This episode continues the work of the previous episode by examining the methods used to convert between decimal and binary and vice versa. We also take a look at the effects of shifting the bits of a binary number both left and right and how those operations can be used to simulate multiplication and division. Oh, and since we will be discussing a lot of different numbers, it couldn’t hurt to have a piece of paper and a pencil close by.

Adaptive modulation is widely employed to improve spectral e ciency. To date, square signal constellations have been used for adaptive modulation. In this disser- tation, triangular constellations are considered for this purpose. Triangle quadrature amplitude modulation (TQAM) for both power-of-two and non-power-of-two mod- ulation orders is examined. A technique for TQAM mapping is presented which is better than existing approaches. A new type of TQAM called semi-regular TQAM (S-TQAM) is introduced. Bit error rate expressions for TQAM are derived, and the detection complexity of S-TQAM is compared with that of regular TQAM (R-TQAM) and irregular TQAM (I-TQAM). The performance of S-TQAM over additive white Gaussian noise and Rayleigh fading channels is compared with that of R-TQAM and I-TQAM. The construction of ternary convolutional codes (TCCs) for ternary phase shift keying (TPSK) modulation is considered. Tables of non-recursive non-systematic TCCs with maximum free distance are given for rates 1=2, 1=3 and 1=4. The conver- sion from binary data to ternary symbols is investigated. The performance of TCCs with binary to ternary conversion using TPSK is compared with the best BCCs using binary phase shift keying (BPSK). / Graduate