This correspondence presents the switch strategies for switch-type hybrid hard decision decoding algorithms for regular low-density parity-check (LDPC) codes. After the piecewise analysis of extrinsic information transfer functions for Gallager decoding algorithm B (GB), the normalized switch scheme (NSS), for which the majority-based algorithms and GB are two examples, is proposed. Then, several other examples of NSSs are presented and their convergence properties are analyzed based on the extrinsic information transfer (EXIT) functions. In simulations, the proposed NSSs show meaningful performance improvements and less sensitivity to channel parameter underestimations compared with GB for small and moderate block length codes.

Besides the traditional accesses to accelerate the convergence of the LMS algorithm, such as step-size control and input signal decorrelation, tap-length control is an emerging technique and attracts more and more attention. Many tap-length control schemes are proposed and most of them are based on the gradient search method. The sufficient condition for tap-length gradient adaption is obtained based on the assumption of white Gaussian input. The analysis reveals that two requirements should be satisfied when using the gradient method to search for optimum tap-length. One is that the unknown impulse response has a decay envelope, while the other requires that the number of the tap difference should be selected carefully.

This letter presents a novel variable-length least mean square algorithm, whose filter length is adjusted dynamically along the negative gradient direction of the squared estimation error. Compared with other variable-length algorithms, the proposed algorithm has faster convergence and more robust performance in diverse environments.

This letter analyzes the mean-square convergence of a deficient-length least mean-square adaptive filter whose length is less than that of the unknown system and proves that filter length and the envelope of impulse response are the important factors in convergence rate control. For the impulse response with an exponential decay envelope, which covers a large set of physical systems, e.g., acoustic echo path, an optimal filter length sequence is figured out to achieve the fastest convergence. The simulations of an exact exponential decay envelope and of a real-life echo path in a car environment are performed via computer, and the results validate our analysis well.