Compute-and-Forward: Harnessing Interference Through Structured Codes

By Bobak Anthony Nazer, Michael C. Gastpar. IEEE Transactions on Information Theory, 2009

1,028 citations recorded by the source corpus.

Interference is usually viewed as an obstacle to communication in wireless networks. This paper proposes a new strategy, compute-and-forward, that exploits interference to obtain significantly higher rates between users in a network. The key idea is that relays should decode linear functions of transmitted messages according to their observed channel coefficients rather than ignoring the interference as noise. After decoding these linear equations, the relays simply send them towards the destinations, which given enough equations, can recover their desired messages. The underlying codes are based on nested lattices whose algebraic structure ensures that integer combinations of codewords can be decoded reliably. Encoders map messages from a finite field to a lattice and decoders recover equations of lattice points which are then mapped back to equations over the finite field. This scheme is applicable even if the transmitters lack channel state information.

Subfields: Computer Networks and Communications, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/3289c4a1843b0e965f5e0ea1eb9e36b1161ac04e

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Citations in the corpus

Making Cell-Free Massive MIMO Competitive With MMSE Processing and Centralized Implementation (2019, background): “Non-linear processing can be useful at Level 3 and the compute-and-forward relaying framework can potential guide the development of such methods [47], [54], [55].”
Physical-layer network coding: Tutorial, survey, and beyond (2011, methodology): “Analog Discrete PNCF Estimate (e.g., MMSE) [10,23] XOR [1] denoising map [11] Compute-and-forward with lattice code [13,14] PNCI ANC (i.e., linear MMSE) [6,7] Compress-and-forward [15] Other estimates (e.g., MMSE) [10] z R = x 1 ⊕ x 2 , and therefore XOR PNC belongs to PNCF.”
Grant-Free Non-Orthogonal Multiple Access for IoT: A Survey (2019, methodology): “The ﬁrst one is an inner binary linear code, whose purpose is to enable the receiver to decode the modulo-2 sum of all codewords transmitted within the same sub-block, which can be referred as the CoF phase.”
Federated Learning in Mobile Edge Networks: A Comprehensive Survey (2019, methodology): “Instead of performing communication and computation separately during global aggregation at the server, the BAA scheme builds on the concept of over-the-air computation [128] to integrate computation and communication through exploiting the signal superposition property of a multiple-access channel.”
Interference Alignment: A New Look at Signal Dimensions in a Communication Network (2011, methodology): “In addition to the evolution of lattice alignment described above, there is another research thread, on computation capacity, which originated as early as 1979 with Korner and Marton’s work in [82], which more recently evolved into a class of compute-and-forward schemes due to Nazer and Gastpar’s wo”
Broadband Analog Aggregation for Low-Latency Federated Edge Learning (2018, methodology): “It is also worth mentioning that, while AirComp is mostly deployed in computation-centric sensor networks as discussed above, the AirComp operation has been also leveraged in rate-maximization cellular systems such as two-way relaying [28] and MIMO lattice decoding [29].”