Expanding the Compute-and-Forward Framework: Unequal Powers, Signal Levels, and Multiple Linear Combinations

Abstract

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.

30 pages, 10 figures, to appear in IEEE Transactions on Information Theory

References in corpus (7)

• Interference Alignment and the Degrees of Freedom for the K User Interference Channel
• Providing Secrecy With Structured Codes: Tools and Applications to Two-User Gaussian Channels
• Expanding the Compute-and-Forward Framework: Unequal Powers, Signal Levels, and Multiple Linear Combinations
• An Achievable rate region for the $3-$user interference channel based on coset codes
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• Full-Duplex Relaying with Half-Duplex Relays

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• Improving Sum-Rate of Cell-Free Massive MIMO with Expanded Compute-and-Forward
• Expanding the Compute-and-Forward Framework: Unequal Powers, Signal Levels, and Multiple Linear Combinations
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• Over-The-Air Computation in Correlated Channels
• Over-The-Air Computation in Correlated Channels
• Computation-aided classical-quantum multiple access to boost network communication speeds
• A Survey on User-Centric Cell-Free Massive MIMO Systems
• Secure physical layer network coding versus secure network coding
• Secure Modulo Sum via Multiple Access Channel
• Low-Complexity Integer-Forcing Methods for Block Fading MIMO Multiple-Access Channels
• Towards an Algebraic Network Information Theory: Simultaneous Joint Typicality Decoding
• An Efficient Optimal Algorithm for the Successive Minima Problem
• Compute-and-forward relaying with LDPC codes over QPSK scheme