Performance Improvement of Chaos-Coded Modulation Method with Non-Binary Error Correction Codes

With the recent increase in mobile devices and Internet of Things (IoT), ensuring security against eavesdropping has become crucial. We focus on physical-layer security and propose chaos-coded modulation (CCM), which encrypts modulation in the physical layer. CCM is a type of symmetric key encryption method that achieves confidentiality against eavesdroppers by convolving multiple bits and the shared key during modulation, while enabling legitimate receivers to obtain coding gain. However, owing to the encryption in the CCM, in principle, no correlation exists between the Hamming distance of the bit sequence and the Euclidean distance of the modulated symbol sequence. Therefore, the bit labeling of CCM is imperfect when compared to the Gray labeling of linear modulation, and the log-likelihood ratio obtained at the receiver is degraded. Consequently, the CCM has significantly limited performance improvement when concatenated with external error correction codes (ECCs), despite its coding gain being uncoded. Additionally, performance degradation increases as the modulation rate increases. To solve this problem, we propose a CCM with a non-binary ECC that matches the code length to the CCM instead of a conventional binary ECC, thereby addressing the aforementioned demodulation problem and improving error-rate performance. Numerical results show that the CCM with non-binary low-density parity-check (NB-LDPC) codes with a code length of 1024 and a coding rate of 0.5 achieves a gain of 1.5 dB at a bit error rate of 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−4</sup> compared to binary phase-shift keying and a gain of 2.9 dB compared to the CCM with binary LDPC codes under the same conditions. Furthermore, the NB-LDPC codes are more effective when the modulation rate is two or higher.