Method and device for coding sequences of data, and associated decoding method and device
AssigneeCanon Kabushiki Kaisha
InventorsPhilippe Piret, Claude Le Dantec
Life of this patent
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Abstract
The coding method to which the present invention relates takes into account: a polynomial without square g(x), N0, the smallest integer such that g(x) is a divisor of the polynomial xN0+1; n, an odd multiple of N0; a sequence u of n symbols ui to be coded; and e, a power of 2 different from 1, which is residue of e modulo N0 is equal to 1. It includes: an operation of forming a concatenated sequence uu* (304) consisting successively of the sequence u and a sequence of symbols u* such that u*(x)=u(xe) modulo xn+1, an operation of coding the concatenated sequence uu* (305), including at least one division of the concatenated sequence uu* by the polynomial g(x).
Claims23
A coding method, which takes into account:
- a polynomial without square g(x),
- N0, the smallest integer such that g(x) is a divisor of the polynomial xN0+1,
- n, an odd multiple of N0,
- a sequence u of n symbols ui, to be coded, and
- e, a power of 2 different from 1, for which the residue of e modulo N0 is equal to 1,
- the method comprising:
- an operation of forming a concatenated sequence uu* by using the sequence of symbols u, having n symbols, and a sequence of symbols u* defined by its polynomial representation u*(x)=u(xe) modulo xn+1;
- and
- an operation of coding the concatenated sequence uu*, including at least one division of the concatenated sequence uu* by the polynomial g(x) in order to form a check sequence.
A decoding method, which takes into account:
- a polynomial without square g(x),
- N0, the smallest integer such that g(x) is a divisor of the polynomial xN0+1,
- n, an odd multiple of N0, and
- e, a power of 2 different from 1, for which the residue of e modulo N0 is equal to 1,
- the method including an operation of receiving signals representing:
- a coded sequence u of n symbols ui;
- and
- the result of the division by g(x) of a concatenated sequence uu* by using the sequence of symbols u, including n symbols, and a sequence of symbols u* defined by its polynomial representation, u*(x)=u(xe) modulo xn+1, and
- the method further including a decoding operation of said received signals including the use of the polynomial g(x).
A coding device, having a processing means adapted to take into account:
- a polynomial without square g(x),
- N0, the smallest integer such that g(x) is a divisor of the polynomial xN0+1,
- n, an odd multiple of N0,
- a sequence u of n symbols ui, to be coded, and
- e, a power of 2 different from 1, for which the residue of e modulo N0 is equal to 1, the coding device adapted:
- to form a concatenated sequence uu* by using the sequence of symbols u, including n symbols, and a sequence of symbols u* defined by its polynomial representation u *(x)=u(xe) modulo xn+1, and
- to code the concatenated sequence by effecting at least one division of the concatenated sequence uu* by the polynomial g(x) in order to form a check sequence.
A decoding device, having a processing means adapted to take into account:
- a polynomial without square g(x),
- N0, the smallest integer such that g(x) is a divisor of the polynomial xN0+1,
- n, an odd multiple of N0, and
- e, a power of 2 different from 1, for which the residue of e modulo N0 is equal to 1,
- the decoding device further comprising means for receiving signals representing:
- a coded sequence u of n symbols ui;
- and
- the result of the division by g(x) of a concatenated sequence uu* by using the sequence of symbols u, including n symbols, and a sequence of symbols u* defined by its polynomial representation u *(x)=u(xe) modulo xn+1,
- wherein the processing means is adapted to decode the sequence u using the polynomial g(x).
Dependencies are inferred from the claim text.