3-Stripes gilbert low density parity-check codes

1. A method comprising:

providing a parity-check matrix of a Gilbert low density parity-check code, the parity-check matrix having a first stripe containing identity matrices and a second stripe containing an initial identity matrix concatenated with cyclic permutation matrices forming a 2-stripe Gilbert code;

adding a third stripe to the parity-check matrix to form a 3-stripes parity-check matrix having the two stripes of the 2-stripe Gilbert code and a minimal distance increased from that of the 2-stripe Gilbert code, the third stripe formed by a second concatenation of cyclic permutation matrices each raised to a respective non-negative integer power, wherein the concatenation of the third stripe includes an initial matrix different from an identity matrix; and

applying the 3-stripes parity-check matrix to a coding process of information in a communication channel.

2. The method of claim 1 , wherein adding a third stripe to the parity-check matrix to form a 3-stripes parity-check matrix includes adding the third stripe to the parity-check matrix to form the 3-stripes parity-check matrix having no cycles of length 4.

3. The method of claim 1 , wherein adding a third stripe to the parity-check matrix to form a 3-stripes parity-check matrix includes adding the third stripe to the parity-check matrix to form the 3-stripes parity-check matrix to provide a minimal distance of at least 6 to a code.

4. The method of claim 1 , wherein adding a third stripe to the parity-check matrix includes adding the third stripe having the cyclic permutation matrix of the concatenation taken from the second stripe of the parity-check matrix.

5. The method of claim 4 , wherein adding the third stripe includes selecting one or more powers for cyclic permutation matrix components such that the selection forms the 3-stripes parity-check matrix having no cycles of length 4.

6. The method of claim 5 , wherein selecting one or more powers includes selecting each power, for a cyclic permutation matrix at a jth component position in the third stripe such that i j ≠j, j ranging from zero to a non-negative non-zero integer.

7. The method of claim 1 , wherein applying the 3-stripes parity-check matrix to a coding process includes decoding a received signal based on the 3-stripes parity-check matrix to provide a valid codeword containing the information.

8. The method of claim 1 , wherein applying the 3-stripes parity-check matrix to a coding process includes encoding the information based on the 3-stripes parity-check matrix.

9. A method comprising:

receiving a signal from a communication channel;

decoding the signal to provide a valid codeword by applying a 3-stripes Gilbert parity-check matrix, the 3-stripes Gilbert parity-check matrix having a third stripe in addition to having a first and a second stripe of a 2-stripe parity-check matrix of a Gilbert low density parity-check code, the first stripe being a concatenation of identity matrices and the second stripe being an initial identity matrix concatenated with cyclic permutation matrices, the 3-stripes parity-check matrix having a minimal distance increased from that of the 2-stripe Gilbert code, the third stripe constructed as a second concatenation of cyclic permutation matrices each raised to a respective non-negative integer power, wherein the concatenation of the third stripe includes an initial matrix different from an identity matrix; and

extracting a message from the codeword.

10. The method of claim 9 , wherein applying a 3-stripes Gilbert parity-check matrix includes applying a 3-stripes Gilbert parity-check matrix having no cycles of length 4.

11. The method of claim 9 , wherein applying a 3-stripes Gilbert parity-check matrix includes applying a 3-stripes Gilbert parity-check matrix with the third stripe having the cyclic permutation matrix taken from the second stripe of the parity-check matrix, each power, i j , for a jth cyclic permutation matrix at a jth position in the third stripe having a value such that i j ≠j, j ranging from zero to a non-negative non-zero integer.

12. A method comprising:

receiving information;

encoding the information to form a codeword corresponding to a 3-stripes Gilbert parity-check matrix, the 3-stripes Gilbert parity-check matrix having a third stripe in addition to having a first and a second stripe of a 2-stripe parity-check matrix of a Gilbert low density parity-check code, the first stripe being a concatenation of identity matrices and the second stripe being an initial identity matrix concatenated with cyclic permutation matrices, the 3-stripes parity-check matrix having a minimal distance increased from that of the 2-stripe Gilbert code, the third stripe constructed as a second concatenation of cyclic permutation matrices each raised to a respective non-negative integer power, wherein the concatenation of the third stripe includes an initial matrix different from an identity matrix; and

transmitting the codeword into a communication channel.

13. The method of claim 12 , wherein applying a 3-stripes Gilbert parity-check matrix includes applying a 3-stripes Gilbert parity-check matrix to provide a minimal distance of at least 6 to a code.

14. The method of claim 12 , wherein applying a 3-stripes Gilbert parity-check matrix includes applying a 3-stripes Gilbert parity-check matrix with the cyclic permutation matrix taken from the second stripe of the parity-check matrix, each power, i j , for a jth cyclic permutation matrix at a jth position in the third stripe having a value such that i j ≠j, j ranging from zero to a non-negative non-zero integer.

