Partially-coherent distributed space-time codes with differential encoder and decoder

Distributed space-time coding is a means of achieving diversity through cooperative communication in a wireless relay network. In this paper, we consider a transmission protocol that follows a two-stage model: transmission from source to relays in the first stage, followed by a simple relaying technique from relays to destination. The relays transmit a vector, which is a transformation of the received vector by a relay-specific unitary transformation. We assume that the relays do not have any channel information, while the destination has only a partial-channel knowledge, by which we mean that destination knows only the relay-to-destination channel. We derive a Chernoff bound on the pairwise error probability and propose code design criteria. A second contribution is the differential encoding and decoding scheme for this setup, which is different from the existing ones. Furthermore, differential codes from cyclic division algebra are proposed that achieve full diversity. For our setup with two relays, a Generalized PSK code is shown to achieve full diversity, for which the decoding complexity is independent of code size.