Hi Loic, I think this gives all the flexibility to define any possible combination for encoding ... When one constructs the steps one has just to be aware that the 'most local' encoding should happen in the end, right? It would be usefule to have a tool which outputs then for each data aND parity chunk the achieved 'redundancy' and the overall volume and maximal reconstruction 'overhead'. Cheers Andreas. ________________________________________ From: Loic Dachary [loic@xxxxxxxxxxx] Sent: 31 May 2014 19:10 To: Andreas Joachim Peters Cc: Ceph Development Subject: Pyramid erasure code description revisited 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 -- To unsubscribe from this list: send the line "unsubscribe ceph-devel" in the body of a message to majordomo@xxxxxxxxxxxxxxx More majordomo info at http://vger.kernel.org/majordomo-info.html
