Ultra-Low Complexity Communication Algorithms Based on (n, n(n-l), n-l) PGCs

This paper first defined the new concept of ultralow complexity algorithm (ULCA) which helps to find and design 1 millisecond algorithms so as to support the future applications of ultra-reliability low-latency communications (URLLC) promoted by 5G. Then it demonstrates the existence of the communication ULCA by introducing an original modulation scheme. This scheme is a new family of ndimensional high-order dual-domain modulation signal permutation array constellations (PAC). The PAC can generate the ULCA, including mapping encoding, decoding and detection algorithms. The time complexity of these algorithms can be counted by the number of clock periods of basic unit circuits instead of the number of additions and multiplications. The best simulation results of the P ACs are 2.0 dB better than the BPSK modulation at the WER of 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−9</sup>.