Soft output detection for MIMO systems using binary polar codes

Abstract

Polar codes are proven capacity-achieving and are shown to have equivalent or even better finite length performance than turbo/LDPC codes under some improved decoding algorithm over the Additive White Gaussian Noise (AWGN) channels. Polar coding is based on the so-called channel polarization phenomenon induced by a transform over the underlying binary-input channel. The channel polarization is found to be universal in many signal processing problems and is applied to the coded modulation schemes. In this paper, a small length polar, encoded for a MIMO (Multiple-Input Multiple-Output) systems with soft output MMSE-SIC (Minimum Mean Square Error-Successive Cancellation) detection, is applied to improve the coded performance while reducing the complexity. In order to prove this theory, we compare the proposed MMSE-SIC BER to Zero Forcing (ZF) and Maximum Likelihood (ML) by using 2*2 MIMO systems into Rayleigh channel with BPSK (Binary Phase-Shift Keying) modulation. Simulation results show that MMSE-SIC complexity is lower than the two others detections. We show that the performance of the proposed approach using polar code (128, 64) at 10−2 BER (Bit Error Rate) is around 3dB i.e. 0,66% compared to the optimal ML, while ZF performance is the worst.