Further results on differential encoding by a table

Recently, we proposed a novel differential encoder for non-constant energy signals, by a look-up table instead of a rule. In this paper, we present further research results on this subject. We first propose a new bit-assigning algorithm and some constellations maximizing minimum noncoherent distance. Then we show that differential encoding by a table is equivalent to differential encoding by a trellis, so we use the Viterbi algorithm at the differential detector to improve the error performance. A theorem about the sufficient number of states for various modulations is proposed. Finally, we extend the proposed differential encoding and detection to differential space-time modulation (DSTM). We propose a new definition of DSTM, by which the transmitted block is determined according to the previously transmitted block and current data bits. The encoding table that determines the transmitted block can be optimized. We also propose a theorem to reduce the number of states of the decoding trellis. The proposed DSTM has satisfactory error performance without constellation expansion.