability of deep space communication(DSC) data transmission under low SNR, large transmission delay and resource constrained environment. As a high gain coding technique with capacity-approaching performances, Low-Density Parity-Check(LDPC) codes has aroused widespread concern in the field of deep space communication channel coding. In order to meet the diverse needs in various scenarios of deep space communications, nonbinary(NB) LDPC codes, with better performance and stronger ability to resist burst error, is considered an appropriate candidate to substitute short block length code specified in DSC Synchronization and Channel Coding for improved performance.As the field order increase, the performance of NB LDPC code improves at the cost of increasing complexity of the decoding algorithm. What is equally important to reducing the decoding complexity, is the construction of check matrix which directly determines the correcting performance of the resulting code. Some works of designs of NB LDPC codes with outstanding performance have emerged, such as structured codes based on finite fields, graph theory and random codes based on computer searching. This thesis analyses the factors that affect the performance of NB LDPC codes including short cycle and girth, nonzero elements distribution and minimum distance, and then propose two design schemes for high performance NB LDPC codes for deep space communication.1. In view of the requirements to code with short to moderate block length for emergency, command/ARQ and other uplink services of deep space communication, this thesis proposes a construction method of non-binary protograph-based LDPC codes based on finite field additive group operation from node perspective. Firstly, nonzero element labels of nodes are optimized to render corresponding binary image of rows of the parity-check matrix larger minimum distance and less multiplicities. Then, quasi-girth calculating method is proposed to jointly optimize node permutation label so as to “cancel” short cycles and low weight codewords introduced by them, thus to raise minimum distance upper bound of global code. Simulation results under DSC channel illustrate the excellent performance of the proposed codes with adequately selected node’s value label and permuting label.2. According to the high power efficiency and the high coding gain requirements of the DSC channel coding, construction method of non-binary quasi-cyclic LDPC codes based on prime field is also presented in this thesis. According to masked base matrix and prime field modular multiplication, independent row-column mapping sequence(IRCMS) algorithm is improved to search permutation sequences of check node and variable node so as to maximize the girth of resulting binary check matrix. And then, nonbinary check matrix is constructed by replacing the elements of prime field with corresponding nonbinary circulant permutation matrix. Based on the Chinese remainder theorem, a new method for the optimization of girth and minimum distance properties of the code is proposed. Simulation results show that the proposed code has a certain performance improvement than other binary and nonbinary codes with similar parameters, especially in the low SNR region. |
