Performance and Convergence Analysis of Improved MIN-SUM Iterative Decoding Algorithm

摘要

Density evolution has recently been used to analyze the iterative decoding of Low Density Parity Check (LDPC) codes, Turbo codes, and Serially Concatenated Convolutional Codes (SCCC). The density evolution technique makes it possible to explain many characteristics of iterative decoding including convergence of performance and preferred structures for the constituent codes. While the analytic density evolution methods were applied to LDPC codes, the simulation based density evolution methods were used for Turbo codes and SCCC due to analytic difficulties. In this paper, several density evolution ideas in the literature are used to analyze common code structures and it is shown that those ideas yield consistent results. In order to do that, we derive expressions for density evolution of SCCC with a simple 2-state constituent code. The analytic expressions are based on the sum-product and min-sum algorithms, and the thresholds are evaluated for both message passing algorithms. Particularly, for the min-sum algorithm, the density evolution with Gaussian approximation is derived and used to analyze the effect of scaling soft information. The scaling of extrinsic information slows down the convergence of soft information or avoids an overestimation effect of it and results in better per- formance, and its gain is maximized in particular constituent codes. Similar approaches are made for LDPC code. We show that the scaling gain is noticeable in the LDPC code as well. This scaling gain is analyzed with both density evolution and simulation performance. The expected scaling gain by density evolution matches well with the achievable scaling gain from simulation results. These results can be extended to the irregular LDPC codes based on the degree distribution for the min-sum algorithm. All density evolution algorithms used in this paper are based on the Gaussian approximation for the exchanged messages.