System for transmitting information data from a transmitter to a receiver over a nested block channel

1. System for transmitting information data from a transmitter to a receiver over nested block channel, the transmitter comprising an encoder following an error correcting code structure, the receiver comprising a decoder defined according to the error correcting code structure, the nested block channel comprising a scaled BPSK binary modulator, the amplitude of which may vary from one bit transmission to the other,

wherein the coding rate (Rc) of the encoder or the parameters (D,L) of the nested block channel made of blocks are selected dependently one from each other to achieve a target diversity order of the system and to maximize the coding gain, and

wherein D represents the diversity orders of each block, and L represents the lengths of each block.

2. System according to claim 1 , a mathematical model of the nested block channel consisting in a concatenation of the blocks, said nested block channel having two parameters which are a set of the diversity orders D={D(1), . . . , D(k), . . . , D(|D|)} and a set of the lengths of blocks L={L(1), . . . , L(k), . . . , L(|D|)}, where |D| is the cardinality of the set of diversity orders D, the number of concatenated blocks being equal to |D|, the fading random variable associated to the i-th block being defined by a combination of a subset S(i) of D(i) random variables with the integer value D(i)≦λ where λ is an integer number of independent fading distributions, such that S(i+1)⊂S(i), which means ∀i<j, D(i)≧D(j) and assuming that D(1)=λ has the highest diversity order,

wherein the coding rate (Rc) of the encoder, the two parameters (D, L) of the nested block channel and the achievable target diversity order δ of the system are linked by the relationship

δ

=

D

⁡

(

i

)

⁢

⁢

where

⁢

⁢

i

⁢

⁢

is

⁢

⁢

given

⁢

⁢

by

⁢

⁢

∑

k

=

1

i

-

1

⁢

L

⁡

(

k

)

<

Rc

⁢

∑

k

=

1



D



⁢

L

⁡

(

k

)

≤

∑

k

=

1

i

⁢

L

⁡

(

k

)

.

3. System according to claim 2 , the nested block channel comprising a binary modulator the output of which are vectors of modulation symbols (zi), a partial linear combiner, a Sliding Triangular channel comprising M time slots and a detector,

wherein the modulation symbols (zi) of a same vector (Z) of modulation symbols are combined together by the linear combiner which provides an output vector (X) of M combined symbols (xi) associated to one transmission over the Sliding Triangular channel.

4. System according to claim 3 , wherein in the first combined symbols (x 1 ) and last s−1 combined symbols (x(M+2−s), . . . , x(M)) of said vector (X) of M combined symbols (xi) are linear combinations of the first s modulation symbols (zl, . . . , zs) and each of the other combined symbols (xi) is equal to one of the last M−s modulation symbols (zi), s being the partial combining size of the linear combiner.

5. System according to claim 4 , the equivalent nested block channel having parameters D={M,M−1. . . , s} and L={sN/M,N/M, . . . , N/M},

wherein the coding rate (Rc) of the encoder, the number M of time slots of the Sliding Triangular channel and the partial combining size s of the linear combiner and the achievable target diversity order δ are selected dependently one from each other by the following relationship:

δ=min( s +└(1 −Rc ) M┘, M ).

6. System according to claim 5 , wherein the partial combining size s of the linear combiner is chosen according to the target diversity order δ, the rate Rc of the encoder and the number M of time slots of the Sliding Triangular channel, by the following relationship:

s

=

arg

⁢

⁢

min

s

′

⁢

{

δ

=

min

⁡

(

s

′

+

⌊

(

1

-

Rc

)

⁢

M

⌋

,

M

)

}

.

7. System according to claim 3 , the number M of time slots of the transmission protocol which define the Sliding Triangular channel is a multiple of the partial linear combining size s of the linear combiner,

wherein the first combined symbols (x 1 ) and last s−1 symbols (x(M+2−s), . . . , x(M)) are linear combinations of the first s modulation symbols (zl, . . . , zs), the second combined symbol (x 2 ) and last s−1 non-already considered combined symbols (x(M+3−2s), . . . , x(M+1−s)) are linear combinations of the s following and non-already considered modulation symbols (z(s+1), . . . , z(2s)), and so on.

