Cooperative Lattice Coding and Decoding

A novel lattice coding framework is proposed for outage-limited cooperative channels. This framework provides practical implementations for the optimal cooperation protocols proposed by Azarian et al. In particular, for the relay channel we implement a variant of the dynamic decode and forward protocol, which uses orthogonal constellations to reduce the channel seen by the destination to a single-input single-output time-selective one, while inheriting the same diversity-multiplexing tradeoff. This simplification allows for building the receiver using traditional belief propagation or tree search architectures. Our framework also generalizes the coding scheme of Yang and Belfiore in the context of amplify and forward cooperation. For the cooperative multiple access channel, a tree coding approach, matched to the optimal linear cooperation protocol of Azarain et al, is developed. For this scenario, the MMSE-DFE Fano decoder is shown to enjoy an excellent tradeoff between performance and complexity. Finally, the utility of the proposed schemes is established via a comprehensive simulation study.Comment: 25 pages, 8 figure

Diversity-Multiplexing Tradeoffs in MIMO Relay Channels

A multi-hop relay channel with multiple antenna terminals in a quasi-static slow fading environment is considered. For both full-duplex and half-duplex relays the fundamental diversity-multiplexing tradeoff (DMT) is analyzed. It is shown that, while decode-and-forward (DF) relaying achieves the optimal DMT in the full-duplex relay scenario, the dynamic decode-and-forward (DDF) protocol is needed to achieve the optimal DMT if the relay is constrained to half-duplex operation. For the latter case, static protocols are considered as well, and the corresponding achievable DMT performance is characterized.Comment: To appear at IEEE Global Communications Conf. (Globecom), New Orleans, LA, Nov. 200

Lattice Coding for the Two-way Two-relay Channel

Lattice coding techniques may be used to derive achievable rate regions which outperform known independent, identically distributed (i.i.d.) random codes in multi-source relay networks and in particular the two-way relay channel. Gains stem from the ability to decode the sum of codewords (or messages) using lattice codes at higher rates than possible with i.i.d. random codes. Here we develop a novel lattice coding scheme for the Two-way Two-relay Channel: 1 2 3 4, where Node 1 and 4 simultaneously communicate with each other through two relay nodes 2 and 3. Each node only communicates with its neighboring nodes. The key technical contribution is the lattice-based achievability strategy, where each relay is able to remove the noise while decoding the sum of several signals in a Block Markov strategy and then re-encode the signal into another lattice codeword using the so-called "Re-distribution Transform". This allows nodes further down the line to again decode sums of lattice codewords. This transform is central to improving the achievable rates, and ensures that the messages traveling in each of the two directions fully utilize the relay's power, even under asymmetric channel conditions. All decoders are lattice decoders and only a single nested lattice codebook pair is needed. The symmetric rate achieved by the proposed lattice coding scheme is within 0.5 log 3 bit/Hz/s of the symmetric rate capacity.Comment: submitted to IEEE Transactions on Information Theory on December 3, 201

An Algebraic Coding Scheme for Wireless Relay Networks With Multiple-Antenna Nodes

We consider the problem of coding over a half-duplex wireless relay network where both the transmitter and the receiver have respectively several transmit and receive antennas, whereas each relay is a small device with only a single antenna. Since, in this scenario, requiring the relays to decode results in severe rate hits, we propose a full rate strategy where the relays do a simple operation before forwarding the signal, based on the idea of distributed space-time coding. Our scheme relies on division algebras, an algebraic object which allows the design of fully diverse matrices. The code construction is applicable to systems with any number of transmit/receive antennas and relays, and has better performance than random code constructions, with much less encoding complexity. Finally, the robustness of the proposed distributed space-time codes to node failures is considered