# How do I compress data vectors in broadcast messages?

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.

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.
• 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. – fhm Nov 24 '20 at 19:48