Binary component codes construction of multilevel block modulation codes with a large minimum Euclidean distance

In multilevel block modulation codes for QPSK and 8-PSK modulation, a construction of binary component codes is given. These codes have a good minimum Euclidean distance by using different forms of the dependency properties of the binary component codes. Interdependency among component codes is formed by using the binary component subcodes which are derived by the coset decomposition of the binary component codes. The algebraic structures of the codes are investigated to find out how interdependency among component codes gives a good minimum Euclidean distance. First, it is shown that cyclic codes over Z(M) For M-PSK (M = 4, 8), where the coding scheme is given by Piret, can be constructed by forming specific interdependency among binary component codes for proposed multilevel coding method. Furthermore, it is shown that better minimum Euclidean distance than above can be obtained by modifying the composition of interdependency among binary component codes. These proposed multilevel codes have algebraic structure of additive group and cyclic property over GF(M). Finally, error performances are compared with those of some code's reference modulation scheme for transmitting the same number of information bits.