Low-Complexity Probability Shaping Scheme Based on Energy-Tier Template Insertion

In this paper, we propose the energy-tier template insertion shaping (ETTIS) probabilistic shaping algorithm, which performs shaping and de-shaping through preset templates and simple bit insertion/deletion operations, thereby significantly reducing the algorithmic complexity. The ETTIS algorithm effectively mitigates the Hamming distance contraction problem commonly observed in traditional probabilistic shaping algorithms and exhibits excellent compatibility, allowing seamless integration with standard forward error correction coding and interleaving algorithms. Moreover, the ETTIS framework utilizes predefined symbol components in the shaping templates to implicitly introduce pilot symbols, enabling real-time estimation of channel gain and noise variance without additional bandwidth overhead. Experimental and simulation results show that, at the same bit rate, the proposed scheme achieves 0.4–0.6 dB performance gains under 16-quadrature amplitude modulation (QAM) and 64-QAM modulation formats, respectively. Compared with other state-of-the-art algorithms, ETTIS attains comparable performance while maintaining significantly lower complexity. During decoding, the absolute deviation of the estimated noise bit error rate remains below 0.75%. These features make ETTIS a promising solution for high-throughput and cost-sensitive optical interconnect systems.