15. A computer readable medium that stores instructions, which when performed by a machine, cause the machine to:

decode a signal received from a communication channel to provide a valid codeword by applying a 3-stripes Gilbert parity-check matrix, the 3-stripes Gilbert parity-check matrix having a third stripe in addition to having a first and a second stripe of a 2-stripe parity-check matrix of a Gilbert low density parity-check code, the first stripe being a concatenation of identity matrices and the second stripe being an initial identity matrix concatenated with cyclic permutation matrices, the 3-stripes parity-check matrix having a minimal distance increased from that of the 2-stripe Gilbert code, the third stripe constructed as a second concatenation of cyclic permutation matrices each raised to a respective non-negative integer power, wherein the concatenation of the third stripe includes an initial matrix different from an identity matrix; and

extract a message from the codeword.

16. The computer readable medium of claim 15 , wherein the 3-stripes Gilbert parity-check matrix includes a 3-stripes Gilbert parity-check matrix having no cycles of length 4.

17. The computer readable medium of claim 15 , wherein the 3-stripes Gilbert parity-check matrix includes a 3-stripes Gilbert parity-check matrix with the cyclic permutation matrix taken from the second stripe of the parity-check matrix, each power, i j , for a jth cyclic permutation matrix at a jth position in the third stripe having a value such that i j ≠j, j ranging from zero to a non-negative non-zero integer.

18. The computer readable medium of claim 15 , wherein the computer readable medium that stores instructions, which when performed by a machine, cause the machine to:

provide the parity-check matrix having the first stripe containing identity matrices and the second stripe containing cyclic permutation matrices; and

add the third stripe to the parity-check matrix to form the 3-stripes parity-check matrix.

19. A computer readable medium that stores instructions, which when performed by a machine, cause the machine to:

encode a message to form a codeword corresponding to a 3-stripes Gilbert parity-check matrix, the 3-stripes Gilbert parity-check matrix having a third stripe in addition to having a first and a second stripe of a 2-stripe parity-check matrix of a Gilbert low density parity-check code, the first stripe being a concatenation of identity matrices and the second stripe being an initial identity matrix concatenated with cyclic permutation matrices, the 3-stripes parity-check matrix having a minimal distance increased from that of the 2-stripe Gilbert code, the third stripe constructed as a second concatenation of cyclic permutation matrices each raised to a respective non-negative integer power, wherein the concatenation of the third stripe includes an initial matrix different from an identity matrix; and

transmit a signal containing the codeword into a communication channel.

20. The computer readable medium of claim 19 , wherein the 3-stripes Gilbert parity-check matrix includes a 3-stripes Gilbert parity-check matrix having no cycles of length 4.

21. The computer readable medium of claim 19 , wherein the 3-stripes Gilbert parity-check matrix includes a 3-stripes Gilbert parity-check matrix with the cyclic permutation matrix taken from the second stripe of the parity-check matrix, each power, i j , for a jth cyclic permutation matrix at a jth position in the third stripe having a value such that i j ≠j, i ranging from zero to a non-negative non-zero integer.

22. An apparatus comprising:

a receiver to receive a signal from a communication channel; and

a low density parity-check decoder having a 3-stripes Gilbert parity-check matrix, the 3-stripes Gilbert parity-check matrix having a third stripe in addition to having a first and a second stripe of a 2-stripe parity-check matrix of a Gilbert low density parity-check code, the first stripe being a concatenation of identity matrices and the second stripe being an initial identity matrix concatenated with cyclic permutation matrices, the 3-stripes parity-check matrix having a minimal distance increased from that of the 2-stripe Gilbert code, the third stripe constructed as a second concatenation of cyclic permutation matrices each raised to a respective non-negative integer power, wherein the concatenation of the third stripe includes an initial matrix different from an identity matrix, the low density parity-check decoder coupled to the receiver to provide a valid codeword from the signal.

23. The apparatus of claim 22 , wherein the 3-stripes Gilbert parity-check matrix includes a 3-stripes Gilbert parity-check matrix having no cycles of length 4.

24. The apparatus of claim 22 , wherein the 3-stripes Gilbert parity-check matrix includes a 3-stripes Gilbert parity-check matrix with the third stripe having a the cyclic permutation matrix taken from the second stripe of the parity-check matrix, each power, i j , for a jth cyclic permutation matrix at a jth position in the third stripe having a value such that i j ≠j, j ranging from zero to a non-negative non-zero integer.

25. The apparatus of claim 22 , wherein apparatus includes:

a low density parity-check encoder to provide an encoded message with respect to the 3-stripes Gilbert parity-check matrix; and

a transmitter to transmit an outgoing signal containing the encoded message.

