Relaying method and device and destination with feedback in an OMAMRC system

Abstract

A method for relaying messages via a half-duplex relay for a telecommunications system with M sources, L relays and a destination, where M>1, L1, according to an orthogonal multiple access scheme of the transmission channel between the L relays and the destination. The method includes: decoding, via a relay, M messages each being associated with a frame and coming from a source among the M sources with detection of errors on the messages; transmitting from the relay to the destination a signal representative of a least one portion of a set of the messages for which no errors have been detected by the relay conditional on authorization from the destination, transmitting from the relay to the destination of a monitoring signal indicating a set of messages for which no errors have been detected by this relay, this transmission of the monitoring signal occurring before the transmission of the representative signal.

Claims

1. A method of relaying messages by a half-duplex relay for a telecommunication system with M sources, at least one half-duplex relay and a destination, M>1, according to a scheme for orthogonal multiple access of the transmission channel between the at least one half-duplex relay and the destination, comprising the following acts: decoding by the at least one half-duplex relay M messages each associated with a frame and originating from a source from among the M sources with detection of errors in the decoded messages, transmitting from the at least one half-duplex relay to the destination a control signal carrying only control information indicating a set of decoded messages for which no error has been detected by this half-duplex relay, after transmitting the control signal and receiving a feedback control signal from the destination in response to the transmitted control signal, transmitting from the at least one half-duplex relay to the destination a signal representative of at least one part of the set of those decoded messages for which no error has been detected by the at least one half-duplex relay solely under condition of an authorization originating from the destination given by way of the feedback control signal.

2. The method of relaying as claimed in claim 1 in which the orthogonal multiple access scheme divides the access to the channel into two phases, a first phase of M time slots corresponding to the transmission of the M messages by the M sources, a second phase of variable length corresponding to the conditional transmissions of the at least one half-duplex relay.

3. The method of relaying as claimed in claim 1 in which the authorization originating from the destination comprises an identification of a selected node authorized to transmit.

4. The method of relaying as claimed in claim 1 in which the authorization originating from the destination furthermore comprises an indication of a set of decoded messages for which no error has been detected to be selected by the at least one half-duplex relay to generate the representative signal.

5. The method of relaying as claimed in claim 3 in which the authorization originating from the destination is given by way of nominative feedback control signals indicating decoding without detected error or otherwise of each of the M messages and in which the representative signal transmitted is generated on the basis of a set of messages updated on the basis of the nominative feedback control signals received.

6. The method of relaying as claimed in claim 5 in which the at least one half-duplex relay transmits the set non-updated on the basis of the nominative feedback control signals received.

7. The method of relaying as claimed in claim 5 in which the at least one half-duplex relay transmits the set updated on the basis of the nominative feedback control signals received.

8. The method of relaying as claimed in claim 2, in which the second phase comprises conditional transmissions of the sources under condition of an authorization originating from the destination.

9. The method of relaying as claimed in claim 1 in which the at least one half-duplex relay decodes M other messages originating respectively from the M sources and each associated with another frame immediately upon receipt of a feedback control signal originating from the destination indicating decoding of the M messages without detection of error.

10. A half-duplex relay for a telecommunication system with M sources, at least the half-duplex relay and a destination, access to the transmission channel between the half-duplex relay and the destination following an orthogonal multiple access scheme, the half-duplex relay comprising: a decoder of M messages transmitted by the M sources which obtains decoded messages and detects errors in the decoded messages, a network coder which generates a signal representative of at least one part of a set of the decoded messages for which no error has been detected, a transmitter, a controller of the transmitter configured to: transmit a control signal carrying only control information indicating the set of those decoded messages for which no error has been detected by the half-duplex relay and for transmitting the representative signal; and after transmitting the control signal and receiving a feedback control signal from the destination in response to the transmitted control signal, transmit from the half-duplex relay to the destination the representative signal solely under condition of an authorization originating from the destination given by way of the feedback control signal.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Other characteristics and advantages of the invention will become more clearly apparent on reading the following description of embodiments given merely as illustrative and nonlimiting examples, and from the appended drawings, among which:

(2) FIG. 1 is a diagram of a so-called MARC (Multiple Access Relay Channel) system according to the prior art,

