Two schemes for differential encoding of blockcoded M-ary PSK signals are presented and compared. Both proposed schemes perform differential encoding after channel decoding for minimizing the performance penalty associated with differential schemes. The first scheme requires the block codes to be rotationally invariant and linear, whereas the second requires rotational invariance only. Examples of bit error rate performance are also presented.>

By using convolutional coding coupled with expanded sets of channel signals, Ungerboeck showed that it is possible to obtain coding gains of several decibels at a given data rate without increasing the transmission bandwidth. In this paper, we construct a class of optimum signal space codes using short binary block (as opposed to convolutional) codes. Our results are compared to those obtained by Ungerboeck. A simplified decoding procedure that is asymptotically optimum is also presented.

We present a necessary condition that optimum two-dimensional signal constellations, used over an additive white Gaussian noise (AWGN) channel, must satisfy. Our condition is contrasted with another condition previously mentioned in the literature. A constellation of five signal points is given as an example. It is shown that the five points comprise the vertices of three equilateral triangles.

Image design involves determining the object distribution which produces a prescribed image at the output of a given imaging system. We solve the problem of generating two parallel lines at the output of an imaging system that is modeled by a linear band-limited system foliowed by a point nonlinearity of the hardlimiting type. It is shown that a solution always exists whatever the system's bandwidth. In principle, infinite two-line resolution is achievable. In practice, resolution much higher than the conventional resolution of the imaging system is possible.