The Performance Comparison Between PA-I Codes And Regular LDPC Codes

Product accumulate (PA) codes are serial concatenation of a single-parity-check-based product code, an interleaver, and a recursive convolutional code. PA codes have regular structure, good performance, low complexity and flexible rate adaptation for all rates above 1/2. PA codes include PA-I codes and PA-II codes which are special cases of PA-I codes.This thesis mainly annlyzes PA-I codes.Recently, it has been found that low density parity check (LDPC) codes have a wider application for their closer distance from Shannon limit and lower decoding complexity than Turbo codes. As a result, LDPC codes have been considered as one of the good choices for channel coding in the next generation wireless communication system and satellite communicationsystem. And it was pointed out that LDPC codes will replace RS codes in the future storage devices. Therefore, it is significant for performances of PA codes and LDPC codes to be analyzed and compared.Based on the comprehension of Tanner graph and sum-product algorithm, this thesis analyzes the encoding and decoding algorithm of PA-I codes and LDPC codes. With a novel tool named EXIT chart, the thresholds of PA-I codes and regular LDPC codes are investigated to prove theoretically that PA-I codes have better convergent performance. The performances of both PA-I codes and regular LDPC codes with sum-product decoding algorithm and min-sum decoding algorithm are simulated under additive white Gaussian noise (AWGN) channels. Simulation results at medium rate (1/2 rate) and high rate (7/8 rate) show that with the increasing of codeword length, the performances of PA-I codes gradually catch up with and even exceed regular LDPC codes, which is consistent with the theoretical analysis. The decoding complexities of PA-I codes and regular LDPC codes are alsocompared and it is found that the decoding complexity of PA-I codes is lower than that of regular LDPC codes with sum-product decoding algorithm. Moreover, the encoding complexity of PA-I codes is proportional with codeword length N , but the encoding complexity of regular LDPC codes is proportional with N 2. And the encoder of a PA-I code is cheap for implementing since it does not require additional storage of a generator matrix needed for a LDPC code. Meanwhile PA-I codes own rate/length adaptation which regular LDPC codes do not have.Based on these results, it could be foreseen that PA-I codes will be a good alternative to regular LDPC codes in future digital communication systems at rates above 1/2.