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In a discussion about private channels, Conner Fromknecht mentioned a concept called Link-Level Multiplexing. What is this and what is it useful for? How does it work?

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It means that one peer can decide what is the best way of reaching another when forwarding a HTLC.
Let Alice and Bob having 2 channels between then, each one with 0.5 on each side, so looks like this:

Bob and Alice have two channels A and B with a balance of 0.5 on each side of each channel

Now, assume Bob gets a HTLC of 0.7 bitcoins going from him to Alice through channel A. Clearly, A cannot forward 0.7 bitcoins, since Bob's capacity there is just 0.5. But Bob can break this HTLC in two different ones, but with the same payment hash, so he forwards e.g 0.4 through A and 0.3 through B.
Alice may forward to the next hop using only one HTLC, or split even more. But this is local and only Alice and Bob knows about this split, hence, link-level.
Notice that this is not MPP. In MPP, the node who is paying breaks the payment, and it should be forward in parts through different peers. This one is inside a path itself, and doesn't reflect in what others see.

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