Improving Polar Codes by Spatial Coupling

In this paper, spatial coupling technique is used to improve the error-correcting performance of finite length polar codes. Polar codes are considered as base codes of coupling. Two types of spatial-coupling methods are investigated. For the first coupling method, some message bits of a polar base code at each coupling position are used as frozen bits of one-side adjacent polar base code. For the second spatial-coupling method, multiple polar codes are associated by combining message bit blocks of adjacent coupling positions with modular-two addition. Simulation results show that, with a little extra iteration complexity, the two types of spatially coupled polar codes can provide better error-correcting performance than original polar codes. When setting the coupling ratio at 0.33 and coupling pattern as Uncertain-Certain, the first spatial-coupling method provides the best performance output. The second spatial-coupling method with coupling width 3 provides better performance than that with coupling width 2. Furthermore, the first spatial-coupling method with short message block length provides better decoding performance, and the second method with large message block length performs better.