A Class of Optimum Block Codes in Signal Space

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.