LDPC–Polar Code Comparison under 5G NR: Toward Hybrid Coding Schemes for 6G

¹ Engineering Sciences Laboratory (LSI), Multidisciplinary Faculty of Taza, Sidi Mohamed Ben Abdellah University, B.P. 1223, Taza Gare, Fes, Morocco, Email : This email address is being protected from spambots. You need JavaScript enabled to view it. , This email address is being protected from spambots. You need JavaScript enabled to view it. , This email address is being protected from spambots. You need JavaScript enabled to view it. , This email address is being protected from spambots. You need JavaScript enabled to view it.
² Laboratory of Mathematical and Informatics Engineering, UIZ, Agadir, 80000, Email : This email address is being protected from spambots. You need JavaScript enabled to view it.

Published online: 24 June 2026

Abstract

This article presents an in-depth analysis of the performance of Low-Density Parity-Check (LDPC) codes and polar codes as defined in the 5G NR standard, with a view to their use in 6G communication systems. Simulations were conducted in MATLAB by varying the block length and coding rate, and evaluating performance according to the criterion: the Bit Error Rate (BER). The decoders used are Normalized Min-Sum (NMS) for LDPCs and Successive Cancellation List (SCL) assisted by a Cyclic Redundancy Check (CRC) for polar codes.

In line with the theoretical results of Arikan and recent analyses, our simulations confirm that polar codes are particularly effective for short block lengths generally below 1700 bits making them ideal for URLLC applications. Conversely, LDPC codes, originally proposed by Gallager, demonstrate clear superiority for longer lengths. Notably, at a length of 1600 bits, LDPCs outperform polar codes in terms of BER, suggesting that the transition between the two performance regimes occurs near this limit. However, this superiority is not systematic: it depends heavily on the considered rate coding. These observations highlight a complementarity that can be exploited in adaptive hybrid architectures, which are essential for meeting the diverse requirements of 6G.