Multi-source data encoding, transmission and decoding using Slepian-Wolf codes based on channel code partitioning

1. A method implemented using a computing device, the method comprising:

(a) the computing device selecting any point in a Slepian-Wolf (SW) admissible rate region, wherein the point includes one rate value for each of L correlated source streams, wherein L is greater than or equal to two;

(b) the computing device identifying L submatrices of a given generator matrix G, wherein the numbers of rows in the L submatrices of the generator matrix G are determined by the selected point in the SW admissible region;

(c) the computing device computing L parity matrices H I , H 2 , . . . , H L from the generator matrix G, wherein each parity matrix Hi is computed from the corresponding submatrix of the generator matrix G;

wherein the parity matrix H i i=1, 2, . . . , L, defines a corresponding encoder C i according to the relation (s i ) T =H i (x i ) T , wherein x i represents a block of samples from the corresponding source stream, wherein s i represents a result of the encoder C i .

2. The method of claim 1 further comprising:

providing the L parity matrices to L transmitters respectively,

wherein each of the L transmitters is configured to multiply the corresponding source stream block x i by the corresponding parity matrix to determine the result s i for the encoder C i .

3. The method of claim 1 further comprising:

providing the matrix G to a receiver;

wherein the receiver is configured to:

receive the results s 1 , s 2 , . . . , s L from L transmitters respectively;

generate L expanded syndromes from the results s 1 , s 2 , . . . , s L by inserting zero or more zero values at appropriate positions into each result, so that each of the expanded syndromes have the same length;

compute a vector sum of the expanded syndromes;

determine a codeword c closest to the vector sum;

multiply each of L portions of a systematic part of the codeword c by a corresponding submatrix of the generator matrix G to determine a corresponding intermediate vector; and

add each of the L intermediate vectors to a corresponding one of the expanded syndromes to obtain a corresponding output representing an estimate of the corresponding source data block x i .

4. The method of claim 1 , wherein each of the source streams is generated by a corresponding one of a plurality of memoryless data sources, wherein the memoryless data sources are spatially distributed.

5. The method of claim 1 , wherein each of the correlated source streams is generated by a corresponding sensor in a distributed sensor network.

6. The method of claim 1 , wherein each of the correlated source streams is generated by a corresponding video source in a distributed video network.

7. The method of claim 1 , wherein the number of rows in each of the L submatrices of the generator matrix G is based on the rate value for the corresponding source stream.

8. The method of claim 1 , further comprising:

storing the parity matrices H 1 , H 2 , . . . , H L on one or more memory media for distribution to L corresponding encoding systems.

9. The method of claim 1 , wherein the computing device includes:

a processor configured to execute program instructions; or

one or more application-specific integrated circuits (ASICs); or

a combination of the processor configured to execute program instructions and one or more ASICs.

10. A method comprising:

L encoders respectively encoding L correlated information sources using, respectively, L distinct submatrices of a parity check matrix, in order to generate L syndromes, wherein L is greater than one; and

the L encoders sending the L syndromes to a joint decoder;

wherein each of the submatrices of the parity check matrix is derived from a corresponding submatrix of a generator matrix G, wherein the submatrices of the generator matrix G have row ranks determined by a point selected anywhere in a Slepian-Wolf admissible rate region.

11. The method of claim 10 , wherein the joint decoder is configured to decode the L syndromes using, respectively, the submatrices of the generator matrix G.

12. The method of claim 10 , wherein the information sources are memoryless information sources, wherein the information sources are spatially distributed.

13. The method of claim 10 , wherein each of the information sources is a sensor in a distributed sensor network.

14. The method of claim 10 , wherein each of the information sources is a video source in a distributed video network.

15. The method of claim 10 , wherein each of the information sources is an audio source.

16. The method of claim 10 , wherein the computing device includes:

a processor configured to execute program instructions; or

one or more application-specific integrated circuits (ASICs); or

a combination of the processor configured to execute program instructions and one or more ASICs.

17. A computer-implemented method comprising:

a computer system partitioning a generator matrix to generate a plurality of sub-matrices corresponding respectively to a plurality of correlated data sources,

wherein the partitioning is performed in accordance with a rate allocation among the plurality of correlated data sources; and

the computer system determining a corresponding plurality of parity matrices based respectively on the sub-matrices,

wherein each parity matrix is configured to encode correlated data for a respective one of the correlated data sources;

computing a plurality of parity matrices from the generator matrix,

wherein a given parity matrix is computed from a corresponding sub-matrix of the generator matrix; and

providing the plurality of parity matrices to respective transmitters.

