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Let us model a wireless broadcast network as an undirected graph $G(V,E)$ where there is an edge between every pair of nodes ${i,j}\in V$ if they are in transmission range of each other. $w_{i\to j}$ is the weight of the link $i\to j$ which can be calculated only by transmitter $i$ and is unique to receiver $j$. All nodes periodically broadcast messages.

Each receiver needs to know all link weights associated to it to calculate $f(w)$. Expecting every node to broadcast a vector of weights associated to its neighbors would be infeasible as the vector size increases with number of nodes and does the size of data.

Question: What strategy/encoding can I adopt to reduce the size of broadcast data and at the same time each receiver can receive its own weight from the received broadcast messages?

Assumptions: weights are float/double values with unknown precision and nodes know ID and location $(x,y)$ of each other. Number of transmission per second is fixed.

Update: A system model picture is added for clarification.

system model

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  • $\begingroup$ I'm a little unclear on the requirements. By "only their own", I assume you're talking about some kind of cryptography. Is part of the problem that you need to broadcast this data over the network itself, and you're trying to minimise the number of messages? $\endgroup$
    – Pseudonym ♦
    Commented Nov 24, 2020 at 6:35
  • $\begingroup$ @Pseudonym number of transmissions (message rate) is fixed, let's say a couple of times a second. However, compressing or reducing size of data is what is needed. General problem: Wireless nodes calculate a weight for each of their neighbors and broadcast an array including all those weights. Each receiver will receive the whole array of weights and only picks the weight associated to itself. As by increasing number of neighbors, array size increases, sending raw array of weights is not feasible in wireless communications. How can the transmitter reduce the array size? $\endgroup$
    – fhm
    Commented Nov 24, 2020 at 19:42
  • $\begingroup$ Since every weight is a single value and wireless nodes know position $(x,y)$ of each other, it first reminded my of techniques similar to grayscale image compression (Huffman, etc), That, however, may not be efficient here as number of unoccupied regions is much more than occupied regions. So there is a chance that even size of compressed data is larger than raw data. $\endgroup$
    – fhm
    Commented Nov 24, 2020 at 19:48

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