Efficient algorithms for iterative decoding based on EXIT analysis

Abstract

Two classes of codes,turbo codes and low-density parity-check (LDPC) codes, show the outstanding performance with iterative decoding scheme. The logarithmic maximum a $\It{posteriori}$ (log-MAP) algorithm [1] and $\It{sum-product}$ algorithm (SPA) [2] are widely used for the optimum decoding scheme of turbo and LDPC codes, respectively. Because of high computational complexity of the optimum decoding schemes, the simplified schemes, max-log-MAP (MLMAP) and min-sum algorithm (MSA), are proposed, but they have significant performance degradations. Several types of modication for the simplified schemes, such as enhanced max-log-MAP (EMLMAP) [3] and normalized MSA [4], are suggested to improve performance of the simplified schemes. In this thesis, we investigate another modification for the simplified schemes by using extrinsic information transfer characteristics (EXIT) analysis. For turbo decoding, we propose modified EMLMAP algorithm which uses variable scaling-factor (VSF) $\hat{\alpha}$. The $\hat{\alpha}$ maximizing the mutual information of extrinsic messages generated from MLMAP algorithm is found by using the EXIT analysis. The improved convergence speed and performance of the modified EMLMAP algorithm applied the $\hat{\alpha}$ are shown by using computer simulations. For decoding of LDPC codes, we propose hybrid belief-propagation (hybrid-BP) algorithm which performs switching implementation from SPA to MSA. To find the optimum switching points $\hat{\eta}$, the EXIT characteristic -curve (EXIT-CC) of MSA should be analyzed. Since the output of MSA is non-Gaussian, the exact EXIT-CC of MSA is not produced directly. For drawing the exact EXIT-CC of MSA, we use correcting factor $\gamma$ which affects distribution of messages sent from variable node. By adopting the $\gamma$, the EXIT-CC of MSA can be obtained under the Gaussian approximation (GA). Using the analyzed the optimum switching points, the performance and efficiency of the hybrid-BP algorith...