# Improving Decodability of Polar Codes by Adding Noise
## 1 Introduction  
The development of fifth generation (5G) communication technology is driven not only by the requirements of faster and higher-capacity extreme mobile broadband (eMBB) applications, but also by the rapidly evolving area of Internet of Things (IoT) that needs a massive connectivity of devices with ultra-reliable and ultra-low-latency connectivity over Internet Protocol [1; 2; 3; 4]. Channel coding is an integral part of any communication system, which plays an important role in meeting the system reliability requirements [5; 6; 7]. A prominent feature of 5G new radio (NR) is the adoption of a new class of error correction codes, i.e., polar codes, for control channels [8; 9]. Future wireless communication technologies are proliferating in the connection between people and things, and their scenarios will place new requirements on the channel coding performances [10]. Polar codes were proposed by [PERSON] [11] in 2009, who also originally indicated the symmetry of polar codes for binary-input discrete memoryless channels (B-DMCs). With the symmetry, the output vector can be divided into equivalence classes in terms of their transition probabilities. Based on the channel polarization theory that entails channel combining and channel splitting, this new coding scheme is capacity achieving as opposed to just capacity approaching in symmetric B-DMCs with efficient construction and low complexity [12; 13]. Several decoding algorithms have recently been developed for polarcodes in the literature [14; 15; 16; 17; 18; 19; 20; 21]. The successive cancellation (SC) algorithm proposed by [PERSON] [11] is an effective method for decoding polar codes. To reduce the decoding latency and algorithmic complexity of the SC decoder, a simplified successive cancellation (SSC) decoder was proposed in [14]. In [15], [PERSON] and [PERSON] proposed the successive cancellation list (SCL) decoder to tackle the problem that only one decoding path was reserved for SC decoding, which may lead to the loss of the correct path. CRC (cyclic redundancy check)-aided decoding schemes were proposed to improve the performance of polar codes in [16]. In addition, the recent development of deep learning methods provides a new insight into the decoding of linear codes [22; 23; 24; 25; 26; 27]. However, deep-learning-based channel decoding is doomed by the curse of dimensionality, in which the learning process is limited by the complexity as the number of information bits increases. In the signal processing area, it can be shown that the performance of a suboptimal detector may be improved by adding noise to the received data under certain conditions [28; 29]. Inspired by this method, some researchers have investigated how to improve the decoding performance of a (suboptimal) decoder by adding noise. In [30], a belief propagation list (BPL) decoding algorithm was proposed, in which adding a small amount of noise enables the decoder to handle non-convergent errors. A dynamic perturbation decoding method for Polar-CRC concatenation codes through dynamically controlling the interference noise was proposed in [31]. In [32], a generalized framework for multi-round BP decoding with input perturbation for short low-density parity-check (LDPC) codes was proposed, where the perturbation is done iteratively on a few symbols to widen the search space. In [33], a CRC-assisted perturbation decoding algorithm for polar codes was proposed, which is called the PB-SSC decoding algorithm in this paper. When the CRC check of the SSC decoder fails, the PB-SSC decoding algorithm can provide multiple possible candidate vectors for re-decoding by adding disturbance noises. However, the performance gain achieved by the PB-SSC decoding algorithm is limited. A decoding algorithm for polar codes based on the perturbation with a convolution neural network (CNN) was proposed in [34].