Distributed Linear Convolutional Space-Time Coding for Two-Relay Full-Duplex Asynchronous Cooperative Networks

In this paper, a two-relay full-duplex asynchronous cooperative network with the amplify-and-forward (AF) protocol is considered. We propose two distributed space-time coding schemes for the cases with and without cross-talks, respectively. In the first case, each relay can receive the signal sent by the other through the cross-talk link. We first study the feasibility of cross-talk cancellation in this network and show that the cross-talk interference cannot be removed well. For this reason, we design space-time codes by utilizing the cross-talk signals instead of removing them. In the other case, the self-coding is realized individually through the loop channel at each relay node and the signals from the two relay nodes form a space-time code. The achievable cooperative diversity of both cases is investigated and the conditions to achieve full cooperative diversity are presented. Simulation results verify the theoretical analysis.Comment: 11 pages, 7 figures, accepted by IEEE transactions on wireless communication

Code Design for Multihop Wireless Relay Networks

We consider a wireless relay network, where a transmitter node communicates with a receiver node with the help of relay nodes. Most coding strategies considered so far assume that the relay nodes are used for one hop. We address the problem of code design when relay nodes may be used for more than one hop. We consider as a protocol a more elaborated version of amplify-and-forward, called distributed space-time coding, where the relay nodes multiply their received signal with a unitary matrix, in such a way that the receiver senses a space-time code. We first show that in this scenario, as expected, the so-called full-diversity condition holds, namely, the codebook of distributed space-time codewords has to be designed such that the difference of any two distinct codewords is full rank. We then compute the diversity of the channel, and show that it is given by the minimum number of relay nodes among the hops. We finally give a systematic way of building fully diverse codebooks and provide simulation results for their performance

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

A new approach to joint full-rate STBC and long-code WCDMA for four transmit antenna MIMO systems

In this work, we propose a novel combination of an extended orthogonal space-time block code (EO- STBC) or a quasi-orthogonal space-time block code (QO-STBC) and a long-code wideband code division multiple access (WCDMA) scheme to exploit spatial diversity in future wireless communication systems. For a mobile communication system, a key parameter is the system capacity. Multiple antennas at the transmitter and receiver in a system have been recognized as a major technology breakthrough to increase the capacity of a wireless communication network. To mitigate this limited capacity problem, two full transmit rate STBCs are integrated into the long-code WCDMA system with four transmit antenna. The bit error rate (BER) performance for the proposed technique is compared with other conventional methods for quasi-static wireless channels. Simulation results show that the proposed full rate STBC scheme when combined with the receive antenna selection technique method yields improved BER performance schemes

Data-driven decoding of quantum error correcting codes using graph neural networks

To leverage the full potential of quantum error-correcting stabilizer codes it is crucial to have an efficient and accurate decoder. Accurate, maximum likelihood, decoders are computationally very expensive whereas decoders based on more efficient algorithms give sub-optimal performance. In addition, the accuracy will depend on the quality of models and estimates of error rates for idling qubits, gates, measurements, and resets, and will typically assume symmetric error channels. In this work, instead, we explore a model-free, data-driven, approach to decoding, using a graph neural network (GNN). The decoding problem is formulated as a graph classification task in which a set of stabilizer measurements is mapped to an annotated detector graph for which the neural network predicts the most likely logical error class. We show that the GNN-based decoder can outperform a matching decoder for circuit level noise on the surface code given only simulated experimental data, even if the matching decoder is given full information of the underlying error model. Although training is computationally demanding, inference is fast and scales approximately linearly with the space-time volume of the code. We also find that we can use large, but more limited, datasets of real experimental data [Google Quantum AI, Nature {\bf 614}, 676 (2023)] for the repetition code, giving decoding accuracies that are on par with minimum weight perfect matching. The results show that a purely data-driven approach to decoding may be a viable future option for practical quantum error correction, which is competitive in terms of speed, accuracy, and versatility.Comment: 15 pages, 12 figure

Distributed space-time codes in wireless relay networks

We apply the idea of space-time coding devised for multiple antenna systems to the communication over a wireless relay network. We use a two stage protocol, where in one stage the transmitter sends information and in the other, the relay nodes encode their received signals into a "distributed" linear dispersion code, and then transmit the coded signals to the receiver. We show that for high SNR the pairwise error probability (PEP) behaves as (log P/P)^(min{T,R}) with T the coherence interval, R the number of relay nodes and P the total transmit power. Thus, apart from the log P factor and assuming T≥R, the system has the same diversity as a multi-antenna system with R transmit antennas, which is the same as assuming that the R relay nodes can fully cooperate and have full knowledge of the transmitted signal. We further show that for a fixed total transmit power across the entire network, the optimal power allocation is for the transmitter to expend half the power and for the relays to collectively expend the other half. We also show that at low and high SNR, the coding gain is the same as that of a multi-antenna system with R antennas. At intermediate SNR, it can be quite different, which has implications for the design of distributed space-time codes