The techniques of the geometry of numbers, especially the Minkowski-Hlawka theorem, are used to modify Shannon's existence proof for optimal channel codes, so that the modified proof applies specifically to lattice codes. The resulting existence proof states that there exist lattice codes which satisfy Shannon's bound to within the factor 4, and hence match the reliability exponent and critical rate bounds which Shannon derived for optimal codes with unspecified structure. Therefore, it is demonstrated that optimal codes need not be random, but rather that some of them have structure, e.g. the structure of a lattice code.>

A construction of the Gosset lattice is considered that has practical advantages over other constructions of the same lattice. Codes derived from this construction have been shown to exhibit a null at DC in their baseband spectrum. A two-stage approach to the demodulation of this construction of the Gosset lattice is discussed. This demodulator consists of an initial stage which may declare erasures and a secondary stage designed to correct erasures. A study of erasure events is made and then used to reduce the number of steps in the second-stage correction algorithm. While the overall demodulator is somewhat more complex than a straight forward maximum-likelihood demodulator designed for this construction, the present structure has the advantage of greater speed.>

A new technique for achieving system synchronization to the switching satellite is described; this technique requires only three earth stations, designated as control stations, to transmit synchronization signals. The three signals are used to measure the three space delays from the control stations to the satellite. The control stations broadcast the space delays to all other stations in the system. Thus, any other earth station can obtain synchronization passively by calculating its own space delay.

A coherent binary FSK modulation system is discussed, that has the following properties: 1) it is phase coherent; 2) it has a low deviation ratio,h = \frac{1}{2}; 3) it occupies a small RF bandwidth, typically only 0.75 times the bit rate, without need for intersymbol interference correction; 4) it uses as receiver a self-synchronizing circuit and a phase detector, which together achieve optimal decisions; and 5) its error performance is about S dB better than that of conventional FSK.