A Simplified Gaussian Approximation Algorithm For Polar Codes

Gaussian approximation (GA) is widely used for constructing polar codes. However, due to the complex integration required in exact GA (EGA) algorithm, the computational complexity will increase exponentially with the polarization levels. Though the conventional approximate GA (AGA) succeeds in reducing the computational complexity, it results in a disastrous loss in the performance of frame error ratio (FER) when the code length goes long. In this paper, we discover some estimable features in the derivatives of GA algorithm. These features reveal the possibility and feasibility to simplify GA by utilizing curve estimation. Therefore, we then design new piecewise functions to approximate the derivatives and conclude some criteria for GA simplification. Guided by new derivative functions and proposed criteria, we design a new GA algorithm, named simplified GA (SGA). Numeric and simulation results show that SGA reduces the computational complexity and at the same time, guarantees remarkable performance with a long code length.