  The problem of designing high rate, full diversity noncoherent space-time
block codes (STBCs) with low encoding and decoding complexity is addressed.
First, the notion of $g$-group encodable and $g$-group decodable linear STBCs
is introduced. Then for a known class of rate-1 linear designs, an explicit
construction of fully-diverse signal sets that lead to four-group encodable and
four-group decodable differential scaled unitary STBCs for any power of two
number of antennas is provided. Previous works on differential STBCs either
sacrifice decoding complexity for higher rate or sacrifice rate for lower
decoding complexity.
