Processing data for encoding and decoding a message

1. A method of encoding a message for transmission through a communication channel having adjacent information known during encoding, the encoding method comprising construction of a surjective correcting code, wherein the surjective correcting code is constructed on the basis of characterization of the adjacent information in a spherical coordinate system, wherein the method comprises the following steps:

a) determining a spherical information vector characterizing the adjacent information in the spherical coordinate system, said spherical information vector being of size n, n being a positive integer,

b) constructing a surjective correcting code using the spherical information vector and carrying out a quantization operation comprising:

determining a quantization interval as a function of a number of code words to be associated with a message, the quantization interval being equal to 2π/q 1/(n−1) , where q is the number of code words to be associated with a message, and

determining, from the quantization interval, a set of code words distributed over the surface of a hypersphere with centre 0 and of radius equal to the value of a given component of the spherical information vector; and

c) encoding the message, using the surjective correcting code.

2. The encoding method according to claim 1 , wherein step c) comprises an operation of selecting a code word closest to the spherical information vector from the code words associated with the message.

3. The encoding method according to claim 2 , wherein step c) comprises an operation of determining a Cartesian code word vector, characterizing the code word selected in a Cartesian coordinate system, from a spherical code word vector, characterizing the code word selected in the spherical coordinate system, the signal generated being a function of the Cartesian code word vector.

4. The encoding method according to claim 1 , wherein, in step a), the spherical information vector is determined from a Cartesian information vector, characterizing the adjacent information in a Cartesian coordinate system, the Cartesian information vector being of size n.

5. The method according to claim 1 , wherein step a) comprises an operation of generating a pseudo-random noise, from a key, the pseudo-random noise generated being added to components of the spherical information vector to ensure confidentiality of transmission.

6. A method of decoding a message encoded by the method according to claim 1 , wherein the method comprises a step of determining a spherical signal vector, characterizing a signal received in a spherical coordinate system, from a Cartesian signal vector, characterizing the signal received in a Cartesian coordinate system.

7. A non-transitory computer readable storage medium comprising instructions for implementing the encoding method according to claim 1 when said program is executed by a processor.

8. A non-transitory computer readable storage medium comprising instructions for implementing the decoding method according to claim 6 when this program is executed by a processor.

9. An encoder of a message intended to be transmitted through

a communication channel having adjacent information that is known during encoding, the encoder comprising means for constructing a surjective correcting code arranged for constructing the surjective code based on characterization of the adjacent information in a spherical coordinate system, wherein the encoder comprises:

a) means for determining a spherical information vector characterizing the adjacent information in the spherical coordinate system, the spherical information vector being of size n, n being a positive integer,

b) means for constructing a surjective correcting code using the spherical information vector and carrying out a quantization operation comprising:

determining a quantization interval as a function of a number of code words to be associated with a message, the quantization interval being equal to 2π/q 1/(n−1 ), where q is the number of code words to be associated with a message, and

determining, from the quantization interval, a set of code words distributed over the surface of a hypersphere with centre 0 and of radius equal to the value of a given component of the spherical information vector, and

c) suitable encoding means for encoding the message, using the surjective correcting code.

10. A transmitting equipment comprising the encoder according to claim 9 .

11. A device for decoding a message encoded by the encoder according to claim 9 , wherein the device comprises means for determining a spherical signal vector, characterizing a signal received in a spherical coordinate system, from a Cartesian signal vector, characterizing the signal received in a Cartesian coordinate system.

12. A receiving equipment comprising the decoding device according to claim 11 .