Further results on differential encoding by a table

Recently we proposed a novel differential encoder by a look-up table. In this paper, we present further research results on this subject. We first propose a bit-assigning algorithm and construct some new tables for various constellations that maximize the minimum noncoherent distance. Then differential encoding for multiple-symbol differential detection is proposed. After that, we indicate that differential encoding by a table is equivalent to differential encoding by a trellis, so we propose a novel differential detector which uses the Viterbi algorithm on the trellis. A theorem about the sufficient number of states for various modulations is proposed. In addition, we further enhance the error performance of the proposed differential encoder by concatenating it with trellis coding. For this noncoherent trellis coding scheme, we propose augmented-state Viterbi decoding. 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 set of transmitted blocks is determined first. The differential encoding is implemented by a look-up table which can be optimized. The proposed DSTM has satisfactory error performance without constellation expansion.