The compute-and-forward framework permits each receiver in a Gaussian network to directly decode a linear combination of the transmitted messages. The resulting linear combinations can then be employed as an end-to-end communication strategy for relaying, interference alignment, and other applications. Recent efforts have demonstrated the advantages of employing unequal powers at the transmitters and decoding more than one linear combination at each receiver. However, neither of these techniques fit naturally within the original formulation of compute-and-forward. This paper proposes an expanded compute-and-forward framework that incorporates both of these possibilities and permits an intuitive interpretation in terms of signal levels. Within this framework, recent achievability and optimality results are unified and generalized.
The original motivation for the compute-and-forward strategy was the possibility of relaying in a multi-hop network while avoiding the harmful effects of interference between users (by decoding linear combinations) as well as noise accumulation (by decoding at every relay). Several works have investigated and improved upon the performance of the original compute-and-forward framework in the context of multi-hop relaying @cite_73 @cite_25 @cite_85 @cite_42 @cite_62 @cite_76 . Our expanded framework can improve performance further by permitting relays to employ unequal powers and decode multiple linear combinations when appropriate. Following the conference publication of this work, Tan al @cite_9 noted that our proposed message representation may be inefficient for multi-hop relaying if each relay naively treats a linear combination over @math as @math information symbols for the next hop. They proposed a lattice-based solution to this issue. It is also possible to resolve this issue directly over the message representation by having each relay only use some of its @math received symbols as information symbols for the next hop. See [Section III.F] ncncarxiv for details.
@cite_62 @cite_9 @cite_85 @cite_42 @cite_76 @cite_73 @cite_25
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The compute-and-forward framework permits each receiver in a Gaussian network to directly decode a linear combination of the transmitted messages. The resulting linear combinations can then be employed as an end-to-end communication strategy for relaying, interference alignment, and other applications. Recent efforts have demonstrated the advantages of employing unequal powers at the transmitters and decoding more than one linear combination at each receiver. However, neither of these techniques fit naturally within the original formulation of compute-and-forward. This paper proposes an expanded compute-and-forward framework that incorporates both of these possibilities and permits an intuitive interpretation in terms of signal levels. Within this framework, recent achievability and optimality results are unified and generalized. In this paper, a point-to-point orthogonal-frequency- division multiplexing (OFDM) system with a decode-and- forward (DF) relay is considered. The transmission consists of two hops. The source transmits in the first hop, and the relay transmits in the second hop. Each hop occupies one time slot. The relay is half-duplex, and capable of decoding the message on a particular subcarrier in one time slot, and re-encoding and forwarding it on a different subcarrier in the next time slot. Thus, each message is transmitted on a pair of subcarriers in two hops. It is assumed that the destination is capable of combining the signals from the source and the relay pertaining to the same message. The goal is to maximize the weighted sum rate of the system by jointly optimizing subcarrier pairing and power allocation on each subcarrier in each hop. The weighting of the rates is to take into account the fact that different subcarriers may carry signals for different services. Both total and individual power constraints for the source and the relay are investigated. For the situations where the relay does not transmit on some subcarriers because doing so does not improve the weighted sum rate, we further allow the source to transmit new messages on these idle subcarriers. To the best of our knowledge, such a joint optimization inclusive of the destination combining has not been discussed in the literature. The problem is first formulated as a mixed integer programming problem. It is then transformed to a convex optimization problem by continuous relaxation, and solved in the dual domain. Based on the optimization results, algorithms to achieve feasible solutions are also proposed. Simulation results show that the proposed algorithms almost achieve the optimal weighted sum rate and outperform the existing methods in various channel conditions. This paper introduces and analyzes relaying techniques that increase the achievable throughput in multi-hop wireless networks by applying network coding over bi-directional traffic flows. We term each such technique as bi-directional amplification of throughput (BAT)-relaying. While network coding is normally performed by combining decoded packets, here we introduce a relaying method based on amplify-and-forward (AF), where the relay node utilizes the inherent combining of packets provided by simultaneous transmissions over a multiple access channel. Under low noise levels, AF BAT-relaying offers a superior throughput performance. The unconventionality of AF BAT relaying opens many possibilities for further research. This paper investigates the impact of inter-user non-orthogonality and asynchronous communication on the information-outage probability performance of multi-user decode-and-forward (DF) cooperative diversity in a code-division multiple-access (CDMA) uplink. Each user in the proposed system transmits its own data towards the base station and also serves as a relay for other users. We assume full-duplex communication so that each user can transmit and receive simultaneously at the same frequency. Each user attempts to decode the messages of a plurality of other users and forwards the superposition of multiple re-encoded and re-spread messages. Our cooperative scheme employs a sub-optimum decorrelating receiver to suppress the multi-user interference at both the base station and the relay-side. We evaluate the information-outage probability performance of the proposed scheme in an underloaded, fully-loaded and overloaded CDMA uplink. We consider combining schemes at the base station where the source information is code combined with the relayed information, while the information from multiple relays is either code combined or diversity combined. Under the system parameters contemplated in this paper, diversity combining of the relayed information is nearly as good as code combining because of the associated probabilities of decoding at the relays. We then examine the effect of using practical modulation formats on the information-outage probability performance of the proposed DF multi-user sharing scheme under diversity combining. We see that the performance loss due to modulation constraints and the use of diversity combining instead of code combining is relatively small.