Polar Coded Repetition

Constructing efficient low-rate error-correcting codes with low-complexity encoding and decoding has become increasingly important for applications involving ultra-low-power devices such as Internet-of-Things (IoT). To this end, schemes based on concatenating the state-of-the-art codes at moderate rates with repetition codes have emerged as practical solutions deployed in various standards. In this paper, we propose a novel mechanism for concatenating outer polar codes with inner repetition codes which we refer to as polar coded repetition. More specifically, we propose to transmit a slightly modified polar codeword by deviating from Arikan's standard 2x2 Kernel in a certain number of polarization recursions at each repetition block. We show how this modification can improve the asymptotic achievable rate of the standard polar-repetition scheme, while ensuring that the overall encoding and decoding complexity is kept almost the same. The achievable rate is analyzed for the binary erasure channel (BEC) and additive white Gaussian noise (AWGN) channel. Moreover, we show that the finite-length performance of the polar coded repetition scheme under cyclic redundancy check (CRC) aided successive cancellation list (SCL) decoder over AWGN channel is better than the uncoded polar repetition scheme at the cost of a slight increase in decoding complexity. We also compare the proposed scheme, in terms of performance and complexity, with other low-rate solution based on polar codes in the literature.

Automated summary

This paper proposes a novel mechanism for concatenating outer polar codes with inner repetition codes, called polar coded repetition. By slightly modifying the polar codeword, the achievable rate of the standard polar-repetition scheme can be improved while maintaining overall encoding and decoding complexity. The performance of the polar coded repetition scheme is analyzed for the binary erasure channel (BEC) and additive white Gaussian noise (AWGN) channel, showing better finite-length performance compared to the uncoded polar repetition scheme at the cost of slightly increased decoding complexity. The proposed scheme is also compared with other low-rate solutions based on polar codes in terms of performance and complexity.