POLAR CODED SIGNALING SIMULATION on a WINDOWS 11 PC

POLAR BINARY CODES & SUCCESSIVE CANCELLATION DECODING: Windows 11 Personal Computer-Based Simulations of Polar Coded Signaling over a Memoryless Channel (MLC)

by Darrell A. Nolta
December 8, 2025

The simulated Bit Error Rate (BER) [Bit Error Probability (P_b) ] results for the N = 256 K = 128 and N = 512 K = 256 5G NR Polar Coded BPSK Signaling over a Memoryless Channel (MLC) are shown below in Figure 1, 2, and 3.

For this Channel Polarization study, we have two cases: 1) using Consecutive Non-UPO (UPO: Universal Partial Order/Universal Reliability Sequence) Bit-Coordinate Channel-to-Frozen Bit assignment; and 2) using the 5G NR UPO standard to specify the UPO Bit-Coordinate Channel-to-Frozen Bit assignment.

These N = 256 & N = 512 5G NR Polar Code results were obtain from AdvDCSMT1DCSS (T1) Version 2 5GNR LDPCC PC simulations that were run on a Windows 11 Personal Computer. The other BER results (UnCoded, N = 8, 64, & 128 5G NR Polar Codes) were obtained from T1 V2 5G NR LDPCC PC based simulations that were run on a Windows 7 Personal Computer.

From Figure 1, 2, and 3, one can clearly observe the 'Channel Polarization' phenomenon.

In Figure 3 (the case of the use of the 5G NR UPO standard Bit-Coordinate Channel-to-Frozen Bit assignment), we observe that as we increase the CodeWord Length (BlockLength) N, the stronger the Channel Polarization phenomenon becomes (i.e,, the BER curve's E_b/N₀ value corresponding to P_b zero value shifts toward the small portion of the E_b/N₀ dB axis).



Figure 1. Bit Error Probability for Successive Cancellation Algorithm of 5G NR Polar Coded (N = 256, & 512; Non-UPO & UPO Bit-Coordinate Channel-to-Frozen Bit Assignment) BPSK Signaling over a Coherent Memoryless Channel (MLC) with AWGN.



Figure 2. Bit Error Probability for Successive Cancellation Algorithm of 5G NR Polar Coded (N = 8, 64, 128, 256, & 512; Non-UPO Bit-Coordinate Channel-to-Frozen Bit Assignment) BPSK Signaling over a Coherent Memoryless Channel (MLC) with AWGN.



Figure 3. Bit Error Probability for Successive Cancellation Algorithm of 5G NR Polar Coded (N = 8, 64, 128, 256, & 512; UPO Bit-Coordinate Channel-to-Frozen Bit Assignment) BPSK Signaling over a Coherent Memoryless Channel (MLC) with AWGN.

NOTE: This section is Under-Edit if necessary: Construction began on December 8, 2025 and was finished on December 17, 2025.