As part of our efforts to continually improve the network, we recently implemented Proof-of-Coverage (PoC) version 4. This blog attempts to detail some of the planning, decisions and analysis that went into overhauling the existing PoC mechanism.

Motivation

The team has learned a lot of valuable lessons from having the first version of PoC out in the wild and watching the network grow organically. The initial PoC design was reliant on geography, simply because we did not have enough RF coverage data to make any decisions about the potential quality of a network generated via RF witnesses.

As the network grew past 500 Hotspots, we began to realize that we had several shortcomings in our PoC algorithm, the most important being:

  • Expensive Computation

    Our path and target calculation were extremely computationally expensive, and did a fair amount of superfluous work. This was exacerbated by the resource constraints of the Hotspot hardware.

  • Favoring localized clusters

    We saw several clusters of 3 and 5 Hotspots which would get challenged more frequently than others. This behavior stems from the fact that we biased paths towards confirming high score, so these clusters would complete their challenges, gain score and enter into a feedback loop which would challenge them again too soon, leading to score inflation. While we originally thought this score bias would be reasonable, we realized that this was prohibitive to organic network growth and it is more equitable and useful to keep PoCs more evenly distributed across all Hotspots on the network.

  • New Hotspots left out

    We soon realized that the old PoC pathing strategy does not account well enough for newly added Hotspots, as there was no way to construct a path with them if they have no geographic neighbors, even if they could hear those neighbors via RF and do useful work in the PoC process. We alleviate this to a degree by allowing every Hotspot to issue PoC challenges and rewarding them for that, but a better way to address this problem was needed. PoC V4 brings in a new concept, which we call “beaconing”, to address this concern.

Getting started: Collecting witness data

Radio propagation is finicky, and you cannot rely on nearby Hotspots to reliably be able to hear each other, especially in cities. To improve things, we needed a way to understand which Hotspots were able to talk to each other during the PoC process.

This realization led to adding “witness” data in the blockchain ledger. A “witness” is a Hotspot which has seen an RF packet over the air for any ongoing PoC. Witnesses allow us to gain another key metric - true RF range between Hotspots. You may have noticed in the Helium mobile app under any PoC challenge that there are now “witnesses” for each step in path.

We activated witness collection in block 89232 to begin the process of data collection while simultaneously deploying the building blocks require to solve the aforementioned issues.

Planning: New Proof-of-Coverage model

Once we had enough witness data, which you can view via the API, we began working on simulating new PoC models.

We started by setting out some motivating questions:

  • Which Hotspot to target?
  • How do we build a high quality PoC challenge path?
  • What do we do if we can’t build a path?

Targeting

We find a “target” Hotspot to be the first Hotspot in the PoC challenge path. The “target” in itself has no special role other than allowing us to narrow our field of search. So rather than looking at the network as a whole, we start building a path outwards from the target Hotspot.

The targeting mechanism is based on the following set of rules:

  • Favor high scoring Hotspots.

    Since the initial PoC challenge gets delivered via p2p over the network to the first Hotspot in the path (target), we require some confidence that this Hotspot will be online to successfully receive the challenge and subsequently broadcast it via RF.

  • Favor loosely connected Hotspots

    We believe it is far more interesting to construct PoC paths on the edge of the existing network because we don’t have as much information about the Hotspots there. This enables newly added Hotspots to get a chance to participate in future Proofs-of-Coverage.

  • Assigning probabilites and weights

    Both the above criteria have chain variable controlled probabilities and weights associated with them to allow us to better tune the selection over time.

  • Filter Hotspots which haven’t issued a PoC request for a long time

    We require that the Hotspots must be synced to the network and have constructed PoC requests within a certain number of blocks. This is to try and ensure that we don’t have targets which have been offline for a long time.

  • A target must ALWAYS be found

    We require that we always find a target Hotspot to be start of the PoC path. If we don’t find one, we simply retry.

Beaconing

The simplest way to describe beaconing is to consider it a PoC challenge with a target no other Hotspot can decrypt, but any can witness.

We believe this is an extremely valuable new addition to the PoC mechanism since it has multiple benefits:

  • New geographically aloof Hotspots now have a way to broadcast that they too are ready for PoC challenges. Prior to beaconing, all a new Hotspot could do (assuming it was alone geographically) was issue network rate-limited PoC challenges. With the introduction of PoC v4 these Hotspots would also be able to construct a beacon which other Hotspots can potentially witness. Both the challengee Hotspot and the potential witness Hotspot add each other to their witness lists, grow the network, and PoC further. We hope the information gathered because of this change will allow us to construct more interesting paths in the future.

  • Even if a Hotspot in a crowded region cannot witness any other Hotspots over RF and was selected as a target, it would still be able to construct the single layer challenge and get a chance to grow its witness list.

Greedy Paths

Prior to PoC V4, the way paths were calculated was dependent on the state of the entire network, which is an expensive calculation to perform every time a Hotspot issues a PoC request, and also when that request needs to be verified.

In V4, we’ve altered the algorithm to be greedy by nature and reduced the size of the input to the path creation by a significant factor.

We start path creation by first finding a candidate target Hotspot and grow the path outwards from it. A brief overview of the algorithm can be described as:

  1. Find target Hotspot, an O(n) operation, where n is the size of the network. We have plans to reduce the cost of this further.
  2. Inspect witness list of the target Hotspot. An O(k) operation, where k is the size of the witness list associated with the target Hotspot. Note that k is usually a significantly lower number than the number of Hotspots present on the network.
  3. Assign weights and probabilities to each of the witness members in the witness list. Detailed further below.
  4. Run an inverse cumulative distribution function to select the next hop from the target.
  5. Repeat step 2, with the selected witness as the next target Hotspot.

The overall asymptotic run time of the algorithm is O(n) + O(m*k) ~ O(n*m), which we know is orders of magnitude faster than the previous PoC version run times. Not only do we get a better run time complexity with V4, we also gain a huge saving from the reduced input sizes in step 2 onwards.

Weights and probabilites for witness selection

The blockchain ledger maintains a list of associated witnesses for each Hotspot in the network (given that there are any) and a witness RSSI histogram.

To select a witness as a next potential hop from a target Hotspot we assign probabilities and weights to each of the target Hotspot’s witnesses.

We defined four distinct probabilities and associated weights with each, these are calculated on the fly given the Hotspot’s behavior on the network, namely:

  • The witness having a good RSSI value.
  • The witness timestamp being stale.
  • The witness being infrequently challenged.
  • A randomness factor.

Each of these probabilities can be controlled via chain variables to allow for easy tuning in the future.

Furthermore, each of the above probabilities have chain variable controlled weights associated with them, which allow even more fine tuning.

The overall probability of selecting a witness thus becomes:

P(Witness) = RSSIWeight * P(WitnessRSSI) +
             TimeWeight * P(WitnessTime) +
             CountWeight * P(WitnessCount) +
             RandomnessWeight * 1.0

Note that the probabilty of a witness being selected as random is set to 1.0 as the controlling factor would be driven by the RandomnessWeight given that all the other weights are scaled accordingly. This was a community suggestion we added to make witness selection slightly more interesting and random. (Thank you,@andrew gifft, for this idea.)

Once we have the probability tagged witness list for the target, we do an inverse cumulative distribution function to pick the next hop and repeat the algorithm to grow the path further.

Summary

We hope that these improvements to Proof-of-Coverage will meaningfully improve both the quality of the PoC system and the consistency of block times, which have suffered of late as receipt counts have climbed and those receipts have grown ever more expensive to validate.

Please visit our Community Slack Chat if you have questions or would like to engage in discussion with the team.