Abstract

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 Arıkan’s standard <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2 \times 2$ </tex-math></inline-formula> 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.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.