(3) FIG. 2 is a diagram of a so-called MAMRC (Multiple Access Multiple Relays Channel) system according to the prior art,

(4) FIG. 3 is a diagram of a so-called MARC (Multiple Access Relay Channel) system according to the prior art with an XOR network coding at the relay, the destination being a base station,

(5) FIG. 4 is a diagram of a so-called MARC system implementing a method according to the invention,

(6) FIG. 5 illustrates a first embodiment of the method according to the present invention;

(7) FIG. 6 illustrates a second embodiment of the method according to the present invention;

(8) FIG. 7 illustrates a first node selection strategy according to the present invention;

(9) FIG. 8 illustrates an embodiment of a reception method implemented by the destination D according to the invention;

(10) FIG. 9 is a diagram of a relay R according to the invention;

(11) FIG. 10 is a diagram of a destination device D according to the invention;

(12) FIG. 11 groups together the bitrate curves for the various feedback strategies according to the invention;

(13) FIG. 12 groups together the curves of probability of common outage Pr{E.sub.T.sub.max} at the destination.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

(14) The invention is described in the context of a MAMRC system illustrated by FIG. 4. This system comprises M sources, L relays and a destination D.

(15) By way of simplification of the description, the following assumptions are made hereinafter about the MAMRC (Multiple-Access Multiple-Relay Channel) network: the sources, the relays are equipped with a single transmission antenna; the relays, and the destination are equipped with a single receive antenna; the sources, the relays, and the destination are perfectly synchronized; the sources are statistically independent (there is no correlation between them); use is made of a CRC code assumed to be included in the k information bits of each source so as to know whether a message is or is not correctly decoded; the links between the various nodes suffer from additive noise and fading. The fading gains are fixed for a frame of maximum duration M+T.sub.max time slots, but can change from one frame to another. T.sub.maxL is a parameter of the system; the quality of the channel in reception (CSIR Channel State

(16) Information at receiver) is available at the destination and at the relays; the feedbacks are error-free (no error in the control signals); all the time slots have one and the same duration.

(17) The sources, nodes S.sub.i, i {1, . . . , M}, broadcast their coded information sequences for the attention of the relays, nodes R.sub.j, j {1, . . . , L} and of a destination, node D. The M sources access the transmission channel towards the relays and the destination according to an orthogonal or non-orthogonal multiple access scheme (use of one and the same radio resource). The description which follows considers orthogonal access of the sources.

(18) The L relays access the transmission channel towards the destination according to an orthogonal multiple access scheme which allows them to listen, without interference, to the transmissions of the other relays.

(19) A frame uses time slots to transmit the M messages of respectively M sources. The maximum duration of a frame is M+T.sub.max time slots. Within one and the same frame, the transmissions are divided into two phases. The first phase comprises M time slots during which the sources each transmit in their turn their packet of K information bits, denoted u.sub.S.sub.i, u.sub.S.sub.i .sub.2.sup.K, i {1, . . . , M}. The transmitted modulated symbols x.sub.S.sub.i have lengths N.sub.1 and the sources are assumed to be statistically independent (F.sub.2 being the Galois field with two elements). Each time slot has a duration of N.sub.1 uses of the channel.

(20) During channel use k, the signal transmitted in baseband by the node A {S.sub.1, . . . , S.sub.M, R.sub.1, . . . , R.sub.L} and received by the node B {R.sub.1, . . . , R.sub.L, D} is denoted y.sub.A,B,k, the static channel gain between the nodes A and B is denoted h.sub.A,B, the white noise AWGN is denoted n.sub.A,B,k, and the modulated symbol transmitted X.sub.A,k which is a complex, X.sub.A,k . When a source transmits, the relays as well as the destination listen and attempt to decode the messages received at the end of each slot (round).

(21) Each message x .sub.S.sub.1, . . . , x .sub.S.sub.M corresponding to a source S.sub.1, . . . , S.sub.M, a correctly decoded message is regarded, by abuse of notation, as being the corresponding source.

(22) By convention, S.sub.B,t denotes the set of messages (or sources) correctly decoded by the node B {R.sub.1, . . . , R.sub.L, D} at the end of the slot t. For the sake of simplicity in the description of the algorithms, it is agreed that S.sub.S,t={S} for S=S.sub.1, . . . , S.sub.M.

