Four-dimensional trellis-coded modulation using sphere packing non-cubic constellations.

In the paper, we introduce the 8-state trellis-coded modulation (TCM) scheme using sphere packing four-dimensional (4D) non-cubic constellations on the basis of a novel set-partitioning (SP) method. Sphere packing four-dimensional formats have a higher asymptotic power efficiency (APE) because the spatial arrangement of constellation points is more dense. The scheme can further alleviate the contradiction between spectral efficiency (SE) and APE in 4D modulation format. The SP process of 4D non-cubic constellations is completed in the condition that the minimum Euclidean distance between the constellation points and the number of nearest neighbors are adequately considered. We compared these 4D TCM formats to their corresponding 4D formats (i.e., dicyclic4_16, b4_32, b4_64, SP-QAM4_128 and 256-D 4) in the 800 km standard single-mode fiber (SSMF) transmission system. Through measurements of bit error rate (BER) performance, at the BER = 1 × 10−3, the coding gains are 5.7 dB, 3.8 dB, 3.6 dB, 3.9 dB and 4.1 dB respectively. [ABSTRACT FROM AUTHOR]