This paper 1 deals with low maximum likelihood (ML) decoding complexity, full-rate and full-diversity space-time block codes (STBCs), which also offer large coding gain, for the 2 transmit antenna, 2 receive antenna (2 × 2) and the 4 transmit antenna, 2 receive antenna (4 × 2) MIMO systems. Presently, the best known STBC for the 2 × 2 system is the Golden code and that for the 4 × 2 system is the DjABBA code. Following the approach by Biglieri, Hong and Viterbo, a new STBC is presented in this paper for the 2 × 2 system. This code matches the Golden code in performance and ML-decoding complexity for square QAM constellations while it has lower ML-decoding complexity with the same performance for non-rectangular QAM constellations. This code is also shown to be information-lossless and diversitymultiplexing gain (DMG) tradeoff optimal. This design procedure is then extended to the 4 × 2 system and a code, which outperforms the DjABBA code for QAM constellations with lower ML-decoding complexity, is presented. So far, the Golden code has been reported to have an ML-decoding complexity of the order of M 4 for square QAM of size M . In this paper, a scheme that reduces its ML-decodingsingle-output (SISO) system. The Alamouti code [1] for two transmit antennas, due to its orthogonality property, allows a low complexity ML-decoder. This scheme led to the development of the generalized orthogonal designs [2]. These designs are famous for the simplified ML-decoding that they provide.They allow all the symbols to be decoupled from one another and hence, are said to be single-symbol decodable. Another bright aspect about these codes is that they have full transmit diversity for arbitrary complex constellation. However, the limiting factor of these designs is the low code rate (refer Section II for a definition of code rate) that they support.At the other extreme are the well known codes from division algebra, first introduced in [3]. The well known perfect codes [4] have also been evolved from division algebra with large coding gains. These codes have full transmit diversity and have the advantage of a very high symbol rate, equal to that of the VBLAST scheme, which, incidentally doesn't have full transmit diversity. But unfortunately, the codes from division algebra including perfect codes have a very high ML-decoding complexity (refer Section II for a definition of ML-decoding complexity), making their use prohibitive in practice.The class of single-symbol decodable codes also includes the codes constructed using co-ordinate interleaving, called co-ordinate interleaved orthogonal designs (CIODs) [5], and the Clifford-UnitaryWeight single-symbol decodable designs (CUW-SSD) [6]. These designs allow a symbol rate higher than that of the orthogonal designs, although not as much as that provided by the codes from division algebra.The disadvantage with these codes when compared with the Orthogonal designs is that they have full transmit diversity for only specific complex constellations.The Golden code [7], developed from divi...

The sum degrees of freedom (DoF) of the two-transmitter, two-receiver multiple-input multipleoutput (MIMO) X-Network (2 × 2 MIMO X-Network) with M antennas at each node is known to be 4M 3 . Transmission schemes which couple local channel-state-information-at-the-transmitter (CSIT) based precoding with space-time block coding to achieve the sum-DoF of this network are known specifically for M = 2, 4. These schemes have been proven to guarantee a diversity gain of M when a finite-sized input constellation is employed. In this paper, an explicit transmission scheme that achieves the 4M 3 sum-DoF of the 2 × 2 X-Network for arbitrary M is presented. The proposed scheme needs only local CSIT unlike the Jafar-Shamai scheme which requires the availability of global CSIT in order to achieve the 4M 3 sum-DoF. Further, it is shown analytically that the proposed scheme guarantees a diversity gain of M + 1 when finite-sized input constellations are employed.Freedom.that cell edge users are susceptible to interference from the neighbouring base stations and vice-versa.These issues have instigated research on better transmission techniques in interference networks, with information-theoretic rate tuples often used as the metric for designing better schemes. Since the capacity of interference networks is unknown in general, degrees of freedom (DoF) [1] is the widely targeted metric due to its relative ease of characterization. The sum-DoF of a Gaussian network is said to be d if its sum-capacity (in bits per channel use) can be approximated as C(SNR) = d log 2 SNR + o(log 2 SNR).Availability of channel-state-information at the transmitters (CSIT) is an important assumption in the characterization of the approximate capacity of Gaussian interference networks. Availability of perfect global CSIT 1 often enables one to design precoders that cast interference onto subspaces independent of the desired signal space at the receivers. This technique, termed interference alignment (IA), was first used implicitly in [2], [3], and explicitly appeared in [4], [5] in the context of 2 × 2 multiple-input multiple-output (MIMO) X-Networks. A K × J X-Network is a Gaussian interference network with K transmitters and J receivers and a total of KJ independent messages meant to be sent over the network, one from every transmitter to every receiver. A 2×2 X-Network with M antennas at each node is referred to as the (2 × 2, M ) X-Network. A lower bound on the sum-DoF was shown to be 4M 3 for such a network in [3], and it was proven in [5] that the sum-DoF equals 4M 3 , achieved using an IA scheme. All the aforementioned works assume the availability of perfect global CSIT.The concept of DoF assumes the use of a codebook with unconstrained alphabet size as well as unlimited peak power, but with an average power constraint. The channel is assumed to be static during the transmission of an entire codeword. Further, information-theoretic rate definitions also assume the usage of unlimited coding length. Clearly, all these assumptions are infeasible in p...

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Abstract-In this paper, a new method is proposed to obtain full-diversity, rate-2 (rate of 2 complex symbols per channel use) space-time block codes (STBCs) that are full-rate for multiple input, double output (MIDO) systems. Using this method, rate-2 STBCs for 4×2, 6×2, 8×2 and 12×2 systems are constructed and these STBCs are fast ML-decodable, have large coding gains and STBC-schemes consisting of these STBCs have a non-vanishing determinant (NVD) so that they are DMT-optimal for their respective MIDO systems. It is also shown that the Srinath-Rajan code [R. Vehkalahti, C. Hollanti, and F. Oggier, "Fast-Decodable Asymmetric Space-Time Codes from Division Algebras," IEEE Trans. Inf. Theory, Apr. 2012] for the 4×2 system, which has the lowest ML-decoding complexity among known rate-2 STBCs for the 4 × 2 MIDO system with a large coding gain for 4-/16-QAM, has the same algebraic structure as the STBC constructed in this paper for the 4 × 2 system. This also settles in positive a previous conjecture that the STBC-scheme that is based on the SrinathRajan code has the NVD property and hence is DMT-optimal for the 4 × 2 system.

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