Paul, Very nice. No extra storage versus traditional RS with lower recover traffic, although not as low as, LRC. I imagine it complicates the logic to recover as well as the metadata required to track the dependencies. Scott On Jul 3, 2013, at 11:06 PM, Paul Von-Stamwitz <PVonStamwitz@xxxxxxxxxxxxxx> wrote: > Scott, et al. > > Here is an interesting paper from Usenix HotStorage Conference which provides local codes without additional capacity overhead. > > Check it out. (abstract with links to paper and slides) > https://www.usenix.org/conference/hotstorage13/solution-network-challenges-data-recovery-erasure-coded-distributed-storage > > Cheers, > pvs > >> On Jul 3, 2013, at 11:19 AM, Paul Von-Stamwitz wrote: >> >> Hi Scott, >> >> Point taken. >> >> I was thinking about Loic's decode description where k+m was requested and >> data was decoded when k blocks were received. But he was referring to full >> stripe reads where all the memory is allocated. >> >> Degraded reads and block repair are a different matter. >> >> pvs >> >>> On Jul 3, 2013, at 4:53 AM Scott Atchley wrote: >>> >>> On Jul 2, 2013, at 10:12 PM, Paul Von-Stamwitz >>> <PVonStamwitz@xxxxxxxxxxxxxx> wrote: >>> >>>> Scott, >>>> >>>> You make a good point comparing (5/3) RS with Xorbas, but a small nit: >>>> >>>> "The I/O to recover from a single failure for both schemes is 5 blocks >>> so it is as efficient as Xorbas." >>>> >>>> Maybe not. You would probably issue I/O to all the remaining 7 blocks >> to >>> cover for the possibility of double errors. The time to reconstruct >> would >>> be about the same, but there could be more disk and network I/O. (LRC >> will >>> need to issue I/O to the rest of the global stripe if it detected >> multiple >>> local errors.) >>> >>> Why would you request more than five? If one cannot be read, request >>> another. >>> >>> Also, I am not sure that you want to request five at once since it will >>> lead to spikes in network traffic and require memory for all five blocks. >>> You will need at least two buffers. Request the first two and start the >>> decoding. You may want a third buffer to overlap the decoding of the >>> current block with the communication for the next block. It may be that >>> the decode time is less than the communication and, in that case, you >> will >>> want to request all of the blocks at once. >>> >>>> What I like about Xorbas is that it is an extension of a (x,y) RS. You >>> can start with traditional RS. If degraded reads and repaired blocks are >>> causing a problem, you can add the LRC. If capacity is an issue, you can >>> take it out. >>> >>> I like it too and Microsoft has something similar with Pyramid codes. >> That >>> said, my example using traditional RS can provide more fault-tolerance >> on >>> average given the same amount of storage overhead. >>> >>>> >>>> Best, >>>> Paul >>>> >>>> On Tue, Jul 2, 2013 at 2:33 PM, Samuel Just wrote: >>>>> I think we should be able to cover most cases by adding an interface >>> like: >>>>> >>>>> set<int> minimum_to_read(const set<int> &want_to_read, const set<int> >>>>> &available_chunks); >>>>> >>>>> which returns the smallest set required to read/rebuild the chunks in >>>>> want_to_read given the chunks in available_chunks. Alternately, we >>> might >>>>> include a "cost" for reading each chunk like >>>>> >>>>> set<int> minimum_to_read_with_cost(const set<int> &want_to_read, >> const >>>>> map<int, int> &available) >>>>> >>>>> which returns the minimum cost set required to read the specified >>> chunks >>>>> given a mapping of available chunks to costs. The costs might allow >> us >>> to >>>>> consider the difference between reading local chunks vs remote chunks. >>>>> This should be sufficient to cover the read case (esp the degraded >> read >>>>> case) and the repair case. >>>>> -Sam >>>>> >>>>> On Tue, Jul 2, 2013 at 10:14 AM, Atchley, Scott <atchleyes@xxxxxxxx> >>>>> wrote: >>>>>> On Jul 2, 2013, at 10:07 AM, "Atchley, Scott" <atchleyes@xxxxxxxx> >>>>> wrote: >>>>>> >>>>>>> On Jul 1, 2013, at 7:00 PM, Loic Dachary <loic@xxxxxxxxxxx> wrote: >>>>>>> >>>>>>>> Hi, >>>>>>>> >>>>>>>> Today Sam pointed out that the API for LRC ( Xorbas Hadoop Project >>>>> Page, Locally Repairable Codes (LRC) http://smahesh.com/HadoopUSC/ >> for >>>>> instance ) would need to be different from the one initialy proposed: >>>>>>> >>>>>>> An interesting video. Not as entertaining as Jim Plank's video. ;-) >>>>>>> >>>>>>> While Plank's focused on the processor requirements for >>>>> encoding/decoding, this video focuses on the network and disk I/O >>>>> requirements. >>>>>>> >>>>>>>> context(k, m, reed-solomon|...) => context* c >>>>>>>> encode(context* c, void* data) => void* chunks[k+m] >>>>>>>> decode(context* c, void* chunk[k+m], int* >>>>>>>> indices_of_erased_chunks) => void* data // erased chunks are not >>> used >>>>>>>> repair(context* c, void* chunk[k+m], int* >>>>>>>> indices_of_erased_chunks) => void* chunks[k+m] // erased chunks >> are >>>>>>>> rebuilt >>>>>>>> >>>>>>>> The decode function must allow for partial read: >>>>>>>> >>>>>>>> decode(context* c, int offset, int length, void* chunk[k+m], int* >>>>>>>> indices_of_erased_chunks, int* missing_chunks) => void* data >>>>>>>> >>>>>>>> If there are not enough chunks to recover the desired data range >>>>> [offset, offset+length) the function returns NULL and sets >>> missing_chunks >>>>> to the list of chunks that must be retrieved in order to be able to >>> read >>>>> the desired data. >>>>>>>> >>>>>>>> If decode is called to read just 1 chunk and it is missing, reed- >>>>> solomon would return on error and ask for all other chunks to repair. >>> If >>>>> the underlying library implements LRC, it would ask for a subset of >> the >>>>> chunks. >>>>>>>> >>>>>>>> An implementation allowing only full reads and using jerasure >>> ( which >>>>> does not do LRC ) requires that offset is always zero, length is the >>> size >>>>> of the object and returns a copy of indices_of_erased_chunks if there >>> are >>>>> not enough chunks to rebuild the missing ones. >>>>>>>> >>>>>>>> Comments are welcome :-) >>>>>>> >>>>>>> I have loosely followed this discussion and I have not looked >> closely >>>>> at the proposed API nor at the jerasure interface. My apologies if >> this >>>>> has already been addressed. >>>>>>> >>>>>>> It is not clear to me from the above proposed API (ignoring the >>> partial >>>>> read) what it would do. Was the original intent to encode the entire >>> file >>>>> using k+m blocks irregardless of the file size and of the rados >> object >>>>> size? >>>>>>> >>>>>>> If so, how will you map rados objects to the logical k+m objects >> and >>>>> vice versa? >>>>>>> >>>>>>> If not, then the initial API needed an offset and length (either >>>>> logical or rados object). >>>>>>> >>>>>>> I would assume that you would want to operate on rados sized >> objects. >>>>> Given a fixed k+m, then you may have more than one set of k+m objects >>> per >>>>> file. This is ignoring the LRC "local" parity blocks. For example, if >>> the >>>>> rados object size if 1 MB and k = 10 and m = 4 (as in the Xorbas >> video), >>>>> then for a 20 MB file one would need two sets of encoding blocks. The >>>>> first for objects 1-10 and the second for objects 11-20. >>>>>>> >>>>>>> Perhaps, this is what the context is above. If so, it should have >> the >>>>> logical offset and rados object size, no? >>>>>>> >>>>>>> I see value in the Xorbas concept and I wonder if the jerasure >>> library >>>>> can be modified to generate the local parity blocks such that they >> can >>> be >>>>> used to generate the global parity blocks. That would be a question >> for >>>>> Jim Plank. >>>>>> >>>>>> The benefits of the Xorbas concept is reduced network and disk I/O >> for >>>>> failures while maintaining traditional RS's higher fault-tolerance >> than >>> 3x >>>>> replication while using less space. >>>>>> >>>>>> You can do almost the same thing with jerasure without modifying it >> at >>>>> all. Using the values from the Xorbas video, they have k data blocks, >> m >>>>> global parity blocks, and 2 local parity blocks (generated from k/2 >>> data >>>>> blocks) for a total of k+m+2 blocks on disk that can tolerate any m >>>>> failures. In their example, k = 10 and m = 4. They store 16 blocks >> for >>>>> each 10 data blocks. >>>>>> >>>>>> If you use traditional RS encoding via jerasure and used the same >>> amount >>>>> of storage (16 blocks for each 10 data blocks), you could encode 3 >>> parity >>>>> blocks for each 5 data blocks. This would consume 16 data blocks for >>> each >>>>> 10 data blocks and the fault-tolerance would be variable from 3-6 >>> failures >>>>> depending on how the failures fell between the two groups of 5 blocks >>>>> which is higher than the static 4 failures for the Xorbas code. The >> I/O >>> to >>>>> recover from a single failure for both schemes is 5 blocks so it is >> as >>>>> efficient as Xorbas. On average, it provides more fault-tolerance, >> but >>> it >>>>> can be less (four failures from one group of 5 data + 3 parity >> blocks), >>>>> but that worst case is the same as 3x replication. >>>>>> >>>>>> Scott-- >>>>>> 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 >>>>> -- >>>>> 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 > -- 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
