A quantum error-correcting code for single deletion errors is provided. To the authors’ best knowledge, this is the first code for deletion errors.

We numerically evaluate Achievable Information Rate (AIR) and Bit Error Rate (BER) performances of Probabilistic Amplitude Shaping (PAS), eight-dimensional modulation with Bit-Interleaved Coded Modulation Iterative Detection (BICM-ID), and conventional two-dimensional 16QAM (Quadrature Amplitude Modulation) for future high-speed optical communication systems. We confirm that end-to-end BER performances of three modulation formats are almost identical at a same transmission rate when the error correction is used once, and the iterative detection makes the performance of eight-dimensional modulation format better. Further, we verify the BER error-free conditions can be estimated by Normalized General Mutual Information (NGMI) for each modulation format.

This letter presents an effective Q factor formula for self-resonant spherical surface antennas. The self-resonant lossless Q factor and radiation efficiency calculated using spherical wave expansion provide an approximated expression for the effective Q factor. The resultant effective Q factor is larger than that of the infinitesimal loop antenna and smaller than that of the infinitesimal dipole antenna. Comparison of the result with the Q factor of spherical helix antennas has shown good agreement. A simple estimation formula can help design a small spherical helix antenna.

This letter investigates the theoretical system capacity of multi-user multiple-input multiple-output (MU-MIMO) orthogonal frequency division multiplexing (OFDM) Tomlinson-Harashima precoding (THP) in the presence of terminal mobility. Considering that MU-MIMO THP has been adopted for OFDM-based mobile broadband systems, analyzing the effects of time-selective fading and the modulo loss peculiar to THP on system capacity is essential. In this study, we theoretically derive both the multi-user interference (MUI) and inter-carrier interference (ICI) resulting from terminal mobility and incorporate these into the modulo loss analysis based on the mod-Λ channel. The theoretical results obtained by the proposed analysis are compared with those of linear precoding, which demonstrates the applicability of THP to OFDM-based mobile broadband systems.