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Add docs for FEC rate calculation (#6788) 

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anatoly yakovenko 2019-11-07 12:44:40 -08:00 committed by Grimes
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book/src/cluster/turbine-block-propagation.md
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@ -36,6 +36,59 @@ Finally, the following diagram shows a two layer cluster with a Fanout of 2.
Currently, configuration is set when the cluster is launched. In the future, these parameters may be hosted on-chain, allowing modification on the fly as the cluster sizes change. Currently, configuration is set when the cluster is launched. In the future, these parameters may be hosted on-chain, allowing modification on the fly as the cluster sizes change.
## Calcuating the required FEC rate
Turbine relies on retransmission of packets between validators. Due to
retransmission, any network wide packet loss is compounded, and the
probability of the packet failing to reach is destination increases
on each hop. The FEC rate needs to take into account the network wide
packet loss, and the propagation depth.
A shred group is the set of data and coding packets that can be used
to reconstruct each other. Each shred group has a chance of failure,
based on the likelyhood of the number of packets failing that exceeds
the FEC rate. If a validator fails to reconstruct the shred group,
then the block cannot be reconstructed, and the validator has to rely
on repair to fixup the blocks.
The probability of the shred group failing can be computed using the
binomial distribution. If the FEC rate is `16:4`, then the group size
is 20, and at least 4 of the shreds must fail for the group to fail.
Which is equal to the sum of the probability of 4 or more trails failing
out of 20.
Probability of a block succeeding in turbine:
* Probability of packet failure: `P = 1 - (1 - network_packet_loss_rate)^2`
* FEC rate: `K:M`
* Number of trials: `N = K + M`
* Shred group failure rate: `S = SUM of i=0 -> M for binomial(prob_failure = P, trials = N, failures = i)`
* Shreds per block: `G`
* Block success rate: `B = (1 - S) ^ (G / N) `
* Binomial distribution for exactly `i` results with probability of P in N trials is defined as `(N choose i) * P^i * (1 - P)^(N-i)`
For example:
* Network packet loss rate is 15%.
* 50kpts network generates 6400 shreds per second.
* FEC rate increases the total shres per block by the FEC ratio.
With a FEC rate: `16:4`
* `G = 8000`
* `P = 1 - 0.85 * 0.85 = 1 - 0.7225 = 0.2775`
* `S = SUM of i=0 -> 4 for binomial(prob_failure = 0.2775, trials = 20, failures = i) = 0.689414`
* `B = (1 - 0.689) ^ (8000 / 20) = 10^-203`
With FEC rate of `16:16`
* `G = 12800`
* `S = SUM of i=0 -> 32 for binomial(prob_failure = 0.2775, trials = 64, failures = i) = 0.002132`
* `B = (1 - 0.002132) ^ (12800 / 32) = 0.42583`
With FEC rate of `32:32`
* `G = 12800`
* `S = SUM of i=0 -> 32 for binomial(prob_failure = 0.2775, trials = 64, failures = i) = 0.000048`
* `B = (1 - 0.000048) ^ (12800 / 64) = 0.99045`
## Neighborhoods ## Neighborhoods
The following diagram shows how two neighborhoods in different layers interact. To cripple a neighborhood, enough nodes \(erasure codes +1\) from the neighborhood above need to fail. Since each neighborhood receives shreds from multiple nodes in a neighborhood in the upper layer, we'd need a big network failure in the upper layers to end up with incomplete data. The following diagram shows how two neighborhoods in different layers interact. To cripple a neighborhood, enough nodes \(erasure codes +1\) from the neighborhood above need to fail. Since each neighborhood receives shreds from multiple nodes in a neighborhood in the upper layer, we'd need a big network failure in the upper layers to end up with incomplete data.