Study of Polarization-Driven Shortening for Polar Codes Designed with the Gaussian Approximation

Abstract: This paper presents a polarization-driven (PD) shortening technique for the design of rate-compatible polar codes. The proposed shortening strategy consists of reducing the generator matrix by relating its row index with the channel polarization index. We assume that the shortened bits are known by both the encoder and the decoder and employ successive cancellation (SC) for decoding the shortened codes constructed by the proposed PD technique. A performance analysis is then carried out based on the Spectrum Distance (SD). Simulations show that the proposed PD-based shortened polar codes outperform existing shortened polar codes.