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 partial-channel 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

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

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

A linear rank-distance code is a set of matrices over a finite field F/sub q/, with the rank over Fq as a distance metric. A space-time block code (STBC) is a finite set of complex matrices with the rank over the complex field as a metric. Rank-distance codes over prime fields F/sub p/ have found applications as space-time codes. In this paper, we extend this result to arbitrary finite fields by providing an isomorphism from F/sub q/ (q = p/sup m/) to a subset of the ring of integers of an appropriate number field. Using this map and a maximal rank-distance code over F/sub q/, we construct STBC that achieve optimal rate-diversity tradeoff for any given diversity order. Simulation results confirm the diversity gain obtained using these codes.

A space-time block-code scheme (STBC-scheme) is a family of STBCs {C(SNR)}, 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/sup k/, 3/spl middot/2/sup k/, 2/spl middot/3/sup k/, and q/sup k/(q-1)/2, where q is any prime of the form 4s+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.

For multiple-input multiple-output (MIMO) channels, at high spectral efficiencies, space-time block codes (STBC) must be designed to maximize the mutual information between the transmit and receive signals. In an uncoiled scheme (spatial multiplexing or V-BLAST), it is well-known that the Gaussian input distribution maximizes the mutual information. Hassibi and Hochwald (2002) introduced a linear dispersion (LD) framework for designing space-time codes, wherein any transmit codeword is a linear combination of a fixed set of matrices called the weight matrices. A LD space-time block code is said to be information-lossless if it does not disturb the maximum mutual information between the transmit and receive signals. In other words, a MIMO scheme using information-lossless LD space-time block codes has the same capacity as the uncoded scheme. Through computer search, information-lossless LD codes with better diversity compared to the uncoded system were found by Hassibi et al., and also by Heath et al. (2002). We give a general algebraic construction of high-rate information-lossless STBC, both square and rectangular, by restricting the weight matrices to those which form a finite group under matrix multiplication.

We study n-length consta-Abelian codes (a generalization of the well-known Abelian codes and constacyclic codes) over Galois rings of characteristic p/sup a/, where n and p are coprime. A twisted discrete Fourier transform (DFT) is used to generalize transform domain results of Abelian and constacyclic codes, to consta-Abelian codes. Further, we characterize consta-Abelian codes invariant under two kinds of monomials, whose underlying permutations are effected by: i) multiplying the coordinates with a unit in the appropriate mixed-radix representation of the coordinate positions and ii) shifting the coordinates by t positions. All the codes studied here belong to the class of quasi-twisted codes which are known to contain some good codes. We show that the dual of a consta-Abelian code invariant under the two monomials is also a consta-Abelian code closed under both monomials.

We study n-length Abelian codes over Galois rings with characteristic p/sup a/, where n and p are relatively prime, having the additional structure of being closed under the following two permutations: (i) permutation effected by multiplying the coordinates with a unit in the appropriate mixed-radix representation of the coordinate positions and (ii) shifting the coordinates by t positions. A code is t-quasi-cyclic (t-QC) if t is an integer such that cyclic shift of a codeword by t positions gives another codeword. We call the Abelian codes closed under the first permutation as unit-invariant Abelian codes and those closed under the second as quasi-cyclic Abelian (QCA) codes. Using a generalized discrete Fourier transform (GDFT) defined over an appropriate extension of the Galois ring, we show that unit-invariant Abelian and QCA codes can be easily characterized in the transform domain. For t=1, QCA codes coincide with those that are cyclic as well as Abelian. The number of such codes for a specified size and length is obtained and we also show that the dual of an unit-invariant t-QCA code is also an unit-invariant t-QCA code. Unit-invariant Abelian (hence unit-invariant cyclic) and t-QCA codes over Galois field F/sub p//sup l/ and over the integer residue rings are obtainable as special cases.