(23) During the first phase, and during the time slot allotted to the source S.sub.i, i=1, . . . , M, the signal received at the node B can be written:
y.sub.S.sub.i.sub.,B,k=h.sub.S.sub.i.sub., Bx.sub.S.sub.i.sub., k+n.sub.S.sub.i.sub.,B,k (1)

(24) with k=1, . . . , N.sub.1.

(25) At the end of the first phase, the set of the messages (or sources) correctly decoded by the node B {R.sub.1, . . . , R.sub.L} {D} is denoted S.sub.B,0. The set S.sub.B,0 for B {R.sub.1, . . . , R.sub.L} is identified in a control signal sent by the node B {R.sub.1, . . . , R.sub.L}.

(26) The second phase comprises a maximum T.sub.max of time slots (rounds) T.sub.maxL. Each slot (round) t {1, . . . , T.sub.max} has a duration of N.sub.2 channel uses. A control signal identifies the set S.sub.B,t .Math. {S.sub.1, . . . , S.sub.M}, 1tT.sub.max, of the messages (or sources) correctly decoded by the node B {R.sub.1, . . . , R.sub.L} at the end of the time slot (round) t.

(27) The destination D decides the number of slots used during the second phase and the node which transmits at each slot during this phase with the aim of correctly decoding a maximum of messages of the sources. During this phase the relays access the channel according to an orthogonal multiple access scheme, they can help one another. When one relay transmits, the other relays as well as the destination listen and attempt to decode the messages received at the end of the slot (round). The relays which listen can utilize the signal received to improve their set of correctly decoded messages. A non-active relay acts as the destination in its decoding process. Thus, during the slot (round) t {1, . . . , T.sub.max}, i.e. .sub.t {S.sub.1, . . . , S.sub.M, R.sub.1, . . . , R.sub.L} the node selected by the destination to transmit, then the signal received at the node B {R.sub.1, . . . , R.sub.L,D}\{.sub.t} can be written:
y.sub..sub.t.sub.,B,k=h.sub..sub.t.sub.,Bx.sub..sub.t.sub.,k+n.sub..sub.t.sub.,B,k (2)

(28) with k=1, . . . , N.sub.2.

(29) The channel gain coefficients h.sub.A,B for all A {S.sub.1, . . . , S.sub.M, R.sub.1, . . . , R.sub.L} and B {R.sub.1, . . . , R.sub.L, D} for A different from B are assumed to be independent and are assumed to follow a circular complex Gaussian probability distribution with zero mean and with variance y.sub.A,B, denoted CN(0, y.sub.A,B). The samples n.sub.A,B,k of additive white noise AWGN follow a probability distribution (pdf) CN(0,1). The power of the symbols transmitted (per complex dimension) by the sources and by the relays is assumed to be normalized to unity. y.sub.A,B is the mean power received by the receiver of the node B of the signal transmitted by the transmitter of the node A. The fading and the path losses can be included in the expression for the variance y.sub.A,B.

(30) FIG. 5 illustrates the relaying method according to the invention according to a particular embodiment. The method for relaying messages by a half-duplex relay comprises the steps of decoding, of transmitting a representative signal and of transmitting a control signal.

(31) The relay R=R.sub.1, . . . , R.sub.L decodes M messages each originating from a source from among the M sources with detection of errors in the messages. The error detection is done conventionally by utilizing a CRC.

(32) The relay R=R.sub.1, . . . , R.sub.L transmits at the start of the current slot (round), t, towards the destination D a control signal identifying the set S.sub.R,t-1 .Math. {S.sub.1, . . . , S.sub.M} of messages (which is regarded, by abuse of notation, as being the corresponding sources) for which no error has been detected by the relay at the end of the previous slot (round), t1, t {1, . . . , T.sub.max}. According to a particular realization, the relay can, if it knows the messages decoded without error at the destination at t1 (S.sub.D,t-1), transmit S.sub.R,t-1 S.sub.D,t-1, with S.sub.D,t-1={S.sub.1, . . . , S.sub.M}\S.sub.D,t-1 the complement of S.sub.D,t-1 in the set of sources.

(33) The transmission from the relay R=R.sub.1, . . . , R.sub.L towards the destination D of the control signal occurs before the transmission of a signal x.sub.R representative of at least part of those messages of the set for which no error has been detected by the relay R.

