A Unified Discretization Approach to Compute-Forward: From Discrete to Continuous Inputs

Compute-forward is a coding technique that enables receiver(s) in a network to directly decode one or more linear combinations of the transmitted codewords. Initial efforts focused on Gaussian channels and derived achievable rate regions via nested lattice codes and single-user (lattice) decoding as...

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Vydáno v:IEEE transactions on information theory Ročník 69; číslo 1; s. 1 - 46
Hlavní autoři: Pastore, Adriano, Lim, Sung Hoon, Feng, Chen, Nazer, Bobak, Gastpar, Michael
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 01.01.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Channels
Codes
Coding
compute–forward
Decoding
Discretization
Entropy
information dimension
Lattices
Linear codes
multiple-access channel
physical-layer network coding
Receivers
Source coding
ISSN:0018-9448, 1557-9654
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Shrnutí:Compute-forward is a coding technique that enables receiver(s) in a network to directly decode one or more linear combinations of the transmitted codewords. Initial efforts focused on Gaussian channels and derived achievable rate regions via nested lattice codes and single-user (lattice) decoding as well as sequential (lattice) decoding. Recently, these results have been generalized to discrete memoryless channels via nested linear codes and joint typicality coding, culminating in a simultaneous-decoding rate region for recovering one or more linear combinations from <inline-formula> <tex-math notation="LaTeX">K </tex-math></inline-formula> users. Using a discretization approach, this paper translates this result into a simultaneous-decoding rate region for a wide class of continuous memoryless channels, including the important special case of Gaussian channels. Additionally, this paper derives a single, unified expression for both discrete and continuous rate regions via an algebraic generalization of Rényi's information dimension.
Bibliografie:ObjectType-Article-1
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2022.3197592