Hybrid Non-Binary Repeated Polar Codes

Abstract

Concatenating the state-of-the-art codes at moderate rates with repetition codes has emerged as a practical solution deployed in various standards for ultra-low-power devices such as in Internet-of-Things (IoT) networks. In this paper, we propose a novel concatenation mechanism for such applications which need to operate at very low signal-to-noise ratio (SNR) regime. In the proposed scheme, the outer code is a hybrid polar code constructed in two stages, one with a binary kernel and another also with a binary kernel but applied over a binary extension field. The inner code is a non-binary multiplicative repetition code. This particular structure inherits low-complexity decoding structures of polar codes while enabling concatenation with an inner non-binary multiplicative repetition scheme. The decoding for the proposed scheme is done using cyclic redundancy check (CRC) aided successive cancellation list (SCL) decoder over additive white Gaussian noise (AWGN) and Rayleigh fading channels. Simulation results demonstrate that the proposed hybrid non-binary repeated polar code provides performance gain compared to a polar-repetition scheme with comparable decoding complexity.