  In this paper, a novel modulation scheme called set partition modulation
(SPM) is proposed. In this scheme, set partitioning and ordered subsets in the
set partitions are used to form codewords. We define different SPM variants and
depict a practical model for using SPM with orthogonal frequency division
multiplexing (OFDM). For the OFDM-SPM schemes, different constellations are
used to distinguish between different subsets in a set partition. To achieve
good distance properties as well as better error performance for the OFDM-SPM
codewords, we define a codebook selection problem and formulate such a problem
as a clique problem in graph theory. In this regard, we propose a fast and
efficient codebook selection algorithm. We analyze error and achievable rate
performance of the proposed schemes and provide asymptotic results for the
performance. It is shown that the proposed SPM variants are general schemes,
which encompass multi-mode OFDM with index modulation (MM-OFDM-IM) and
dual-mode OFDM with index modulation (DM-OFDM-IM) as special cases. It is also
shown that OFDM-SPM schemes are capable of exhibiting better error performance
and improved achievable rate than conventional OFDM, OFDM-IM, DM-OFDM-IM, and
MM-OFDM-IM.