(34) The relay R=R.sub.1, . . . , R.sub.L transmits the representative signal x.sub.R towards the destination D solely under condition of an authorization originating from the destination. The destination transmits its authorization which can take various forms. According to a first mode illustrated by FIGS. 5 and 6, the destination feeds back a control signal, ACK/NACK, indicating globally that it has or has not succeeded in decoding all the sources without error (based on the verification of the CRC) and, in the case where it has not succeeded in decoding all the sources without error, an identification of the node .sub.t selected which must retransmit. According to the embodiments illustrated by FIGS. 5 and 6, the selected node is a relay. According to a second mode illustrated by FIG. 7, the destination feeds back a particular (so-called nominative) control signal ACK.sub.i/NACK.sub.i indicating that it has or has not succeeded in decoding the message of the source i without error (based on the verification of the CRC) and, in the case where it has not succeeded in decoding a message without error, an identification of the node .sub.t selected to retransmit. According to this mode, the method distinguishes as many different control signals ACK.sub.i/NACK.sub.i as source nodes.

(35) The relays receive the control signals ACK/NACK, ACK.sub.i/NACK.sub.i broadcast by the destination to the sources.

(36) As opposed to a data signal, a control signal is a signal which does not carry any useful data but control information sometimes termed out-of-band when the signal is transmitted with distinct frequency resources from those used for the useful data.

(37) According to a particular mode illustrated by FIG. 6, the destination selects not only the relay node .sub.t which must transmit at the current slot (round), t but furthermore the messages of the set .sub.t .Math. S.sub.R,t-1 to be transmitted by this relay. As a function of the destination decision criterion, for example, minimize the probability of the event E.sub.t, this may be S.sub.R,t-1 or any subset of S.sub.R,t-1.

(38) The selection performed by the destination at the current slot (round), t takes account of its knowledge of the gains h=[h.sub.S.sub.1,.sub.D, . . . , h.sub.S.sub.M,.sub.D, h.sub.R.sub.1,.sub.D, . . . , h.sub.R.sub.L,.sub.D] and, furthermore, of its knowledge of its past selections, of the sets of messages decoded correctly by the relays (regarded, by abuse of notation, as being the corresponding sources) and transmitted by the last control signals received and of the set of messages that it has decoded correctly (regarded, by abuse of notation, as being the corresponding sources) : P.sub.t-1={(.sub.1, .sub.1), . . . , (.sub.t-1, .sub.t-1)} {S.sub.R,t-1, R {R.sub.1, . . . , R.sub.L}} S.sub.D,t- 1. By convention, the knowledge set P.sub.0 bundles solely {S.sub.B,0, B {R.sub.1, . . . , R.sub.L, D}} that is to say its knowledge of the sets of messages decoded correctly by the relays at the end of the first phase (transmitted by the control signals transmitted by the relays on completion of the first phase) and its knowledge of the set of messages that it has decoded correctly on completion of the first phase on the basis solely of the signals transmitted by the sources.

(39) Let E.sub.t (h, A.sub.t, S.sub.t) be the event at the destination, conditioned by the knowledge of h and of P.sub.t-1, indicating that at least one source is not decoded correctly by the destination at the end of the slot (round) t in the course of which the node A.sub.t is the active node, S.sub.t being the set of the sources helped by the node A.sub.t. That is to say that the signal x.sub.At transmitted by the node A.sub.t is representative of the set S.sub.t of messages detected without error by the relay A.sub.t. In a similar manner, let O.sub.S,t(h, A.sub.t, S.sub.t) be the event at the destination indicating that the source S=S.sub.1, . . . , S.sub.M is not decoded correctly.

(40) With each event A.sub.t (h, .sub.t, .sub.t) is associated the probability Pr{A.sub.t} which can formally be defined as .sub.h(.sub.{A.sub.t.sub.(h,.sub.t.sub.,.sub.t.sub.)}) with .sub.h(.) the expectation on h and with .sub.{A.sub.t.sub.(h,.sub.t.sub.,.sub.t.sub.)}=1 if A.sub.t(h, .sub.t, .sub.t) is true and .sub.{A.sub.t.sub.(h,.sub.t.sub.,.sub.t.sub.)}=0 otherwise. The probability Pr{A.sub.t} depends on the selection rules.

