Re: QPACK proposal: wrap absolute index values

[Martin Thomson <[e-mail]>]

Table State Synchronize is relative, so it wouldn't benefit from a
change here.  That's something I missed initially, so it's probably a
candidate for clearer text.

I've no real opinion on the wrapping proposal.  It seems like it might
work for the Largest Reference.  The math is a tiny bit annoying to
decode in the same way the packet number encoding is, but it is
doable.  I imagine that you reconstruct the Largest Reference based on
the smallest index in the table.  That is:

rotation = floor(table_size / 32)
base = minimum - (minimum % rotation)
# equivalently: base = floor(minimum / rotation) * rotation
largest = encoded + base
if largest < minimum:
  largest += rotation
On Mon, Aug 6, 2018 at 1:47 AM Dmitri Tikhonov
<[e-mail]> wrote:
>
> Abstract
> --------
>
> The practical and theoretical problems caused by the unbounded absolute
> index values in the current QPACK Internet Draft are discussed.  The
> proposal to impose a limit on the range of absolute index values by
> wrapping them is presented.
>
> Background
> ----------
>
> The current QPACK draft states that
>
>    [the] first entry inserted has an absolute index of "1"; indices
>    increase sequentially with each insertion.
>
> No upper limit is specified.  This is reasonable, as it is impossible
> to run out of numbers.
>
> Nevertheless, an absolute index whose value is ever-increasing creates
> significant problems.
>
> Problem 1: Compression Impact
> -----------------------------
>
> A large absolute index value has a negative effect on compression.
> There are two places in QPACK that use the unadjusted value of the
> absolute index:
>
>     - the Largest Reference field in the Header Data Prefix; and
>     - the Table State Synchronize instruction.
>
> Larger values mean that more bytes are necessary to encode them.
> For example, using 8-bit prefix integer encoding, values larger than
> 254 encode to 2 bytes, larger than 382 to 3 bytes, and larger than
> 16638 to 4 bytes.
>
> Relatively quickly, the overhead associated with communicating the
> absolute index doubles and then triples.
>
> Problem 2: Theoretical Concerns
> -------------------------------
>
> Why should compression at t(1) be worse than at t(0)?  An ability
> to operate at the optimum level in perpetuity is a good property
> for a protocol to have.
>
> Problem 3: Implementation Efficiency
> ------------------------------------
>
> A QPACK implementation has to place some limits on the value of the
> absolute index -- simply because it has to pick an integral type to
> store it.  For example, uint64_t is likely large enough for all uses of
> the protocol, but it is wider than uint32_t and may be more expensive
> to process.  On other platforms, uint16_t may be the fastest integer;
> the unbounded nature of the absolute index would rule out its use.
>
> Such limit also requires an extra check [1] to cease inserting entries
> into the dynamic table once the maximum value for the integer is
> reached.  (One can run out of numbers in practice...)
>
> Solution: Have the Absolute Index Wrap Around
> ---------------------------------------------
>
> The main insight of the proposal is that the dynamic table has a bounded
> number of entries, that both encoder and decoder know what this number is,
> and that both can use this information to place an absolute index value
> communicated to it by its peer at the correct place in the sequence.
>
> The dynamic table has a maximum size which is specified at the beginning
> of the connection and which never changes afterwards.  The current size
> of the table is the sum of all its entry sizes.  The entry size is the sum
> of the fixed overhead plus the lengths of the name and the value strings.
> It is this fixed entry overhead that places a hard limit on the number
> of entries in the dynamic table:
>
>     MaxEntries = MaxTableSize / FixedEntryOverhead
>
> For example, using the current QPACK defaults, this number is
>
>     MaxEntries = 4096 / 32 = 128
>
> Imagine an encoder or decoder whose largest absolute index value (referred
> to as the total number of insertions in the QPACK draft) is X.  The
> smallest valid absolute index value its peer could possibly communicate
> to it is X - MaxEntries + 1.  The largest value is X + MaxEntries.  (All
> other values would indicate a bug at one or both sides.)  The maximum
> size of the valid absolute index values window, then, is MaxEntries * 2.
>
> Therefore, we can wrap the absolute index value without loss of
> information.  The proposal is to limit the absolute index values to
> the range
>
>     [ 1, MaxEntries * 2 ]
>
> Continuing with the QPACK defaults example above, the sequence would
> go
>
>     1, 2, 3, ... 254, 255, 256, 1, 2, ... (and so on).
>
> The compression overhead cost is now a function of the maximum table
> size (and not a function of time as before).
>
> To continue with our example, out of 256 possible values, 254 encode
> to 1 byte and 2 to two bytes.  A 64 KB table results in a maximum
> encoding of 3 bytes, while a 1 MB table has a maximum encoding of 4
> bytes.
>
> Changes to the Draft
> --------------------
>
> The changes to the draft are small.  Only the definition of the
> absolute index has to change; all instructions and encodings stay
> the same.
>
> Conclusion
> ----------
>
> Limiting the range of values the absolute index can have improves
> compression and implementation efficiency and removes the time penalty
> from the QPACK protocol.  A mechanism to do just that using existing
> QPACK parameters and with minimal changes to the draft has been proposed.
> I suggest that it be examined for flaws.  If none be found, I say let's
> include it in the next version of the QPACK Internet Draft.
>
>
>   - Dmitri.
>
> 1. https://github.com/litespeedtech/ls-qpack/blob/122d1163eaca359f5d79cd608722b1b19acad15f/src/lsqpack.c#L1110
>