Method and devices for a reduced repair and update erasure code

1. An apparatus comprising:

processing circuitry configured to:

encode data using a Mojette transform based on generating encoded representations of data blocks, wherein the processing circuitry, for generating the encoded representations of data blocks, is further configured to:

read data in the form of a data block formatted according to specified settings to comprise rows and columns,

create a set of projections that includes the processing circuitry further configured to:

apply the Mojette transform on the data block, and

create a first number of projections based on mapping each row of the data block to a corresponding projection, the first number of projections including the same information as a corresponding row,

output the created set of projections to enable a storage of the data in the form of the set of projections, and

transmit the encoded data over a network to another device.

2. The apparatus of claim 1 , wherein the processing circuitry, for creating the set of projections, is further configured to

create a number of second projections, wherein a number of second projections is any number that can be obtained by specifying the indices in proj (p i , q i ≠0), where proj is projection, p is a row of the projection, and q is a column of the projection.

3. The apparatus of claim 1 , wherein the processing circuitry, for creating the set of projections, is further configured to

create a number of third projections, wherein a number of third projections is any number that can be obtained by specifying the indices in proj (p i , q i ≠0), where proj is projection, p is a row of the projection, and q is a column of the projection.

4. The apparatus of claim 1 , wherein the encoded data is generated with one or more reduced repair effort locally recoverable (RRE-LR) codes.

5. The apparatus of claim 4 , wherein the RRE-LR codes are configured to produce a set of m, k, lr projections,

wherein m is a parity chunk, lr is a parity fragment having sub-block parity chunks (SBPC) from a RRE-LR configuration, and k is a number of chunks.

6. The apparatus of claim 5 , wherein the RRE-LR codes, in combination with distributed nodes in the network, are configured to reduced network traffic for a repair.

7. The apparatus of claim 6 , wherein a distributed lr projection is configured to reduce one or more of a decoding effort and a repair effort.

8. The apparatus of claim 6 , wherein a combination of m, k, lr projections is configured to optimize decoding.

9. The apparatus of claim 1 , wherein the processing circuitry is further configured to

repair the data block in response to one or more rows being lost.

10. The apparatus of claim 9 , wherein the processing circuitry, for repairing the data block, is further configured to

select a parity chunk one from the set of projections that is connected with the one or more lost rows, the parity chunk being one of a first number of projections, a second number of projections, and a third number of projections,

identify a location of the first number of projections connected to the selected parity chunk, and

compress the first number of projections per node connected to the selected parity chunk by applying the Mojette transform.

11. The apparatus of claim 10 , wherein in response to the one or more lost rows being from the first number of projections, the processing circuitry, for repairing the data block, is further configured to

apply the Mojette transform to the compressed first number of projections and the selected parity chunk, and

generate the one or more lost rows, wherein the one or more lost rows correspond to one or more of the first number of projections.

12. The apparatus of claim 10 , wherein in response to the one or more lost rows being from the second or third number of projections, the processing circuitry, for repairing the data block, is further configured to

apply the Mojette transform to the compressed first number of projections, and

generate the one or more lost rows, wherein the one or more lost rows correspond to a missing parity chunk.

13. The apparatus of claim 1 , wherein one or more reduced repair effort-sub-packetization (RRE-SP) codes are configured to reduce an amount of data required for a final decoding using distributed Mojette transform operations.

14. The apparatus of claim 13 , wherein the one or more RRE-SP codes, in combination with distributed nodes in the network, are configured to reduce network traffic for a repair.

15. The apparatus of claim 14 , wherein a distributed lr projection is configured to reduce one or more of a decoding effort and a repair effort.

16. The apparatus of claim 1 , wherein one or more reduced repair effort-Partial Update (RRE-PU) codes are configured to reduce a number of operations for a partial update using distributed Mojette transform operations.

17. The apparatus of claim 16 , wherein the one or more RRE-PU codes, in combination with distributed nodes in the network, are configured to reduce network traffic.

18. A method for generating encoded representations of data blocks, comprising:

encoding, via processing circuitry, data using a Mojette transform based on generating encoded representations of data blocks, wherein generating encoded representations of data blocks includes

reading, via the processing circuitry, data in the form of a data block formatted according to specified settings to comprise rows and columns;

creating, via the processing circuitry, a set of projections, the creating including:

applying a Mojette transform on the data block; and

creating a first number of projections based on mapping each row of the data block to a corresponding projection, wherein the first number of projections carry the same information as a corresponding row; and

outputting, via the processing circuitry, the created set of projections to enable a storage of the data in the form of the set of projections.

19. The method of claim 18 , wherein the creating the set of projections includes

creating a number of second projections, wherein the number of second projections is any number that can be obtained by specifying the indices in proj (p i , q i ≠0), where proj is projection, p is a row of the projection, and q is a column of the projection.

20. The method of claim 18 , wherein the creating the set of projections further includes

creating a number of third projections, wherein the number of third projections is any number that can be obtained by specifying the indices in proj (p i , q i ≠0), where proj is projection, p is a row of the projection, and q is a column of the projection.

21. The method of claim 18 , wherein the encoded data is generated with one or more reduced repair effort-locally recoverable (RRE-LR) codes.

22. The method of claim 18 , further comprising:

repairing the data block in response to one or more rows being lost.

23. The method of claim 22 , wherein the repairing the data block includes

selecting a parity chunk one from the set of projections that is connected with the one or more lost rows, the parity chunk being one of a first number of projections, a second number of projections, and a third number of projections;

identifying a location of the first number of projections connected to the selected parity chunk; and

compressing the first number of projections per node connected to the selected parity chunk by applying the Mojette transform.

24. The method of claim 23 , wherein in response to the one or more lost rows being from the first number of projections, the repairing the data block includes

applying the Mojette transform to the compressed first number of projections and the selected parity chunk; and

generating the one or more lost rows, wherein the one or more lost rows correspond to one or more of the first number of projections.

25. The method of claim 23 , wherein in response to the one or more lost rows being from the second or third number of projections, the repairing the data block includes

applying the Mojette transform to the compressed first number of projections; and

generating the one or more lost rows, wherein the one or more lost rows correspond to a missing parity chunk.

26. An apparatus comprising:

circuitry configured to

receive encoded data from another device,

determine whether the encoded data is decodable, wherein a determination whether the encoded data is decodable is performed by the circuitry being configured to

compare a total number of errors to a predetermined number of parity chunks, wherein the comparison includes determining whether the total number of errors is greater than m+lr, whether the total number of errors is not greater than m+lr(x), and whether the total number of errors is greater than a redundancy set by m+lr within any of the lr parity chunks, where m is a parity chunk, lr is a parity fragment having sub-block parity chunks (SBPC) from a reduced repair effort—locally recoverable codes (RRE-LR) configuration, and lr(x) is all lr sub-parity chunks, and

in response to the total number of errors being greater than to m+lr and the total number of errors not being greater than m+lr(x), the encoded data is determined to be decodable, and

decode the encoded data using a Mojette transform (MT) and one or more RRE-LR codes.