METHODS, SYSTEMS, AND MEDIA FOR FORMING LINEAR COMBINATIONS OF DATA

• US 20140161206A1
• Filed: 02/14/2014
• Published: 06/12/2014
• Est. Priority Date: 03/03/2006
• Status: Abandoned Application

• Current Assignee: Trustees Of Columbia University In The City Of New York (Columbia University)
• Original Assignee: Trustees Of Columbia University In The City Of New York (Columbia University)
• Inventors: KAMRA, Abhinav, MISRA, Vishal, FELDMAN, Jon, RUBENSTEIN, Daniel
• Application Number:
  US14/150,192
• Publication Number:
  US 20140161206A1
• Time in Patent Office: Days
• US Class Current: 375/295
• CPC Class Codes: G01V 1/003 Seismic data acquisition in general, e.g. survey design G01V1/3808, G01V1/42 take precedence
• CPC Class Codes: H04L 25/02 Details ; arrangements for supplying electrical power along data transmission lines systems for transmitting signals via power distribution lines H04B3/54

Abstract

Methods, systems, and media for forming linear combinations of data are provided. In some embodiments, methods for forming a linear combination of data include: receiving at a device a first codeword, wherein the first codeword comprises a linear combination of at least a first data unit including data, and a second data unit including data; encoding at the device the first codeword and a third data unit including data to form a second codeword, wherein the second codeword includes a linear combination of at least the first data unit, the second data unit, and the third data unit; and transmitting from the device the second codeword.

Claims

1. A method for forming a linear combination of data, comprising:

receiving at a device a first codeword, wherein the first codeword comprises a linear combination of at least a first data unit, comprising data, and a second data unit, comprising data;

encoding at the device the first codeword and a third data unit comprising data to form a second codeword, wherein the second codeword comprises a linear combination of at least the first data unit, the second data unit, and the third data unit; and

transmitting from the device the second codeword.

2. The method of claim 1, wherein the encoding comprises performing a bitwise exclusive-or (XOR) operation on the first codeword and the third data unit.

3. The method of claim 1, wherein the encoding further comprises compressing the third data unit to reduce a size of the third data unit.

4. The method of claim 1, wherein the receiving, the encoding and the transmitting are repeated at predetermined time intervals.

5. The method of claim 1, wherein the device comprises a sensor, and wherein the first data unit, the second data unit, and the third data unit comprise sensor data.

6. The method of claim 5, further comprising periodically acquiring new sensor data at the device.

7. The method of claim 1, wherein the device comprises a computing device in a peer-to-peer (P2P) network, and wherein the first data unit, the second data unit, and the third data unit comprise at least a portion of a file.

8. The method of claim 7, further comprising distributing the first data unit, the second data unit, and the third data unit to one or more additional computing devices in the peer-to-peer network.

9. The method of claim 1, wherein the second codeword further comprises identification information identifying the first data unit, the second data unit, and the third data unit.

10. The method of claim 9, further comprising:

determining a format for storing the identification information based on a number of data units encoded by the second codeword.

11. The method of claim 9, further comprising:

storing the first codeword and a third codeword at the device,

wherein the first codeword and the third codeword share identification information that identifies data units encoded by the first codeword and the third codeword.

12. The method of claim 1, further comprising:

receiving the first codeword at a first point in time; and

decoding the first codeword to recover the first data unit.

13. The method of claim 12, further comprising:

receiving the second codeword at a second point in time that is subsequent to the first point in time; and

decoding the second codeword to recover the third data unit using the first data unit and the second data unit.

14. A system for forming a linear combination of data, comprising:

a device that;

receives a first codeword, wherein the first codeword comprises a linear combination of at least a first data unit, comprising data, and a second data unit, comprising data;

encodes the first codeword and a third data unit to form a second codeword, wherein the second codeword comprises a linear combination of at least the first data unit, the second data unit, and the third data unit; and

transmits the second codeword.

15. The system of claim 14, wherein in encoding, the device performs a bitwise exclusive-or (XOR) operation on the first codeword and the third data unit.

16. The system of claim 14, wherein in encoding, device also compresses the third data unit to reduce a size of the third data unit.

17. The system of claim 14, wherein the device receives, encodes and transmits at predetermined time intervals.

18. The system of claim 14, wherein the device comprises a sensor, and wherein the first data unit, the second data unit, and the third data unit comprise sensor data.

19. The system of claim 18, wherein the sensor periodically acquires new sensor data.

20. The system of claim 14, wherein the device comprises a computing device, in a peer-to-peer (P2P) network, and wherein the first data unit, the second data unit, and the third data unit comprise at least a portion of a file.

21. The system of claim 14, wherein the second codeword further comprises information identifying the first data unit, the second data unit, and the third data unit.

22. The system of claim 21, wherein the device further determines a format for storing the identification information based on a number of data units encoded by the second codeword.

23. The system of claim 21, wherein the device further stores the first codeword and a third codeword, the first codeword and the third codeword share identification information that identifies data units encoded by the first codeword and the third codeword.

24. The system of claim 14, wherein the device also:

receives the first codeword at a first point in time; and

decodes the first codeword to recover the first data unit.

25. The system of claim 23, wherein the device also:

receives the second codeword at a second point in time that is subsequent to the first point in time; and

decodes the second codeword to recover the third data unit using the first data unit and the second data unit.

26. A computer-readable medium containing computer executable instructions that, when executed by a processor, cause the processor to perform a method for forming a linear combination of data, the method comprising:

receiving at a device a first codeword, wherein the first codeword comprises a linear combination of at least a first data unit, comprising data, and a second data unit, comprising data;

encoding at the device the first codeword and a third data unit comprising data to form a second codeword, wherein the second codeword comprises a linear combination of at least the first data unit, the second data unit, and the third data unit; and

transmitting from the device the second codeword.

27. The medium of claim 26, wherein the encoding comprises performing a bitwise exclusive-or (XOR) operation on the first codeword and the third data unit.

28. The medium of claim 26, wherein, the encoding further comprises compressing the third data unit to reduce a size of the third data unit.

29. The medium of claim 26, wherein the device comprises a sensor, and wherein the first data unit, the second data unit, and the third data unit comprise sensor data.

30. The medium of claim 26, wherein the device comprises a computing device in a peer-to-peer (P2P) network, and wherein the first data unit, the second data unit, and the third data unit comprise at least a portion of a file.

31. The medium of claim 26, wherein the second codeword further comprises identification information identifying the first data unit, the second data unit, and the third data unit.

32. The medium of claim 31, wherein the method further comprises:

determining a format for storing the identification information based on a number of data units encoded by the second codeword.

33. The medium of claim 31, wherein the method further comprises:

storing the first codeword and a third codeword at the device,

wherein the first codeword and the third codeword share identification information that identifies data units encoded by the first codeword and the third codeword.

34. The medium of claim 26, wherein the method further comprises:

receiving the first codeword at a first point in time, and

decoding the first codeword to recover the first data unit.

35. The medium of claim 26, wherein the method further comprises:

receiving the second codeword at a second point in time that is subsequent to the first point in time; and

decoding the second codeword to recover the third data unit using the first data unit and the second data unit.