18. The method of claim 17 , wherein the data sources are memoryless data sources, wherein the memoryless data sources are spatially distributed.

19. The method of claim 17 , wherein each of the data sources is a sensor in a distributed sensor network.

20. The method of claim 17 , wherein each of the data sources is a video source in a distributed video network.

21. The method of claim 17 , further comprising:

the computer system distributing the parity matrices to a plurality of encoding systems.

22. The method of claim 17 , further comprising:

the computer system sending the submatrices of the generator matrix to a decoding system.

23. The method of claim 17 , wherein the sub-matrices have rows, and wherein the numbers of rows in the sub-matrices of the generator matrix are determined by a corresponding selected point in a Slepian-Wolf admissible region.

24. The method of claim 17 , wherein the partitioning further comprises:

selecting a point in a Slepian-Wolf admissible region,

wherein the Slepian-Wolf point includes a rate value for a given correlated data source of the plurality of correlated data sources; and

determining a sub-matrix dimension for a first sub-matrix of the plurality of sub-matrices corresponding to the generator matrix,

wherein the determination of the sub-matrix dimension is based on the selected point in a Slepian-Wolf admissible region.

25. An apparatus comprising:

one or more processors; and

a memory storing instructions that, when executed by the one or more processors, cause the one or more processors to perform operations comprising:

(a) selecting a point in a Slepian-Wolf (SW) admissible rate region, wherein the point includes a rate value for each of L correlated source streams, wherein L is greater than or equal to two;

(b) identifying L submatrices of a given generator matrix G, wherein the numbers of rows in the L submatrices of the generator matrix G are determined by the selected point in the SW admissible region;

(c) computing L parity matrices H I , H 2 , . . . , H L from the generator matrix G, wherein each parity matrix H i is computed from the corresponding submatrix of the generator matrix G;

wherein the parity matrix H i i=1, 2, . . . , L, defines a corresponding encoder C i according to the relation (s i ) T =H i (x i ) T , wherein x i represents a block of samples from the corresponding source stream, wherein s i represents a result of the encoder C i .

26. The apparatus of claim 25 , the operations further comprising:

providing the L parity matrices to L transmitters respectively,

wherein each of the L transmitters is configured to multiply the corresponding source stream block x i by the corresponding parity matrix H i to determine the result s i for the encoder C i .

27. The apparatus of claim 25 , wherein the source streams are generated by at least one of:

a plurality of memoryless data sources, wherein the memoryless data sources are spatially distributed;

sensors in a distributed sensor network;

video sources in a distributed video network.

28. A tangible computer-readable medium having computer-executable instructions stored thereon that, if executed by a computing device, cause the computing device to perform operations comprising:

(a) selecting a point in a Slepian-Wolf (SW) admissible rate region, wherein the point includes a rate value for each of L correlated source streams, wherein L is greater than or equal to two;

(b) identifying L submatrices of a given generator matrix G, wherein the numbers of rows in the L submatrices of the generator matrix G are determined by the selected point in the SW admissible region;

(c) computing L parity matrices H I , H 2 , . . . , H L from the generator matrix G, wherein each parity matrix H i is computed from the corresponding submatrix of the generator matrix G;

wherein the parity matrix H i i=1, 2, . . . , L, defines a corresponding encoder C i according to the relation (s i ) T =H i (x i ) T , wherein x i represents a block of samples from the corresponding source stream, wherein s, represents a result of the encoder C i .

29. The tangible computer-readable medium of claim 28 , the operations further comprising receiving the L correlated source streams from at least one of:

a plurality of memoryless data sources, wherein the memoryless data sources are spatially distributed;

sensors in a distributed sensor network; or

video source in a distributed video network.

30. An apparatus comprising:

one or more processors; and

a memory storing instructions that, when executed by the one or more processors, cause the one or more processors to perform operations comprising:

using L encoders, respectively encoding L correlated information sources using, respectively, L distinct submatrices of a parity check matrix, in order to generate L syndromes, wherein L is greater than one; and

sending the L syndromes to a joint decoder;

wherein each of the submatrices of the parity check matrix is derived from a corresponding submatrix of a generator matrix G,

wherein the submatrices of the generator matrix G have row ranks determined by a point selected anywhere in a Slepian-Wolf admissible rate region.