8. System according to claim 7 , the equivalent nested block channel having parameters D={M,M−1 . . . , M+1−M/s} and L={sN/M, . . . , sN/M}, wherein the coding rate (Rc) of the encoder, the number M of time slots of the Sliding Triangular channel and the partial combining size s of the linear combiner and the achievable target diversity order δ are selected dependently one from each other by the following relationship:

δ

=

min

(

M

⁡

(

s

-

1

)

s

+

1

+

⌊

(

1

-

Rc

)

⁢

M

s

⌋

,

M

)

.

9. System according to claim 8 , wherein the partial combining size s of the linear combiner is chosen according to the target diversity order δ, the coding rate (Rc) of the encoder and the number M of time slots of the Sliding Triangular channel, by the following relationship:

s

=

arg

⁢

⁢

⁢

min

s

′

⁢

{

δ

=

min

(

M

⁡

(

s

′

-

1

)

s

′

+

1

+

⌊

(

1

-

Rc

)

⁢

M

s

′

⌋

,

M

)

}

.

10. System according to claim 3 , wherein the detector performs an exhaustive marginalization to get estimates of the coded data bits being version of the information bits encoded through the encoder under the form of Log Likelihood Ratio.

11. System according to claim 3 , wherein the Sliding Triangular channel is defined by a Slotted Amplify-and-Forward protocol using β relays, one use of said Sliding Triangular channel including (β+1) time slots of the Slotted Amplify-and-Forward protocol and the size of the linear combining matrix M equals β+1.

12. System according to claim 1 , wherein the transmitter comprises a bit interleaver and the receiver comprises a de-interleaver, the bit interleaver being designed according to the error correcting code structure to ensure that the performance at the output of the associated decoder exhibits the achievable target diversity order.

13. System according to claim 12 , wherein the error correcting code is systematic and the bit interleaver places the systematic bits on the blocks of highest diversity order of the equivalent nested block channel.

14. Transmitter of a system for transmitting information data to a receiver over nested block channel, the transmitter comprising an encoder following an error correcting code structure, the receiver comprising a decoder defined according to the error correcting code structure, the nested block channel comprising a scaled BPSK binary modulator, the amplitude of which may vary from one bit transmission to the other,

wherein the coding rate (Rc) of the encoder or the parameters (D,L) of the nested block channel made of blocks are selected dependently one from each other to achieve a target diversity order of the system and to maximize the coding gain, and

wherein D represents the diversity orders of each block, and L represents the lengths of each block.

15. Transmitter according to claim 14 , a mathematical model of the nested block channel consisting in a concatenation of the blocks, said nested block channel having two parameters which are a set of the diversity orders D={D(1), . . . , D(k), . . . , D(|D|)} and a set of the lengths of blocks L={L(1), . . . , L(k), . . . , L(|D|)}, where |D| is the cardinality of the set of the diversity orders D, the number of concatenated blocks being equal to |D| the fading random variable associated to the i-th block being defined by a combination of a subset S(i) of D(i) random variables with the integer value D(i)≦λ where λ is an integer number of independent fading distributions, such that S(i+1)⊂S(i), which means ∀i<j, D(i)≧D(j) and assuming that D(1)=λ has the highest diversity order,

wherein the coding rate (Rc) of the encoder, the two parameters (D, L) of the nested block channel and the achievable target diversity order δ of the system are linked by the relationship

δ

=

D

⁡

(

i

)

⁢

⁢

where

⁢

⁢

i

⁢

⁢

is

⁢

⁢

given

⁢

⁢

by

⁢

⁢

∑

k

=

1

i

-

1

⁢

L

⁡

(

k

)

<

Rc

⁢

∑

k

=

1



D



⁢

L

⁡

(

k

)

≤

∑

k

=

1

i

⁢

L

⁡

(

k

)

.

