A new construction method of multilevel coded modulation with a good Euclidean minimum distance

For multilevel block codes with mutually independent binary component codes, Sayegh (1986) has shown optimum binary codes which maximize the minimum Euclidean distance. Our proposed multilevel codes, however, are constructed from mutually interdependent binary component codes. To investigate how interdependency should be composed for good minimum distance, the algebraic structures of the codes are discussed. Cyclic codes over Z_M for M-PSK presented by Piret (1995) can be constructed by the multilevel coding method. Comparing with these codes, furthermore, we can obtain better minimum distances. Such multilevel codes have the algebraic structure of a cyclic (additive) group over GF(M). The authors show the constellations of QPSK and 8-PSK with three mappings