Towards the Optimal Amplify-and-Forward Cooperative Diversity Scheme

In a slow fading channel, how to find a cooperative diversity scheme that achieves the transmit diversity bound is still an open problem. In fact, all previously proposed amplify-and-forward (AF) and decode-and-forward (DF) schemes do not improve with the number of relays in terms of the diversity multiplexing tradeoff (DMT) for multiplexing gains r higher than 0.5. In this work, we study the class of slotted amplify-and-forward (SAF) schemes. We first establish an upper bound on the DMT for any SAF scheme with an arbitrary number of relays N and number of slots M. Then, we propose a sequential SAF scheme that can exploit the potential diversity gain in the high multiplexing gain regime. More precisely, in certain conditions, the sequential SAF scheme achieves the proposed DMT upper bound which tends to the transmit diversity bound when M goes to infinity. In particular, for the two-relay case, the three-slot sequential SAF scheme achieves the proposed upper bound and outperforms the two-relay non-orthorgonal amplify-and-forward (NAF) scheme of Azarian et al. for multiplexing gains r < 2/3. Numerical results reveal a significant gain of our scheme over the previously proposed AF schemes, especially in high spectral efficiency and large network size regime.Comment: 30 pages, 11 figures, submitted to IEEE trans. IT, revised versio

Optimal space-time codes for the MIMO amplify-and-forward cooperative channel

In this work, we extend the non-orthogonal amplify-and-forward (NAF) cooperative diversity scheme to the MIMO channel. A family of space-time block codes for a half-duplex MIMO NAF fading cooperative channel with N relays is constructed. The code construction is based on the non-vanishing determinant criterion (NVD) and is shown to achieve the optimal diversity-multiplexing tradeoff (DMT) of the channel. We provide a general explicit algebraic construction, followed by some examples. In particular, in the single relay case, it is proved that the Golden code and the 4x4 Perfect code are optimal for the single-antenna and two-antenna case, respectively. Simulation results reveal that a significant gain (up to 10dB) can be obtained with the proposed codes, especially in the single-antenna case.Comment: submitted to IEEE Transactions on Information Theory, revised versio

An Error Probability Approach to MIMO Wiretap Channels

We consider MIMO (Multiple Input Multiple Output) wiretap channels, where a legitimate transmitter Alice is communicating with a legitimate receiver Bob in the presence of an eavesdropper Eve, and communication is done via MIMO channels. We suppose that Alice's strategy is to use a codebook which has a lattice structure, which then allows her to perform coset encoding. We analyze Eve's probability of correctly decoding the message Alice meant to Bob, and from minimizing this probability, we derive a code design criterion for MIMO lattice wiretap codes. The case of block fading channels is treated similarly, and fast fading channels are derived as a particular case. The Alamouti code is carefully studied as an illustration of the analysis provided.Comment: 27 pages, 4 figure

Semantically Secure Lattice Codes for Compound MIMO Channels

We consider compound multi-input multi-output (MIMO) wiretap channels where minimal channel state information at the transmitter (CSIT) is assumed. Code construction is given for the special case of isotropic mutual information, which serves as a conservative strategy for general cases. Using the flatness factor for MIMO channels, we propose lattice codes universally achieving the secrecy capacity of compound MIMO wiretap channels up to a constant gap (measured in nats) that is equal to the number of transmit antennas. The proposed approach improves upon existing works on secrecy coding for MIMO wiretap channels from an error probability perspective, and establishes information theoretic security (in fact semantic security). We also give an algebraic construction to reduce the code design complexity, as well as the decoding complexity of the legitimate receiver. Thanks to the algebraic structures of number fields and division algebras, our code construction for compound MIMO wiretap channels can be reduced to that for Gaussian wiretap channels, up to some additional gap to secrecy capacity.Comment: IEEE Trans. Information Theory, to appea