PAC Code Rate-Profile Design Using Search-Constrained Optimization Algorithms

TL;DR

This paper tackles designing rate profiles for polarization-adjusted convolutional (PAC) codes under sequential Fano decoding by introducing a search-constrained optimization framework that leverages polarization of the cutoff rate. The authors propose a dynamic rate-profile optimization (DRPO) method with an adaptive MLUBV-based fitness function and a polarization-guided search space, enabling parallel evaluation and dramatic reductions in large-list decoding calls while preserving error-correction performance. Results for PAC$(256,128)$, $(64,32)$, $(128,105)$, and $(64,51)$ demonstrate substantial improvements in decoding complexity (ANV) with competitive FER performance compared to state-of-the-art approaches, often outperforming or matching existing RM-based and GA-based constructions. The approach offers a practical pathway to ultra-reliable, low-latency communications by producing high-rate, short PAC codes that maintain near-optimal performance with significantly reduced computational burden during design and decoding.

Abstract

In this paper, we introduce a novel rate-profile design based on search-constrained optimization techniques to assess the performance of polarization-adjusted convolutional (PAC) codes under Fano (sequential) decoding. The results demonstrate that the resulting PAC code offers much reduced computational complexity compared to a construction based on a conventional genetic algorithm without a performance loss in error-correction performance. As the fitness function of our algorithm, we propose an adaptive successive cancellation list decoding algorithm to determine the weight distribution of the rate profiles. The simulation results indicate that, for a PAC(256, 128) code, only 8% of the population requires that their fitness function be evaluated with a large list size. This represents an improvement of almost 92% over a conventional evolutionary algorithm. For a PAC(64, 32) code, this improvement is about 99%. We also plotted the performance of the high-rate PAC(128, 105) and PAC(64, 51) codes, and the results show that they exhibit superior performance compared to other algorithms.

Figures (6)

• Figure 1: Fitness function values of a PAC$(256, 128)$ code for different iterations.
• Figure 2: Performance comparison of PAC$(256, 128)$ codes.
• Figure 3: Fitness function value of a PAC$(64, 32)$ code for different iterations.
• Figure 4: Performance comparison of PAC$(64, 32)$ codes.
• Figure 5: Performance comparison of $(128, 105)$ codes.