Blind Recogntion Of RS Codes And Research On Carrier Synchronization Based On LDPC Codes

Due to the presence of noise, errors may occur during the transmission of information. In order to improve the performance of the communication system, channel coding technology is adapted. Channel coding adds redundant information to the transmitted information sequences regularly, which can be used to detect or correct errors by the receiver. There are lots of channel codes, which are widely used. The thesis studies some application of RS codes and LDPC codes, including blind recognition of RS codes, fast encoding of Quasi-Cyclic LDPC codes, and LDPC code-aided iterative carrier estimation for synchronization parameters.The primary works are as follows:(1) After introducing the fundamental knowledge of finite field, the thesis explains how to construct the finite field. And then, one method of representing finite field in computer is proposed.(2) The blind recognition of RS codes is researched. With no error, according to the relationship between RS codes and its binary derivative codes, RS codes can be recognized after identifying the generator matrix of binary derivative codes by reduced row echelon form. Under the condition of occurring error bits, based on the Galois Field Fourier Transformation (GFFT), RS codes can be identified by observing the pattern of consecutive zero coefficients of GFFT.(3) Since generator matrix is qualic-cyclic, the encoding speed of QC-LDPC codes can be improved. The thesis researches and implements two fast encoding algorithm from the aspect of hardware circuit:serial encoding and parallel encoding. Both of them have linear time complexity. For the serial encoding, its encoding time is proportional to the number of information bits. On the contrary, the encoding time of parallel encoding is proportional to the number of parity bits.(4) After introducing the Expectation-Maximization (EM) algorithm and belief propagation decoding algorithm, considering jointing dection and decoding, the thesis proposes the system model of parameter estimation for carrier synchronization in M-ary modulations with the help of LDPC codes.This method can estimate frequency offset and phase offset. Based on the system that exploits posterior probability of coded bits, which is produced by LDPC decoder, to estimate carrier synchronization parameters, the thesis derives the general formula of estimating frequency offset and phase offset. The thesis also verifies the proposed algorithm under the condition of BPSK and16-QAM.The simulation results show the proposed method can efficiently reduce the degradation casued by frequency offset and phase offset.