16. Transmitter according to claim 15 , the nested block channel comprising a binary modulator the output of which are vectors of modulation symbols (zi), a partial linear combiner, a Sliding Triangular channel comprising M time slots and a detector,

wherein the modulation symbols (zi) of a same vector (Z) of modulation symbols are combined together by the linear combiner which provides an output vector (X) of M combined symbols (xi) associated to one transmission over the Sliding Triangular channel.

17. Transmitter according to claim 16 , wherein the first combined symbols (x 1 ) and last s−1 combined symbols (x(M+2−s), . . . , x(M)) of said vector (X) of M combined symbols (xi) are linear combinations of the first s modulation symbols (zl, . . . , zs) and each of the other combined symbols (xi) is equal to one of the last M−s modulation symbols (zi), s being the partial combining size of the linear combiner.

18. Transmitter according to claim 17 , the equivalent nested block channel having parameters D={M,M−1 . . . , s} and L={sN/M,N/M, . . . , N/M},

wherein the coding rate (Rc) of the encoder, the number M of time slots of the Sliding Triangular channel and the partial combining size s of the linear combiner and the achievable target diversity order δ are selected dependently one from each other by the following relationship:

δ=min( s +└(1 −Rc ) M┘,M ).

19. Transmitter according to claim 18 ,

wherein the partial combining size s of the linear combiner is chosen according to the target diversity order δ, the coding rate (Rc) of the encoder and the number M of time slots of the Sliding Triangular channel, by the following relationship:

s

=

arg

⁢

⁢

min

s

′

⁢

{

δ

=

min

⁡

(

s

′

+

⌊

(

1

-

Rc

)

⁢

M

⌋

,

M

)

}

.

20. Transmitter according to claim 16 , the number M of time slots of the transmission protocol which define the Sliding Triangular channel is a multiple of the partial linear combining size s of the linear combiner,

wherein the first combined symbols (x 1 ) and last s−1 symbols (x(M+2−s), . . . , x(M)) are linear combinations of the first s modulation symbols (zl, . . . , zs), the second combined symbol (x 2 ) and last s−1 non-already considered combined symbols (x(M+3−2s), . . . , x(M+1−s)) are linear combinations of the s following and non-already considered modulation symbols (z(s+1), . . . , z(2s)), and so on.

21. Transmitter according to claim 20 , the equivalent nested block channel having parameters D={M,M−1 . . . , M+1−M/s} and L={sN/M, . . . , sN/M},

wherein that the coding rate (Rc) of the encoder, the number M of time slots of the Sliding Triangular channel and the partial combining size s of the linear combiner and the achievable target diversity order δ are selected dependently one from each other by the following relationship:

δ

=

min

(

M

⁡

(

s

-

1

)

s

+

1

+

⌊

(

1

-

Rc

)

⁢

M

s

⌋

,

M

)

.

22. Transmitter according to claim 21 , wherein the partial combining size s of the linear combiner is chosen according to the target diversity order δ, the coding rate (Rc) of the encoder and the number M of time slots of the Sliding Triangular channel, by the following relationship:

s

=

arg

⁢

⁢

⁢

min

s

′

⁢

{

δ

=

min

(

M

⁡

(

s

′

-

1

)

s

′

+

1

+

⌊

(

1

-

Rc

)

⁢

M

s

′

⌋

,

M

)

}

.

23. Transmitter according to claim 14 , wherein the transmitter comprises a bit interleaver and the receiver comprises a de-interleaver, the bit interleaver being designed according to the error correcting code structure in order to ensure that the performance at the output of the associated decoder exhibits the achievable target diversity order.

24. Transmitter according to claim 23 , wherein the error correcting code is systematic and the bit interleaver places the systematic bits on the blocks of highest diversity order of the equivalent nested block channel.