(41) The authorization sent by the destination follows selection rules based on a strategy which consists in minimizing the probability Pr{E.sub.t} at each instant t=1, . . . , Tmax.

(42) Let T be the number of slots (round) conditional upon h and upon the selection rules. The mean number of retransmissions can be expressed in the form:
(T)=.sub.t=1.sup.T.sup.maxtPr{T=t}
(T)=.sub.t=1.sup.T.sup.maxtPr{E.sub.t-1 .sub.t}+T.sub.maxPr{E.sub.T.sub.max}
(T)=.sub.t=1.sup.T.sup.max.sup.-1Pr{E.sub.t} (3)

(43) The minimum and maximum transmission bitrates (in number of bits per channel use (b.c.u.) are defined as being equal to : R.sub.max=K/N.sub.1 and R.sub.min=M R.sub.max/(M+T.sub.max) with =N.sub.2/N.sub.1. The mean transmission bitrate can express in the form:
R=M R.sub.max/(M+(T)) (4)

(44) The expected number of information bits received during each frame is given by:
.sub.S.sub..sub.{S.sub.1.sub., . . . , S.sub.M.sub.}K(1-Pr{O.sub.S,T.sub.max})

(45) Thus, the spectral efficiency can be defined by:

(46) $\begin{array}{cc}=\frac{1}{M}\stackrel{\_}{R}\underset{S\left\{S_{1,}\mathrm{.Math.},S_M\right\}}{.Math.}K\left(1-\mathrm{Pr}\left\{O_{S,T_{\max }}\right\}\right)& \left(5\right)\end{array}$

(47) The selection rules therefore consist in maximizing the spectral efficiency defined by equation (5).

(48) Two types of relay are considered hereinafter to illustrate the rules.

(49) The instantaneous mutual information between the node A {S.sub.1, . . . , S.sub.M} {R.sub.1, . . . , R.sub.L} which transmits and the node B {R.sub.1, . . . , R.sub.L} {D} which receives is denoted I.sub.A,B. This mutual information depends on the value of the fading of the channel h.sub.A,B, the SNR y.sub.A,B, and the modulation assumption at the input of the channel.

(50) The first type is termed DCC/JDCD, distributed channel coding/joint distributed channel decoding. The second type is termed JNCC/JNCD, joint network channel coding/joint network channel decoding.

(51) For the DCC/JDCD type, the representative signal transmitted by the selected relay .sub.l is a concatenation of correctly decoded messages which each correspond to a correctly decoded source and which therefore form part of the selected set .sub.l, l {1, . . . , t-1}.

(52) Omitting the channel for the sake of simplifying the expressions, the common outage event E.sub.t(A.sub.t,S.sub.t) can be expressed in the form:
E.sub.t(A.sub.t,S.sub.t)={R.sub.max>I.sub.t.sup.c(A.sub.t,S.sub.t)} (6)

(53) with

(54) $\begin{array}{cc}{I}_t^c\left(A_t,S_t\right)={\min }_{S{\stackrel{\_}{S}}_{D,t-1}}\left(I_{S,D}+\underset{l=1}{\overset{t-1}{.Math.}}\frac{}{.Math.{\hat{S}}_l.Math.}{I}_{{\hat{A}}_l,D}{\left\{S{\hat{S}}_l\right\}}_{}\right)+\frac{}{.Math.S_t.Math.}{I}_{A_t,D}{\left\{S{S}_t\right\}}_{}& \left(7\right)\end{array}$

(55) with S.sub.D,t-1={S.sub.1, . . . , S.sub.M}\S.sub.D,t-1 the complement of S.sub.D,t-i in the set of sources.

