Publication

CFMA (Compute-Forward Multiple Access) and its Applications in Network Information Theory

Jingge Zhu
2016
Thèse EPFL
Résumé

While both fundamental limits and system implementations are well understood for the point-to-point communication system, much less is developed for general communication networks. This thesis contributes towards the design and analysis of advanced coding schemes for multi-user communication networks with structured codes. The first part of the thesis investigates the usefulness of lattice codes in Gaussian networks with a generalized compute-and-forward scheme. As an application, we introduce a novel multiple access technique --- Compute-Forward Multiple Access (CFMA), and show that it achieves the capacity region of the Gaussian multiple access channel (MAC) with low receiver complexities. Similar coding schemes are also devised for other multi-user networks, including the Gaussian MAC with states, the two-way relay channel, the many-to-one interference channel, etc., demonstrating improvements of system performance because of the good interference mitigation property of lattice codes. As a common theme in the thesis, computing the sum of codewords over a Gaussian MAC is of particular theoretical importance. We study this problem with nested linear codes, and improve upon the currently best known results obtained by nested lattice codes. Inspired by the advantages of linear and lattice codes in Gaussian networks, we make a further step towards understanding intrinsic properties of the sum of linear codes. The final part of the thesis introduces the notion of typical sumset and presents asymptotic results on the typical sumset size of linear codes. The results offer new insight to coding schemes with structured codes.

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Concepts associés (34)
Block code
In coding theory, block codes are a large and important family of error-correcting codes that encode data in blocks. There is a vast number of examples for block codes, many of which have a wide range of practical applications. The abstract definition of block codes is conceptually useful because it allows coding theorists, mathematicians, and computer scientists to study the limitations of all block codes in a unified way.
Canal de communication (théorie de l'information)
vignette En théorie de l'information, un canal de communication ou canal de transmission est un support (physique ou non) permettant la transmission d'une certaine quantité d'information, depuis une source (ou émetteur) vers un destinataire (ou récepteur). Souvent, le canal altère l'information transmise, par exemple en ajoutant un bruit aléatoire. La quantité d'information qu'un canal de communication peut transporter est limitée : on parle de capacité du canal.
Théorie des codes
En théorie de l'information, la théorie des codes traite des codes et de leurs propriétés et de leurs aptitudes à servir sur différents canaux de communication. On distingue deux modèles de communication : avec et sans bruit. Sans bruit, le codage de source suffit à la communication. Avec bruit, la communication est possible avec les codes correcteurs. En définissant l'information de façon mathématique, l'étape fondatrice de la théorie des codes a été franchie par Claude Shannon.
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