Geon Choi

Geon Choi, Namyoon Lee

In this paper, we introduce a novel class of pre-transformed polar codes, termed as deep polar codes. We first present a deep polar encoder that harnesses a series of multi-layered polar transformations with varying sizes. Our approach to encoding enables a low-complexity implementation while significantly enhancing the weight distribution of the code. Moreover, our encoding method offers flexibility in rate-profiling, embracing a wide range of code rates and blocklengths. Next, we put forth a low-complexity decoding algorithm called successive cancellation list with backpropagation parity checks (SCL-BPC). This decoding algorithm leverages the parity check equations in the reverse process of the multi-layered pre-transformed encoding for SCL decoding. Additionally, we present a low-latency decoding algorithm that employs parallel-SCL decoding by treating partially pre-transformed bit patterns as additional frozen bits. Through simulations, we demonstrate that deep polar codes outperform existing pre-transformed polar codes in terms of block error rates across various code rates under short block lengths, while maintaining low encoding and decoding complexity. Furthermore, we show that concatenating deep polar codes with cyclic-redundancy-check codes can achieve the meta-converse bound of the finite block length capacity within 0.4 dB in some instances.

Geon Choi, Jeonghun Park, Nir Shlezinger et al.

Simultaneous localization and mapping (SLAM) is a method that constructs a map of an unknown environment and localizes the position of a moving agent on the map simultaneously. Extended Kalman filter (EKF) has been widely adopted as a low complexity solution for online SLAM, which relies on a motion and measurement model of the moving agent. In practice, however, acquiring precise information about these models is very challenging, and the model mismatch effect causes severe performance loss in SLAM. In this paper, inspired by the recently proposed KalmanNet, we present a robust EKF algorithm using the power of deep learning for online SLAM, referred to as Split-KalmanNet. The key idea of Split-KalmanNet is to compute the Kalman gain using the Jacobian matrix of a measurement function and two recurrent neural networks (RNNs). The two RNNs independently learn the covariance matrices for a prior state estimate and the innovation from data. The proposed split structure in the computation of the Kalman gain allows to compensate for state and measurement model mismatch effects independently. Numerical simulation results verify that Split-KalmanNet outperforms the traditional EKF and the state-of-the-art KalmanNet algorithm in various model mismatch scenarios.