Re: Locally repairable code description revisited (was Pyramid ...)

[Loic Dachary <loic@dachary.org>]

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Hi Andreas,

Here is a preliminary implementation https://github.com/ceph/ceph/pull/1921 . It does not have tests yet, nor does it run but but it compiles and I think it makes sense. It is indeed simpler than the previous implementation.

It would be great if you could quickly browse 

   https://github.com/dachary/ceph/commit/5661c72864eca04c5dac9494a3f7e7a13515fca6

and let me know if you have any concerns.

Cheers

On 31/05/2014 19:10, Loic Dachary wrote:
> Hi Andreas,
> 
> After a few weeks and a fresh eye, I revisited the way pyramid erasure code could be described by the system administrator. Here is a proposal that is hopefully more intuitive than the one from the last CDS ( http://pad.ceph.com/p/cdsgiant-pyramid-erasure-code ).
> 
> These are the steps to create all coding chunks. The upper case letters are data chunks and the lower case letters are coding chunks.
> 
> "__ABC__DE_" data chunks placement
> 
> Step 1
> "__ABC__DE_"
> "_yVWX_zYZ_" K=5, M=2
> "_aABC_bDE_"
> 
> Step 2
> "_aABC_bDE_"
> "z_XYZ_____" K=3, M=1
> "caABC_bDE_"
> 
> Step 3
> "caABC_bDE_"
> "_____zXYZ_" K=3, M=1
> "caABCdbDE_"
> 
> Step 4
> "caABCdbDE_"
> "_____WXYZz" K=4, M=1
> "caABCdbDEe"
> 
> The interpretation of Step 3 is as follows:
> 
> Given the output of the previous step ( "caABC_bDE_" ), the bDE chunks are considered to be data chunks at this stage and they are marked with XYZ. A K=3, M=1 coding chunk is calculated and placed in the chunk marked with z ( "_____zXYZ_" ). The output of this coding step is the previous step plus the coding chunk that was just calculated, named d ( "caABCdbDE_" ). 
> 
> This gives the flexibility of deciding wether or not a coding chunk from a previous step is used as data to compute the coding chunk of the next step. It also allows for unbalanced steps such as step 4.
> 
> For decoding, the steps are walked from the bottom up. If E is missing, it can be reconstructed from dbD.e in step 4 and the other steps are skipped because it was the only missing chunk. If AB are missing, all steps that have not be used to encode it are ignored, up to step 2 that will fail to recover them because M=1 and yeild to step 1 that will use a..CbDE successfully because M=2.
> 
> Giving up the recursion and favor iteration seems to simplify how it can be explained. And I suspect the implementation is also simpler. What do you think ?
> 
> Cheers
> 

-- 
Loïc Dachary, Artisan Logiciel Libre


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