Method for transmitting a binary information word
View Patent ↗A method is for transmitting a binary information word (MI) coded on r bits to which is attached a redundancy (CRC) coded on s bits, s and r being integers. The redundancy (CRC) signals the appearance of erroneous bits after the transmission, and is obtained by carrying out a Euclidian division of the information word (MI) to be transmitted by a generator polynomial coded on at most s bits. The generator polynomial is chosen so that it satisfies at least one of the following conditions, namely that the Hamming weight of the multiples of the generator polynomial is greater than or equal to a chosen threshold, or the generator polynomial allows the detection of at least 2 s-1 -3 consecutive erroneous bits.
1. A method for transmitting a binary word comprising r bits and a cyclic redundancy check (CRC) comprising s bits, the method comprising:
performing a Euclidian division of the binary word by a generator polynomial of at most s bits to thereby generate the CRC;
the generator polynomial being such that a Hamming weight of multiples of the generator polynomial is at least at a threshold value; and
transmitting the binary word and the CRC.
2. A method according to claim 1 , wherein the generator polynomial comprises 8 bits.
3. A method according to claim 1 , wherein the threshold value is at least 4.
4. A method according to claim 1 , wherein the generator polynomial allows the detection of at least 125 consecutive errored bits.
5. A method according to claim 1 , wherein the threshold value is at least 3.
6. A method according to claim 1 , wherein the generator polynomial allows the detection of at least 126 consecutive errored bits.
7. A method according to claim 1 , wherein the generator polynomial is selected by:
for each polynomial belonging to a chosen set, performing a first test to verify whether the polynomial allows the detection of 126 consecutive errored bits, and whether the polynomial allows the detection of 125 consecutive errored bits;
for each polynomial passing the first test, performing a second test to verify whether the polynomial allows the detection of less than 126 errored bits if the polynomial allows the detection of 126 consecutive errored bits, and whether the polynomial allows the detection of less than 125 errored bits if the polynomial allows the detection of 125 consecutive errored bits;
for each polynomial failing the second test, performing a third test to verify whether the Hamming weight of the multiples of the polynomial is at least 4;
classifying each polynomial passing the second test as belonging to a first family of generator polynomials;
for each polynomial failing the third test, performing a fourth test to verify whether the Hamming weight of the multiples of the polynomial is at least 3;
classifying each polynomial passing the third test as belonging to a second family of generator polynomials.
8. A method according to claim 7 , wherein generator polynomials belonging to the first family of generator polynomials take a form of x 7 +x 4 +x 2 +1.
9. A method according to claim 7 , wherein polynomials belonging to the second family of generator polynomials take a form of one of x 7 +x 6 +x 3 +x+1, x 7 +x 6 +x 4 x+1, x 7 +x+1, and x 7 +x 6 +x 5 +x 3 +x.
10. A method for transmitting a binary word comprising r bits and a cyclic redundancy check (CRC) comprising s bits, the method comprising:
performing a Euclidian division of the binary word by a generator polynomial of at most s bits to thereby generate the CRC;
the generator polynomial being such that the generator polynomial allows detection of at least 2 s-1 -3 consecutive errored bits, where s≧3; and
transmitting the binary word and the CRC.
11. A method according to claim 10 , wherein the generator polynomial is selected by:
for each polynomial belonging to a chosen set, performing a first test to verify whether the polynomial allows the detection of 126 consecutive errored bits, and whether the polynomial allows the detection of 125 consecutive errored bits;
for each polynomial passing the first test, performing a second test to verify whether the polynomial allows the detection of less than 126 errored bits if the polynomial allows the detection of 126 consecutive errored bits, and whether the polynomial allows the detection of less than 125 errored bits if the polynomial allows the detection of 125 consecutive errored bits;
for each polynomial failing the second test, performing a third test to verify whether the Hamming weight of the multiples of the polynomial is at least 4;
classifying each polynomial passing the second test as belonging to a first family of generator polynomials;
for each polynomial failing the third test, performing a fourth test to verify whether the Hamming weight of the multiples of the polynomial is at least 3;
classifying each polynomial passing the third test as belonging to a second family of generator polynomials.
12. A method according to claim 11 , wherein generator polynomials belonging to the first family of generator polynomials take a form of x 7+x 4 +x 2 +1.
