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From: Karl Johan Alm <karljohan-alm@garage.co.jp>
Date: Thu, 1 Jun 2017 11:11:48 +0900
Message-ID: <CALJw2w6zrdbn-xvDk9CpayqoDedbi5pFuwDyipeNO4hd9WjOog@mail.gmail.com>
To: Bitcoin Protocol Discussion <bitcoin-dev@lists.linuxfoundation.org>
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Subject: [bitcoin-dev] Block Filter Digest profiling
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Hello,

I have spent a fair bit of time trying to nail how exactly block
filter digests[1] should be done to optimize bandwidth, space,
resource usage.

The report can be found here: http://bc-2.jp/bfd-profile.pdf

This graph shows bandwidth use of 200 wallets simulated over 5000
blocks: http://bc-2.jp/bandwidth_bfd.png (black line is "sync once per
block" wallet, yellow is "sync once per 144 blocks" wallet, red is
average across all wallets).

An interesting insight made during the experiments: when allowing
digests to contain multiple blocks, the false positive rate of high
block count digests can be higher than normal, because the probability
of a false positive hit for a given entry in multiple digests,
assuming their sizes differ, is almost completely independent.

The results look rather promising to me, but I would like to hear
comments, in particular on the approach taken, if I made any faulty
assumptions, bad math mistakes, etc.

I am also curious what people consider to be acceptable costs in terms
of bandwidth use and memory (I couldn't find any stats on bandwidth
use of bloom filters). In the profiling, I restricted the field sizes
to 2^27 = 128 MB. I assumed this was appropriate as these fields are
very short lived, and in worst case, a client *could* do the scan and
decode simultaneously, without allocating up the space for the field
at all. For high block count digests (e.g. 1024 blocks), this is
sometimes overfilled. I wonder if 2^28 (256 MB) fields would be at all
acceptable or if an over-filled (high false positive rate) field is
better.

For that matter, I am not entirely sure 1024-block digests are
necessary, but they do come with an average 15 kb/block which is
pretty good.

I also wonder if the serialization approach taken is overkill or not.
It does save some space instead of simply storing "BBBAAAAA" but adds
some complexity that may not be warranted.

[1] https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2016-May/012636.html