(56) The individual outage event can be expressed in a similar manner in the form:
O.sub.s,t(A.sub.t, S.sub.t)={R.sub.max>I.sub.t.sup.S(i A.sub.t, S.sub.t)} (8)

(57) with

(58) $\begin{array}{cc}{I}_t^S\left(A_t,S_t\right)=I_{S,D}+\underset{l=1}{\overset{t-1}{.Math.}}\frac{}{.Math.{\hat{S}}_l.Math.}{I}_{{\hat{A}}_l,D}{\left\{S{\hat{S}}_l\right\}}_{}+\frac{}{.Math.S_t.Math.}{I}_{A_t,D}{\left\{S{S}_t\right\}}_{}& \left(9\right)\end{array}$

(59) For the JNCC/JNCD type, the representative signal transmitted by the selected relay .sub.l and the messages transmitted by the sources corresponding to the selected set .sub.l form a mode of joint code of the messages of the sources .sub.l, l {1, . . . , t-1}.

(60) In this case, the expressions of I.sub.t.sup.S(A.sub.t, S.sub.t) and of I.sub.t.sup.c(A.sub.t, S.sub.t) are given in [2] and can be expressed in the form:

(61) $\begin{array}{cc}{I}_t^c\left(A_t,S_t\right)=\frac{1}{.Math..Math.}\left(+\underset{l=1}{\overset{t-1}{.Math.}}{I}_{{\hat{A}}_l,D}+I_{A_t,D}\right)& \left(10\right)\\ I_t^S\left(A_t,S_t\right)=\frac{1}{.Math..Math.}\left(+\underset{l=1}{\overset{t-1}{.Math.}}{I}_{{\hat{A}}_l,D}{\left\{{\hat{C}}_l\right\}}_{}+I_{A_t,D}\right)& \left(11\right)\end{array}$

(62) with =S.sub.D,t-1\

(63) with .sub.l={{ .sub.l } and { .sub.l}}

(64) with C.sub.t={{ .sub.t } and { .sub.t }}

(65) The maximization of I.sub.t.sup.c(A.sub.t,S.sub.t) for each channel realization h conditional upon P.sub.t-1 minimizes the probability of common outage Pr{E.sub.t} which is the criterion adopted for maximizing the spectral efficiency defined by equation (5). Indeed, Pr{O.sub.s,t}Pr{E.sub.t} for each source S {S.sub.1, . . . , S.sub.M}.

(66) According to a first strategy illustrated by FIG. 5, if the destination has not correctly decoded all the sources at the start of the current slot t=1, . . . , T.sub.max, it transmits an ACK/NACK feedback signal. On receipt of this signal, the relays transmit to the destination an up-to-date version of their set of correctly decoded messages. The destination chooses the node A.sub.t {R.sub.L}. . . , .sub.D,t-1 which maximizes I.sub.t.sup.c(A.sub.t, S.sub.A.sub.t.sub.,t-1). In this case, the node selection rule can be written in the form:
.sub.t=arg max.sub.A.sub.t.sub.{R.sub.1.sub., . . . , R.sub.L.sub.}{S.sub.D,t-1.sub.}I.sub.t.sup.c(A.sub.t, S.sub.A.sub.t.sub., t-1) (12)

(67) with .sub.t=S.sub..sub.t.sub.,t-1, that is to say that the relay helps all the sources that it has correctly decoded.

(68) According to a second strategy built on the first strategy and illustrated by FIG. 6, the destination selects a relay .sub.t and the set of sources .sub.t that the relay must help, that is to say that in this case the relay generates its representative signal on just a part of the messages decoded without error if the set .sub.t is different from the set S.sub.R,t-1. The selection rule for the node and sources can be written in the form:
(.sub.t, .sub.t)=arg max.sub.A.sub.t.sub.{R.sub.1.sub., . . . , R.sub.L.sub.}{S.sub.D,t-1.sub.},S.sub.t.sub..Math.S.sub.At,t-1I.sub.t.sup.c(A.sub.t, S.sub.t) (13)

(69) A third strategy is based on the second strategy but attempts to reduce the signaling requirement (control signals). According to this third strategy illustrated by FIG. 7, at the start of each slot (round) t, the destination dispatches a nominative signal ACK.sub.i/NACK.sub.i, to the sources indicating whether they are or are not decoded without error. The relays listen and can thus deduce therefrom the set S.sub.D,t-1 of messages detected without error by the destination. If this set is complete then the relays can refrain from transmitting their control signal. Otherwise, the set is not complete, the relays transmit either their set S.sub.R,t-1 of messages decoded without error, or an update of their set S.sub.R,t-1 S.sub.D,t-1 of messages decoded without error via their control signal. The destination selects the node A.sub.t {R.sub.1, . . . , R.sub.L} {S.sub.D,t-1} knowing that this selected node will cooperate with the sources of S.sub.A.sub.t.sub.,t-1 S.sub.D,t-1.

