Spectral Comb Shaping by Polar Codes

2025-06-16

AI Summary

To address communication robustness under periodic spectral interference, this paper proposes a polar code information-bit indexing method that actively constructs a comb-shaped spectrum under BPSK modulation—i.e., enforcing uniformly spaced nulls and notches in the frequency domain to inherently avoid interfered bands. This work is the first to deeply integrate polar code construction theory with spectral shaping, transcending the traditional coding paradigm focused solely on bit-error rate (BER) performance. Additionally, a BER compensation mechanism is designed to mitigate the signal-to-noise ratio (SNR) loss induced by comb-shaped spectral shaping in additive white Gaussian noise (AWGN) channels. Simulation results demonstrate that, under composite periodic-interference-plus-AWGN channels, the proposed scheme achieves significant SNR gains over standard polar codes—up to 2.1 dB—validating both its interference resilience and recoverability of BER performance.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Search and Optimization: Combinatorial Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Assisted, interactive, and conversational search

Abstract

A scheme to select information indices in polar codes is proposed to form signals with spectral comb shapes under BPSK modulation, whereby the signal could be separated from periodic interference in spectrum. By selecting proper indices to load information bits in polar coding, a spectral comb shape signal is formed, which has periodic zeros and notch bands uniformly distributed in its frequency spectrum. Furthermore, to mitigate the negative impact of proposed polar code on the AWGN performance, a scheme termed error performance enhancement scheme is proposed, whereby the performance loss under AWGN noise could be alleviated. Numerical results are given under periodic interference and AWGN noise, indicating that a considerable signal-to-noise power ratio (SNR) gain is accomplished in comparison with conventional polar codes.

Problem

• Design polar codes to create spectral comb-shaped signals
• Separate signals from periodic interference in spectrum
• Enhance error performance under AWGN noise

Innovation

• Polar codes shape spectral combs via index selection
• Error enhancement scheme improves AWGN performance
• Comb-shaped signals separate from periodic interference