  In this paper, we propose a partial interference cancellation (PIC) group
decoding for linear dispersive space-time block codes (STBC) and a design
criterion for the codes to achieve full diversity when the PIC group decoding
is used at the receiver. A PIC group decoding decodes the symbols embedded in
an STBC by dividing them into several groups and decoding each group separately
after a linear PIC operation is implemented. It can be viewed as an
intermediate decoding between the maximum likelihood (ML) receiver that decodes
all the embedded symbols together, i.e., all the embedded symbols are in a
single group, and the zero-forcing (ZF) receiver that decodes all the embedded
symbols separately and independently, i.e., each group has and only has one
embedded symbol, after the ZF operation is implemented. Our proposed design
criterion for the PIC group decoding to achieve full diversity is an
intermediate condition between the loosest ML full rank criterion of codewords
and the strongest ZF linear independence condition of the column vectors in the
equivalent channel matrix. We also propose asymptotically optimal (AO) group
decoding algorithm, which is an intermediate decoding between the MMSE decoding
algorithm and the ML decoding algorithm. The design criterion for the PIC group
decoding applies to the AO group decoding algorithm. It is well-known that the
symbol rate for a full rank linear STBC can be full, i.e., n_t for n_t transmit
antennas. It has been recently shown that its rate is upper bounded by 1 if a
code achieves full diversity with a linear receiver. The intermediate criterion
proposed in this paper provides the possibility for codes of rates between n_t
and 1 that achieve full diversity with a PIC group decoding. This therefore
provides a complexity-performance-rate tradeoff.
