CRISP: CURRICULUM BASED SEQUENTIAL NEURAL DECODERS FOR POLAR CODE FAMILY

Abstract

Polar codes are widely used state-of-the-art codes for reliable communication that have recently been included in the 5 th generation wireless standards (5G). However, there remains room for the design of polar decoders that are both efficient and reliable in the short blocklength regime. Motivated by recent successes of data-driven channel decoders, we introduce a novel CurRIculum based Sequential neural decoder for Polar codes (CRISP) 1 . We design a principled curriculum, guided by information-theoretic insights, to train CRISP and show that it outperforms the successive-cancellation (SC) decoder and attains near-optimal reliability performance on the Polar(32, 16) and Polar(64, 22) codes. The choice of the proposed curriculum is critical in achieving the accuracy gains of CRISP, as we show by comparing against other curricula. More notably, CRISP can be readily extended to Polarization-Adjusted-Convolutional (PAC) codes, where existing SC decoders are significantly less reliable. To the best of our knowledge, CRISP constructs the first data-driven decoder for PAC codes and attains near-optimal performance on the PAC(32, 16) code.

1. INTRODUCTION

Error-correcting codes (codes) are the backbone of modern digital communication. Codes, composed of (encoder, decoder) pairs, ensure reliable data transmission even under noisy conditions. Since the groundbreaking work of Shannon (1948) , several landmark codes have been proposed: Convolutional codes, low-density parity-check (LDPC) codes, Turbo codes, Polar codes, and more recently, Polarization-Adjusted-Convolutional (PAC) codes (Richardson & Urbanke, 2008) . In particular, polar codes, introduced by Arikan (2009), are widely used in practice owing to their reliable performance in the short blocklength regime. A family of variants of polar codes known as PAC codes further improves performance, nearly achieving the fundamental lower bound on the performance of any code at finite lengths, albeit at a higher decoding complexity (Arıkan, 2019) . In this paper, we focus on the decoding of these two classes of codes, jointly termed the "Polar code family". The polar family exhibits several crucial information-theoretic properties; practical finite-length performance, however, depends on high complexity decoders. This search for the design of efficient and reliable decoders for the Polar family is the focus of substantial research in the past decade. (a) Polar codes: The classical successive cancellation (SC) decoder achieves information-theoretic capacity asymptotically, but performs poorly at finite blocklengths compared to the optimal maximum a posteriori (MAP) decoder (Arıkan, 2019). To improve upon the reliability of SC, several polar decoders have been proposed in the literature (Sec. 6). One such notable result is the celebrated Successive-Cancellation-with-List (SCL) decoder (Tal & Vardy, 2015) . SCL improves upon the reliability of SC and approaches that of the MAP with increasing list size (and complexity). (b) PAC codes: The sequential "Fano decoder" (Fano, 1963) allows PAC codes to perform informationtheoretically near-optimally; however, the decoding time is long and variable (Rowshan et al., 2020a) . Although SC is efficient, O(n log n), its performance with PAC codes is significantly worse than that of the Fano decoder. Several works (Yao et al., 2021; Rowshan et al., 2020b; Zhu et al., 2020; Rowshan & Viterbo, 2021b; a; Sun et al., 2021) propose ameliorations; it is safe to say that constructing efficient and reliable decoders for the Polar family is an active area of research and of 1 Source code available at the following link. 1

