Abstract-We address the problem of distributed space-time coding with reduced decoding complexity for wireless relay network. The transmission protocol follows a two-hop model wherein the source transmits a vector in the first hop and in the second hop the relays transmit a vector, which is a transformation of the received vector by a relay-specific unitary transformation. Design criteria is derived for this system model and codes are proposed that achieve full diversity. For a fixed number of relay nodes, the general system model considered in this paper admits code constructions with lower decoding complexity compared to codes based on some earlier system models.

Abstract-Distributed space-time coding is a mean 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 partialchannel knowledge, by which we mean that destination knows only the relay-to-destination channel. For such a setup, 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.

A space-time block-code scheme (STBC-scheme) is a family of STBCs () , indexed by the signal-to-noise ratio (SNR) such that the rate of each STBC scales with SNR. An STBC-scheme is said to have a nonvanishing determinant if the coding gain of every STBC in the scheme is lower-bounded by a fixed nonzero value. The nonvanishing determinant property is important from the perspective of the diversity multiplexing-gain (DM-G) tradeoff: a concept that characterizes the maximum diversity gain achievable by any STBC-scheme transmitting at a particular rate. This correspondence presents a systematic technique for constructing STBC-schemes with nonvanishing determinant, based on cyclic division algebras. Prior constructions of STBC-schemes from cyclic division algebra have either used transcendental elements, in which case the scheme may have vanishing determinant, or is available with nonvanishing determinant only for two, three, four, and six transmit antennas. In this correspondence, we construct STBC-schemes with nonvanishing determinant for the number of transmit antennas of the form 2 3 2 2 3 , and (1) 2, where is any prime of the form 4 + 3. For cyclic division algebra based STBC-schemes, in a recent work by Elia et al., the nonvanishing determinant property has been shown to be sufficient for achieving DM-G tradeoff. In particular, it has been shown that the class of STBC-schemes constructed in this correspondence achieve the optimal DM-G tradeoff. Moreover, the results presented in this correspondence have been used for constructing optimal STBC-schemes for arbitrary number of transmit antennas, by Elia et al..

Abstract-This paper presents a systematic technique for constructing STBC-schemes (Space-Time Block Code schemes) with non-vanishing determinant, based on cyclic division algebras. Prior constructions of STBC-schemes with non-vanishing determinant are available only for 2, 3, 4 and 6 transmit antennas. In this paper, by using an appropriate representation of a cyclic division algebra over a maximal subfield, we construct STBC-schemes with non-vanishing determinant for the number of transmit antennas of the form 2, where q is a prime of the form 4s + 3 and s is any arbitrary integer.In a recent work, Elia et.al. have proved that non-vanishing determinant is a sufficient condition for STBC-schemes from cyclic division algebra to achieve the optimal Diversity-Multiplexing Gain (D-MG) tradeoff; thus proving that the STBC-schemes constructed in this paper achieve the optimal D-MG tradeoff. I. INTRODUCTION AND MATHEMATICAL PRELIMINARIESA quasi-static Rayleigh fading multiple-input multipleoutput (MIMO) channel with n t transmit and n r receive antennas is modeled as Y nr×l = H nr×nt X nt×l + W nr×l , where Y nr×l is the received matrix over l channel uses, X nt×l is the transmitted matrix, H nr×nt is the channel matrix and W nr×l is the additive noise matrix, with the subscripts denoting the dimension of the matrices. The matrices H nr×nt and W nr×l have entries which are i.i.d, complex circularly symmetric Gaussian random variables. The collection of all possible transmit codewords X nt×l forms a space-time block code (STBC) C. From the pair-wise error probability (PEP) point of view, it is well-known that the performance of a space-time code at high SNRs is dependent on two parameters: diversity gain and coding gain. Diversity gain is the minimum of rank of the difference matrix (X − X ), for any X = X ∈ C, also called the rank of the code C. When C is fullrank, the coding gain is proportional to the determinant of (X − X ) (X − X ) H .

Abstract-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 partialchannel 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.