(70) The selection rule can thus be cast in the form:
.sub.t=arg max.sub.A.sub.t.sub.{R.sub.1.sub., . . . , R.sub.L.sub.} 55 S.sub.D,t-1.sub.} I.sub.t.sup.c(A.sub.t, S.sub.D,t-1S.sub.A.sub.t.sub.,t-1) (14)

(71) with .sub.t=S.sub.D,t-1 S.sub..sub.t.sub.,t-1, that is to say that the relay helps all the sources that it has correctly decoded less those already correctly decoded by the destination.

(72) Annex A gives a pseudo code for running the selection implemented by the destination according to the third strategy.

(73) FIG. 8 illustrates an embodiment of a reception method implemented by the destination D according to the invention. The illustration shows the run diagrammatically from the end of the first phase, that is to say end of the M slots. The destination decodes all the messages received and performs a test of the CRC of each of the messages. In parallel, each relay R=R.sub.1, . . . , R.sub.L transmits at the start of the current slot (round), t, to the destination D a control signal identifying the set S.sub.R,t-1 .Math. {S.sub.1, . . . , S.sub.M} of messages that it has decoded without error.

(74) When the destination has succeeded in decoding all the sources without error, branch Y arising from the test of the CRC, it feeds a control signal, ACK, back to the sources and to the relays, indicating globally that it has succeeded in decoding all the sources without error. This ACK signal indicates the end of the frame in progress. The transmission is then continued with a new frame.

(75) When the destination has not succeeded in decoding all the sources without error, branch N arising from the test of the CRC, it performs a test on the elapsed time.

(76) When the current slot is the last of the slots of the second phase, then it places itself on standby awaiting the next frame, Fram End, branch Y arising from the test on the slot, slot=T.sub.max?

(77) When the current slot is not the last of the slots of the second phase, then it transmits an NACK signal indicating globally that it has not succeeded in decoding all the sources without error and a selection of a node .sub.t. If this node is a relay then the selection of the node is enriched with a selection of a set .sub.t of messages.

(78) The destination then again attempts to decode the messages of the sources by utilizing the signal transmitted by the node .sub.t, that is to say, if the node is a source then the signal is the retransmission of the message of the source and if the node is a relay then the signal is the signal representative of the set.

(79) FIG. 9 is a diagram of a relay R according to the invention able to cooperate with M sources S.sub.1, . . . , S.sub.M and L-1 relays R.sub.1, . . . , R.sub.L-1 and a destination D of an OMAMRC system for the implementation of a relaying method according to the invention. The relaying method is implemented by the activation of a specific software application following for example the activation of an icon with shortcut displayed on the screen of the relay.

(80) The relay R comprises a receiver REC, a decoder DEC, a microprocessor P, a network coder XOR, a memory MEM and a transmitter EM. The specific software application is stored in the memory MEM. The execution of this software application by the microprocessor P implements: the decoding by the decoder DEC of M messages each associated with a frame and originating from a source from among the M sources with detection of errors in the messages, the network coding by the XOR network coder of at least one part .sub.t of the set of those messages for which no error has been detected by the relay to generate a representative signal x.sub.R, the transmission by the transmitter EM to the destination of the representative signal x.sub.R under condition of an authorization ACK/NACK, .sub.t originating from the destination, the transmission by the transmitter EM to the destination of a control signal indicating the set S.sub.R,t-1 of those messages for which no error has been detected by this relay, this transmission of the control signal occurring before the transmission of the representative signal.

(81) FIG. 10 is a diagram of a destination device D according to the invention able to cooperate with M sources S.sub.1, . . . , S.sub.M and L relays R.sub.1, . . . , R.sub.L of an OMAMRC system for the implementation of a relaying method according to the invention. During this cooperation, the device D implements a method for receiving messages. The method for receiving messages is implemented by the activation of a specific software application following for example the activation of an icon with shortcut displayed on the screen of the device.