13. A method according to claim 11 , wherein polynomials belonging to the second family of generator polynomials take a form of one of x 7 +x 6 +x 3 +x+1, x 7 +x 6 +x 4 x+1, x 7 +x+1, and x 7 +x 6 +x 5 +x 3 +x.
14. A system for transmitting a binary word comprising r bits and a cyclic redundancy check (CRC) comprising s bits, the system comprising:
CRC generation circuitry for
performing a Euclidian division of the binary word by a generator polynomial of at most s bits to thereby generate the CRC,
the generator polynomial being such that a Hamming weight of multiples of the generator polynomial is at least at a threshold value; and
a transmitter to transmit the binary word and the CRC.
15. A system according to claim 14 , wherein the generator polynomial comprises 8 bits.
16. A system according to claim 14 , wherein the threshold value is least 4.
17. A system according to claim 14 , wherein the generator polynomial allows the detection of at least 125 consecutive errored bits.
18. A system according to claim 14 , wherein the threshold value is at least 3.
19. A system according to claim 14 , wherein the generator polynomial allows the detection of at least 126 consecutive errored bits.
20. A system according to claim 14 , wherein the CRC generation circuitry selects the generator polynomial by:
for each polynomial belonging to a chosen set, performing a first test to verify whether the polynomial allows the detection of 126 consecutive errored bits, and whether the polynomial allows the detection of 125 consecutive errored bits;
for each polynomial passing the first test, performing a second test to verify whether the polynomial allows the detection of less than 126 errored bits if the polynomial allows the detection of 126 consecutive errored bits, and whether the polynomial allows the detection of less than 125 errored bits if the polynomial allows the detection of 125 consecutive errored bits;
for each polynomial failing the second test, performing a third test to verify whether the Hamming weight of the multiples of the polynomial is at least 4;
classifying each polynomial passing the second test as belonging to a first family of generator polynomials;
for each polynomial failing the third test, performing a fourth test to verify whether the Hamming weight of the multiples of the polynomial is at least 3;
classifying each polynomial passing the third test as belonging to a second family of generator polynomials.
21. A system according to claim 20 , wherein polynomials belonging to the first family of generator polynomials take a form of x 7 +x 4 +x 2 +1.
22. A system according to claim 20 , wherein polynomials belonging to the second family of generator polynomials take a form of one of x 7 +x 6 +x 3 +x+1, x 7 +x 6 +x 4 x+1, x 7 +x+1, and x 7 +x 6 +x 5 +x 3 +x.
23. A system for transmitting a binary word comprising r bits and a cyclic redundancy check (CRC) comprising s bits, the system comprising:
CRC generation circuitry for
performing a Euclidian division of the binary word by a generator polynomial of at most s bits to thereby generate the CRC,
the generator polynomial being such that the generator polynomial allows detection of at least 2 s-1 -3 consecutive errored bits, where s≧3; and
a transmitter to transmit the binary word and the CRC.
24. A system according to claim 23 , wherein the CRC generation circuitry selects the generator polynomial by:
for each polynomial belonging to a chosen set, performing a first test to verify whether the polynomial allows the detection of 126 consecutive errored bits, and whether the polynomial allows the detection of 125 consecutive errored bits;
for each polynomial passing the first test, performing a second test to verify whether the polynomial allows the detection of less than 126 errored bits if the polynomial allows the detection of 126 consecutive errored bits, and whether the polynomial allows the detection of less than 125 errored bits if the polynomial allows the detection of 125 consecutive errored bits;
for each polynomial failing the second test, performing a third test to verify whether the Hamming weight of the multiples of the polynomial is at least 4;
classifying each polynomial passing the second test as belonging to a first family of generator polynomials;
for each polynomial failing the third test, performing a fourth test to verify whether the Hamming weight of the multiples of the polynomial is at least 3;
classifying each polynomial passing the third test as belonging to a second family of generator polynomials.
25. A system according to claim 24 , wherein polynomials belonging to the first family of generator polynomials take a form of x 7 +x 4 +x 2 +1.
26. A system according to claim 24 , wherein polynomials belonging to the second family of generator polynomials take a form of one of x 7 +x 6 +x 3 +x+1, x 7 +x 6 +x 4 x+1, x 7 +x+1, and x 7 +x 6 +x 5 +x 3 +x.