Application of set-membership techniques to symbol-by-symbol decoding for binary data-transmission systems

The application of set theory methods to problems in estimation, system identification, and classification is emerging as a viable approach to a number of different problems. This correspondence studies the use of set-membership methods in symbol-by-symbol decoding of binary data in data-transmission systems. Theorems for necessary and sufficient conditions for error-free decoding are presented. Following these theorems, an algorithm is presented for selection of decode threshold levels based on set-membership properties of the system. A second algorithm is presented for automatic generation of logic truth tables for the decoder.