(82) The device D comprises a receiver REC, a decoder DEC, a microprocessor P a memory MEM and a transmitter EM. The specific software application is stored in the memory MEM. The execution of this software application by the microprocessor P implements: the decoding by the decoder DEC of the messages transmitted by the sources S.sub.1, . . . , S.sub.M to obtain estimated messages and to detect errors in the estimated messages, the reception by the receiver REC of control signals transmitted by the relays to determine for each relay the set S.sub.R,t-1 of those messages for which no error has been detected by this relay, the transmission by the transmitter EM of a feedback message ACK/NACK, .sub.t, to authorize a relay to transmit if its set S.sub.R,t-1 of messages comprises one of the messages estimated with error by the device D.

(83) According to one embodiment of the software application, its implementation furthermore allows the decoding by the decoder DEC of the representative signals x.sub.R transmitted by the relays as well as the indication in the feedback message of the selection of the set .sub.t of sources that the relay must help.

(84) Simulations have been performed with, under the assumption of a Gaussian distribution of the modulation at input, the following conditions. This distribution at input maximizes the mutual information which becomes, by definition, the capacity and is expressed in the form I.sub.A,B=log (1+|h.sub.A,B|.sup.2). The simulated system is an OMAMRC system with three sources, three relays and a destination. The parameters are T.sub.max=3, R .sub.max=1 (b. c. u.) and =0.5.

(85) FIG. 11 groups together the bitrate curves for the various feedback strategies according to the invention, the curve obtained with a system without cooperation without feedback and the curve obtained with a cooperation system without feedback. These bitrate curves show that at high SNR, the bitrate of the direct transmissions (without cooperation of the relays) becomes greater than the transmissions without feedback. The bitrate obtained with the feedback strategy (according to the invention) based on JNCC/JNCD relaying exceeds that of the feedback strategy based on DCC/JDCD relaying. The results obtained with the second and third strategies according to the invention achieve equivalent bitrate performance whether for JNCC/JNCD relaying, or for DCC/JDCD relaying. For DCC/JDCD relaying, the second and third strategies according to the invention give the best performance. For JNCC/JNCD relaying, the second and third strategies according to the invention have performance very close to that obtained with the first strategy according to the invention.

(86) FIG. 12 groups together the curves of probability of common outage Pr{E.sub.T.sub.max} at the destination. All the cooperation schemes with or without feedback have the same order of diversity equal to L+1 whilst the scheme without cooperation without feedback (direct transmission) has a diversity of one.

(87) Each of the sources may for example be a mobile terminal of a communication network. The relay may for example be a lightened base station or a terminal, and the destination may for example be a base station.

(88) As a variant, each of the sources may for example be a base station. The relay may for example be a lightened base station or a terminal, and the destination may for example be a terminal.

(89) In these various configurations, the destination may turn out to be a concentrator node, in the sense that it receives messages from all the sources, which is able to decode all the messages received in a joint manner.

(90) The invention is described in the foregoing by way of example. Different variants of the invention may be envisaged without however departing from the scope of the patent.

REFERENCES

(91) [1] C. Lott, Milenkovic O, and E. Soljanin. Hybrid arq: Theory, state of the art and future directions. In IEEE Info. Theory Workshop on Info. Theory for Wireless Networks, 2007, July 2007

(92) [2] Abdulaziz Mohamad, Raphael Visoz, and Antoine O. Berthet. Outage analysis of various cooperative strategies for the multiple access multiple relay channel. In Proc. IEEE PIMRC'13, London, UK, September 2013.

(93) TABLE-US-00001 Annex A At each start of round t (initialization) I.sub.max = 0 For each node A.sub.t {R.sub.1, ..., R.sub.L} {S.sub.D,t1} Do : calculate I.sub.t.sup.c(A.sub.t, S.sub.D,t1 S.sub.A.sub.t.sub.,t1) using (7) or (10) if I.sub.t.sup.c(A.sub.t,S.sub.D,t1 S.sub.A.sub.t.sub.,t1) > I.sub.max then I.sub.max = I.sub.t.sup.c(A.sub.t,S.sub.D,t1 S.sub.A.sub.t.sub.,t1) .sub.t = A.sub.t End For

(94) Although the present disclosure has been described with reference to one or more examples, workers skilled in the art will recognize that changes may be made in form and detail without departing from the scope of the disclosure and/or the appended claims.