31. The apparatus of claim 30 , the operations further comprising receiving correlated information from at least one of:

a plurality of memoryless data sources, wherein the memoryless data sources are spatially distributed;

sensors in a distributed sensor network; or

video sources in a distributed video network.

32. A tangible computer-readable medium having computer-executable instructions stored thereon that, if executed by a computing device, cause the computing device to perform operations comprising:

using L encoders, respectively encoding L correlated information sources using, respectively, L distinct submatrices of a parity check matrix, in order to generate L syndromes, wherein L is greater than one; and

sending the L syndromes to a joint decoder;

wherein each of the submatrices of the parity check matrix is derived from a corresponding submatrix of a generator matrix G,

wherein the submatrices of the generator matrix G have row ranks determined by a point selected anywhere in a Slepian-Wolf admissible rate region.

33. The tangible computer-readable of claim 32 , the operations further comprising receiving correlated information from at least one of:

a plurality of memoryless data sources, wherein the memoryless data sources are spatially distributed;

sensors in a distributed sensor network; or

video source in a distributed video network.

34. An apparatus comprising:

one or more processors; and

a memory storing instructions that, in response to execution by the one or more processors, cause the one or more processors to perform operations comprising:

partitioning a generator matrix to generate a plurality of sub-matrices corresponding respectively to a plurality of correlated data sources,

wherein the partitioning is performed in accordance with a rate allocation among the plurality of correlated data sources;

determining a corresponding plurality of parity matrices based respectively on the sub-matrices,

wherein each parity matrix is configured to encode correlated data for a respective one of the correlated data sources;

the operations further comprising:

computing a plurality of parity matrices from the generator matrix,

wherein a given parity matrix is computed from a corresponding sub-matrix of the generator matrix; and

providing the plurality of parity matrices to respective transmitters.

35. The apparatus of claim 34 , wherein the sub-matrices have rows, and wherein the numbers of rows in the sub-matrices of the generator matrix are determined by a corresponding selected point in a Slepian-Wolf admissible region.

36. The apparatus of claim 34 , the operations further comprising:

selecting a point in a Slepian-Wolf admissible region,

wherein the Slepian-Wolf point includes a rate value for a given correlated data source of the plurality of correlated data sources; and

determining a sub-matrix dimension for a first sub-matrix of the plurality of sub-matrices corresponding to the generator matrix,

wherein the determination of the sub-matrix dimension is based on the selected point in a Slepian-Wolf admissible region.

37. The apparatus of claim 34 , the operations further comprising receiving correlated data from at least one of:

a plurality of memoryless data sources, wherein the memoryless data sources are spatially distributed;

sensors in a distributed sensor network; or

video source in a distributed video network.

38. A tangible computer-readable medium having computer-executable instructions stored thereon that, if executed by a computing device, cause the computing device to perform operations comprising:

partitioning a generator matrix to generate a plurality of sub-matrices corresponding respectively to a plurality of correlated data sources,

wherein the partitioning is performed in accordance with a rate allocation among the plurality of correlated data sources;

determining a corresponding plurality of parity matrices based respectively on the sub-matrices,

wherein each parity matrix is configured to encode correlated data for a respective one of the correlated data sources,

the operations further comprising:

computing a plurality of parity matrices from the generator matrix,

wherein a given parity matrix is computed from a corresponding sub-matrix of the generator matrix; and

providing the plurality of parity matrices to respective transmitters.

39. The tangible computer-readable of claim 38 , wherein the sub-matrices have rows, and wherein the numbers of rows in the sub-matrices of the generator matrix are determined by a corresponding selected point in a Slepian-Wolf admissible region.

40. The tangible computer-readable of claim 38 , the operations further comprising:

selecting a point in a Slepian-Wolf admissible region,

wherein the Slepian-Wolf point includes a rate value for a given correlated data source of the plurality of correlated data sources; and

determining a sub-matrix dimension for a first sub-matrix of the plurality of sub-matrices corresponding to the generator matrix,

wherein the determination of the sub-matrix dimension is based on the selected point in a Slepian-Wolf admissible region.

41. The tangible computer-readable of claim 38 , the operations further comprising receiving correlated data from at least one of:

a plurality of memoryless data sources, wherein the memoryless data sources are spatially distributed;

sensors in a distributed sensor network; or

video source in a distributed video network.