System and method for detecting codeword errors in error correction code or cyclic redundancy check code
A method for detecting errors in data that comprises encoding the data into a codeword using a generation polynomial, transmitting the codeword over a channel, receiving the transmitted codeword, generating syndromes for the received codeword using the generation polynomial, the syndromes comprising a plurality of syndrome symbols, providing a plurality of syndrome windows, each of the syndrome windows comprising a plurality of sub-windows and corresponding to a set of syndrome symbols, determining a number of non-zero terms of sub-windows of each of the syndrome windows, and selecting at least one syndrome window having a least number of non-zero terms of sub-windows.
1. A method for detecting errors in data, comprising:
encoding the data into a codeword using a generation polynomial;
transmitting the codeword over a channel;
receiving the transmitted codeword;
generating syndromes for the received codeword using the generation polynomial, the syndromes comprising a plurality of syndrome symbols;
providing a plurality of syndrome windows, each of the syndrome windows comprising a plurality of sub-windows and corresponding to a set of syndrome symbols;
determining a number of non-zero terms of sub-windows of each of the syndrome windows; and
selecting at least one syndrome window having a least number of non-zero terms of sub-windows.
2. The method of claim 1 comprising determining a number of non-zero bits of sub-windows of each of the syndrome windows, and selecting at least one syndrome window having a least number of non-zero bits of sub-windows.
3. The method of claim 1 comprising determining a number of non-zero bytes of sub-windows of each of the syndrome windows, and selecting at least one syndrome window having a least number of non-zero bytes of sub-windows.
4. The method of claim 1 comprising encoding the data into a codeword having N data symbols and K parity symbols, wherein N is an integer, and K is the highest degree of the generation polynomial.
5. The method of claim 4 comprising providing N+K syndrome windows for the codeword.
6. The method of claim 5 comprising providing each of the N+K syndrome windows with K sub-windows.
7. The method of claim 4 comprising providing N+1 syndrome windows for the codeword.
8. The method of claim 7 comprising providing each of the N+1 syndrome windows with K sub-windows.
9. A method for detecting errors in data, comprising:
encoding the data into a codeword using a generation polynomial;
transmitting the codeword over a channel;
receiving the transmitted codeword;
generating syndromes for the received codeword using the generation polynomial;
providing a plurality of syndrome windows, each of the syndrome windows including a plurality of symbols and corresponding to an error pattern;
selecting one of the syndrome windows;
mapping into the selected syndrome window at least one symbol from at least one of the syndrome windows other than the selected syndrome window; and
determining a number of non-zero terms in an error pattern corresponding to the mapped syndrome window.
10. The method of claim 9 comprising selecting another one of the syndrome windows, and mapping into the selected syndrome window at least one symbol from at least one of the syndrome windows other than the selected syndrome window.
11. The method of claim 10 comprising selecting at least one syndrome window corresponding to an error pattern having a least number of non-zero terms.
12. The method of claim 9 comprising determining a number of non-zero bits in an error pattern corresponding to the mapped syndrome window.
13. The method of claim 9 comprising determining a number of non-zero bytes in an error pattern corresponding to the mapped syndrome window.
14. The method of claim 9 comprising repeating the steps of selecting, mapping and determining until all of the syndrome windows are selected and mapped.
15. A method for detecting errors in a codeword, comprising:
generating syndromes for the codeword using a generation polynomial;
providing a plurality of syndrome windows, each of the syndrome windows including a plurality of symbols and corresponding to an error pattern;
selecting one of the syndrome windows;
mapping into the selected syndrome window at least one symbol from at least one of the syndrome windows other than the selected syndrome window;
determining a number of non-zero terms in an error pattern corresponding to the mapped syndrome window; and
repeating the steps of selecting, mapping and determining until all of the syndrome windows are selected and mapped.
16. The method of claim 15 comprising determining a number of non-zero bits in an error pattern corresponding to the mapped syndrome window.
17. The method of claim 15 comprising determining a number of non-zero bytes in an error pattern corresponding to the mapped syndrome window.
18. The method of claim 15 comprising selecting at least one syndrome window corresponding to an error pattern having a least number of non-zero terms.
19. The method of claim 16 comprising selecting at least one syndrome window corresponding to an error pattern having a least number of non-zero bits.
20. The method of claim 17 comprising selecting at least one syndrome window corresponding to an error pattern having a least number of non-zero bytes.
21. A system for detecting errors in data, comprising:
an encoder for encoding the data into a codeword using a generation polynomial;
a transmitter for transmitting the codeword over a channel;
a receiver for receiving the transmitted codeword;
a plurality of syndromes generated for the received codeword using the generation polynomial, the plurality of syndromes comprising a plurality of syndrome symbols; and
a plurality of syndrome windows, each of the syndrome windows comprising a plurality of sub-windows and corresponding to a set of syndrome symbols;
wherein a number of non-zero terms of sub-windows of each of the syndrome windows is determined.
22. The system of claim 21 wherein at least one syndrome window has a least number of non-zero terms of sub-windows.
23. The system of claim 21 wherein a number of non-zero bits of sub-windows of each of the syndrome windows is determined.
24. The system of claim 21 wherein at least one syndrome window has a least number of non-zero bits of sub-windows.
25. The system of claim 21 wherein a number of non-zero bytes of sub-windows of each of the syndrome windows is determined.
26. The system of claim 21 wherein at least one syndrome window has a least number of non-zero bytes of sub-windows.
27. The system of claim 21 , the codeword comprising data symbols and parity symbols.
28. The system of claim 21 , the codeword comprising N data symbols and K parity symbols, wherein N is an integer, and K is the highest degree of the generation polynomial.
29. The system of claim 28 , the codeword comprising N+K syndrome windows.
30. The system of claim 28 , the codeword comprising N+1 syndrome windows.