Binary Decoding Extended to Nonbinary Demodulation of Phase Shift Keying

The required energy per information bit
E_{B}/N_{o}
to achieve a specified error probability with a binary error correcting code is reduced by retaining partial knowledge of digit amplitudes. Quantization to three or four levels is the minimum step of demodulator complexity beyond hard decisions. A simple extension of binary decoding is described which achieves a large part of the maximum improvement theoretically available with unquantized demodulation. The usual decoding process is modified only to the extent that two decoding operations are performed, rather than one. Also, storage is needed to compare the two resulting words to select the preferred one. With four-level demodulation, an improvement of more than one decibel is demonstrated even for small code word lengths over a nonfading phase shift keyed (PSK) coherent channel with white Gaussian noise.