CRC-Aided List Decoding of Convolutional and Polar Codes for Short Messages in 5G

TL;DR

This paper enhances short message decoding in 5G by optimizing CRC lengths and replacing polar codes with tail-biting convolutional codes, achieving better error performance and faster decoding.

Contribution

It introduces an optimized CRC length and a novel TBCC/CRC scheme that outperform standard 5G polar codes in error rate and decoding speed.

Findings

Optimized CRC length improves $E_b/N_0$ performance.

TBCC/CRC scheme surpasses 5G polar codes in FER.

Proposed method reduces decoding run time.

Abstract

This paper explores list decoding of convolutional and polar codes for short messages such as those found in the 5G physical broadcast channel. A cyclic redundancy check (CRC) is used to select a codeword from a list of likely codewords. One example in the 5G standard encodes a 32-bit message with a 24-bit CRC and a 512-bit polar code with additional bits added by repetition to achieve a very low rate of 32/864. This paper shows that optimizing the CRC length improves the $E_b/N_0$ performance of this polar code, where $E_b/N_0$ is the ratio of the energy per data bit to the noise power spectral density. Furthermore, even better $E_b/N_0$ performance is achieved by replacing the polar code with a tail-biting convolutional code (TBCC) with a distance-spectrum-optimal (DSO) CRC. This paper identifies the optimal CRC length to minimize the frame error rate (FER) of a rate-1/5 TBCC at a specific value of $E_b/N_0$. We also show that this optimized TBCC/CRC can attain the same excellent $E_b/N_0$ performance with the very low rate of 32/864 of the 5G polar code, where the low rate is achieved through repetition. We show that the proposed TBCC/CRC concatenated code outperforms the PBCH polar code described in the 5G standard both in terms of FER and decoding run time. We also explore the tradeoff between undetected error rate and erasure rate as the CRC size varies.