Non-Linear Function Computation Broadcast

This work addresses the K -user computation broadcast problem consisting of a master node, which holds all datasets, and users for a general class of function demands, including linear and non-linear functions, over finite fields. The master node sends a broadcast message to enable each of K distrib...

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Published in:Proceedings / IEEE International Symposium on Information Theory pp. 1 - 6
Main Authors: Salehi, Mohammad Reza Deylam, Purakkal, Vijith Kumar Kizhakke, Malak, Derya
Format: Conference Proceeding
Language:English
Published: IEEE 22.06.2025
Subjects:
characteristic graphs
Computation broadcast
Computational modeling
distributed non-linear function computation
Encoding
Galois fields
Lower bound
union graphs
ISSN:2157-8117
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Abstract This work addresses the K -user computation broadcast problem consisting of a master node, which holds all datasets, and users for a general class of function demands, including linear and non-linear functions, over finite fields. The master node sends a broadcast message to enable each of K distributed users to compute its demanded function in an asymptotically lossless manner with user's side information. We derive bounds on the optimal K -user computation broadcast rate that allows the users to compute their demanded functions by capturing the structures of the computations and available side information. Our achievability scheme involves the design of a novel graph-based coding model to build a broadcast message to meet each user's demand, by leveraging the structural dependencies among the datasets, the user demands, and the side information of each user, drawing on Körner's characteristic graph framework. The converse uses the structures of the demands and the side information available at K users to yield a tight lower bound on the broadcast rate. With the help of examples, we demonstrate our scheme achieves a better communication rate than the existing state of the art.
AbstractList This work addresses the K -user computation broadcast problem consisting of a master node, which holds all datasets, and users for a general class of function demands, including linear and non-linear functions, over finite fields. The master node sends a broadcast message to enable each of K distributed users to compute its demanded function in an asymptotically lossless manner with user's side information. We derive bounds on the optimal K -user computation broadcast rate that allows the users to compute their demanded functions by capturing the structures of the computations and available side information. Our achievability scheme involves the design of a novel graph-based coding model to build a broadcast message to meet each user's demand, by leveraging the structural dependencies among the datasets, the user demands, and the side information of each user, drawing on Körner's characteristic graph framework. The converse uses the structures of the demands and the side information available at K users to yield a tight lower bound on the broadcast rate. With the help of examples, we demonstrate our scheme achieves a better communication rate than the existing state of the art.
Author Salehi, Mohammad Reza Deylam
Purakkal, Vijith Kumar Kizhakke
Malak, Derya
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  givenname: Vijith Kumar Kizhakke
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  givenname: Derya
  surname: Malak
  fullname: Malak, Derya
  email: malak@eurecom.fr
  organization: EURECOM,Communication Systems Department,France
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Snippet This work addresses the K -user computation broadcast problem consisting of a master node, which holds all datasets, and users for a general class of function...
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SubjectTerms characteristic graphs
Computation broadcast
Computational modeling
distributed non-linear function computation
Encoding
Galois fields
Lower bound
union graphs
Title Non-Linear Function Computation Broadcast
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