26. An apparatus comprising:

a low density parity-check encoder to encode a message to generate a codeword with respect to a 3-stripes Gilbert parity-check matrix, the 3-stripes Gilbert parity-check matrix having a third stripe in addition to having a first and a second stripe of a 2-stripe parity-check matrix of a Gilbert low density parity-check code, the first stripe being a concatenation of identity matrices and the second stripe being an initial identity matrix concatenated with cyclic permutation matrices, the 3-stripes parity-check matrix having a minimal distance increased from that of the 2-stripe Gilbert code, the third stripe constructed as a second concatenation of cyclic permutation matrices each raised to a respective non-negative integer power, wherein the concatenation of the third stripe includes an initial matrix different from an identity matrix; and

a transmitter to transmit a signal containing the codeword.

27. The apparatus of claim 26 , wherein low density parity-check encoder provides a set of codewords having a minimum distance greater than 4.

28. The apparatus of claim 26 , wherein the 3-stripes Gilbert parity-check matrix includes a 3-stripes Gilbert parity-check matrix having no cycles of length 4.

29. The apparatus of claim 26 , wherein the 3-stripes Gilbert parity-check matrix includes a 3-stripes Gilbert parity-check matrix with the cyclic permutation matrix taken from the second stripe of the parity-check matrix, each power, i j , for a jth cyclic permutation matrix at a jth position in the third stripe having a value such that i j ≠j, j ranging from zero to a non-negative non-zero integer.

30. A system comprising:

an apparatus having connections to couple to a wired communication network, the apparatus including:

a receiver to receive a signal coupled from the wired communication network; and

a low density parity-check decoder having a 3-stripes Gilbert parity-check matrix, the 3-stripes Gilbert parity-check matrix having a third stripe in addition to having a first and a second stripe of a 2-stripe parity-check matrix of a Gilbert low density parity-check code, the first stripe being a concatenation of identity matrices and the second stripe being an initial identity matrix concatenated with cyclic permutation matrices, the 3-stripes parity-check matrix having a minimal distance increased from that of the 2-stripe Gilbert code, the third stripe constructed as a second concatenation of cyclic permutation matrices each raised to a respective non-negative integer power, wherein the concatenation of the third stripe includes an initial matrix different from an identity matrix, the low density parity-check decoder coupled to the receiver to provide a valid codeword from the signal; and

a host system communicatively coupled to the apparatus.

31. The system of claim 30 , wherein the 3-stripes Gilbert parity-check matrix includes a 3-stripes Gilbert parity-check matrix having no cycles of length 4.

32. The system of claim 30 , wherein the 3-stripes Gilbert parity-check matrix includes a 3-stripes Gilbert parity-check matrix with the cyclic permutation matrix taken from the second stripe of the parity-check matrix, each power, i j , for a jth cyclic permutation matrix at a jth position in the third stripe having a value such that i j ≠j, j ranging from zero to a non-negative non-zero integer.

33. The system of claim 30 , wherein the apparatus includes a network interface card.

34. The system of claim 30 , wherein the apparatus includes a network interface compliant with 10 GBase-T.

35. The system of claim 30 , wherein the host system includes at least one of a computer, a switch, a router, or a server.

36. The system of claim 30 , wherein the apparatus includes a bus to couple information signals to the receiver, the bus being compatible with PCI.

37. The system of claim 30 , wherein the apparatus includes a bus to couple information signals to the receiver, the bus being compatible with PCI express.

38. The system of claim 30 , wherein the system includes:

a low density parity-check encoder to encode a message to generate an outgoing codeword with respect to the 3-stripes Gilbert parity-check matrix; and

a transmitter to transmit an outgoing signal containing the outgoing codeword.

39. A system comprising:

a substantially omnidirectional antenna;

a receiver coupled to the omnidirectional antenna to receive a signal; and

a low density parity-check decoder having a 3-stripes Gilbert parity-check matrix, the 3-stripes Gilbert parity-check matrix having a third stripe in addition to having a first and a second stripe of a 2-stripe parity-check matrix of a Gilbert low density parity-check code, the first stripe being a concatenation of identity matrices and the second stripe being an initial identity matrix concatenated with cyclic permutation matrices, the 3-stripes parity-check matrix having a minimal distance increased from that of the 2-stripe Gilbert code, the third stripe constructed as a second concatenation of cyclic permutation matrices each raised to a respective non-negative integer power, wherein the concatenation of the third stripe includes an initial matrix different from an identity matrix, the low density parity-check decoder coupled to the receiver to provide a valid codeword from the signal.

40. The system of claim 39 , wherein the 3-stripes Gilbert parity-check matrix includes a 3-stripes Gilbert parity-check matrix having no cycles of length 4.

41. The system of claim 39 , wherein the 3-stripes Gilbert parity-check matrix includes a 3-stripes Gilbert parity-check matrix with the cyclic permutation matrix taken from the second stripe of the parity-check matrix, each power, i j , for a jth cyclic permutation matrix at a jth position in the third stripe having a value such that i j ≠j, j ranging from zero to a non-negative non-zero integer.

42. The system of claim 39 , wherein the system includes:

a low density parity-check encoder to encode a message to generate an outgoing codeword with respect to the 3-stripes Gilbert parity-check matrix; and

a transmitter to transmit an outgoing signal containing the outgoing codeword.