Transmission method and omamrc system with a selection strategy during retransmissions taking into account the throughput of the sources and of one or more control exchanges

Abstract

The present invention relates to a method for transmitting a frame carrying messages for an OMAMRC telecommunication system having N nodes, including M sources si ie{1,..., M} and a destination, where N ≥ M ≥ 2. The method involves: - estimating a number of retransmission intervals sufficient for the destination to decode a source not yet correctly decoded and correctly decoded by at least one node on the basis of the quality of an equivalent channel for said source between said at least one node and the destination and of a throughput assigned to said source (sj), - having the destination select the sources to be assisted taking into account the estimated numbers of retransmission intervals sufficient for the destination to decode the sources not yet correctly decoded and of a sum of throughputs assigned to the sources, - a number of retransmission intervals per source defining a so-called allowed duration for assisting a source during said allowed duration limited by a time remaining until T max even if the estimated number of retransmission intervals sufficient for this source is greater than the remaining time.

Description

[0001] DESCRIPTION

[0002] TITLE: Transmission method and OMAMRC system with a selection strategy during retransmissions taking into account the flow rate of the sources and one or more control exchanges Field of the invention

[0003] The present invention relates to the field of digital communications. Within this field, the invention relates more particularly to the transmission of coded data between at least two sources and a destination with relaying by at least one node which may be a relay or a source.

[0004] It is understood that a relay does not have a message to transmit. A relay is a node dedicated to relaying messages from sources while a source has its own message to transmit and can also in certain cases relay messages from other sources i.e. the source is said to be cooperative in this case.

[0005] There are many relaying techniques known by their Anglo-Saxon names: "amplify and forward", "decode and forward", "compress-and-forward", "non-orthogonal amplify and forward", "dynamic decode and forward", etc.

[0006] The invention applies in particular, but not exclusively, to the transmission of data via mobile networks, for example for real-time applications, or via, for example, sensor networks.

[0007] Such a sensor network is a multi-user network, consisting of several sources, several relays and a recipient using an orthogonal multiple access scheme in time of the transmission channel between the relays and the sources, noted OMAMRC ("Orthogonal Multiple-Access Multiple-Relay Channel" according to English terminology).

[0008] Prior art

[0009] The considered OMAMRC telecommunication system illustrated in Figure 1 has N nodes and one destination with an implementation of a time orthogonal multiple access scheme of the transmission channel that applies between the N nodes. The N nodes include M sources and L relays. The maximum number of time slots per transmitted frame is M + T max with M intervals allocated during a first phase to the successive transmission of the M sources and T used T max intervals for one or more cooperative transmissions allocated during a second phase to one or more nodes selected by the destination according to a selection strategy.

[0010] Such an OMAMRC transmission system implementing a selection strategy in the second phase is known from the article by S. Cerovic, R. Visoz, and L. Madier entitled "Efficient Cooperative HARQ for Multi-Source Multi-Relay Wireless Networks.", 14th International Conference on Wireless and Mobile Computing, Networking and Communications (WiMob). IEEE, 2018. The OMAMRC transmission system described is such that each of the sources can operate at different times either exclusively as a source or as a relay node. The node terminology covers both a relay and a source acting as a relay node or as a source. A relay is distinguished from a source because it has no message to transmit of its own, i.e. it only retransmits messages from other nodes.

[0011] The links between the different nodes of the system are subject to slow fading and Gaussian white noise. Knowledge of all the links in the system (CSI: Channel State Information) by the destination is not available. Indeed, the links between sources, between relays, between relays and sources are not directly observable by the destination and their knowledge by the destination would require too much information exchange between the sources, the relays and the destination. To limit the cost of the feedback overhead, represented by dotted lines in Figure 1, only information on the channel distribution / statistics (CDI: Channel Distribution Information) of all the links, e.g. average quality (e.g. average SNR, average SINR) of all the links, is assumed to be known by the destination in order to determine the rates allocated to the sources.

[0012] Link adaptation is said to be slow type, that is to say that before any transmission, the destination allocates initial rates to the sources knowing the distribution of all the channels (CDI: Channel Distribution Information). In general, it is possible to go back to the CDI distribution on the basis of knowledge of the average SNR or SINR of each link in the system.

[0013] Message transmissions from sources are formatted into frames during which the CSI of the links are assumed to be constant (slow fading assumption). The rate allocation is assumed not to change for several hundred frames, it changes only with CDI changes.

[0014] The process distinguishes three phases: an initial phase and, for each frame to be transmitted, a 1st phase and a 2nd phase. The transmission of a frame takes place in two phases which are possibly preceded by an additional phase called the initial phase.

[0015] During the initialization phase, the destination determines an initial rate Rt for each source Si by taking into account the average quality (e.g. SNR) of each of the links in the system. The destination estimates the quality (e.g. SNR) of the direct links: source to destination and relay to destination according to known techniques based on the exploitation of reference signals. The quality of the source-source, relay-relay and source-relay links is estimated by the sources and relays by exploiting for example the reference signals. The sources and relays transmit to the destination the average qualities of the links. This transmission occurs before the initialization phase. Since only the average value of the quality of a link is taken into account, its refresh occurs on a long time scale, i.e. over a time which makes it possible to average the rapid variations (fast fading) of the channel.This time is of the order of the time required to travel several tens of wavelengths of the transmitted signal frequency for a given speed of a node in the system. The initialization phase occurs, for example, every 200 to 1000 frames. The destination sends the initial rates it has determined back to the sources via a return path. The initial rates remain constant between two occurrences of the initialization phase.

[0016] In the first phase, the M sources successively transmit their message during the M time slots using modulation and coding schemes determined from the initial bit rates. During this phase, the number N r channel use (ie resource element according to 3GPP terminology) is fixed and identical for each of the sources.

[0017] During the first phase, independent sources broadcast their coded information sequences in the form of messages to a single recipient. Each source broadcasts its messages at its initial rate. The destination communicates its initial rate to each source via very limited rate control channels. Thus, during the first phase, the sources each transmit their respective messages in turn during time slots, each dedicated to a source.

[0018] Sources other than the one transmitting and possibly relays, of the “Half Duplex” type, receive successive messages from the sources and decode them.

[0019] In the second phase, the destination selects for the current interval t a single node taken from the sources and the relays to cooperate. This node randomly selects the source it helps from among the one it has correctly decoded and that the destination has not yet correctly decoded by transmitting a redundancy of the message from this source.

[0020] This phase lasts a maximum of T max time slots. During this phase, the number N2 of channel uses is fixed and identical for each of the selected nodes (sources and relays).

[0021] This article teaches control signals which consist, for the destination to broadcast M bits which indicate its set of correctly decoded sources at the interval t — 1, for the nodes which have correctly decoded a source that the destination has not yet correctly decoded to transmit a signal on a dedicated unicast channel and for the others to remain silent and finally for the destination to broadcast the result of its selection according to the chosen selection strategy. Although these exchanges limit the overhead linked to signaling while allowing a maximization of the average spectral efficiency (utility metric) within the considered system under the constraint of respecting an individual quality of service (QoS) per source, it may be desirable to further limit the signaling overhead while making the best use of the time for the transmission of a frame.

[0022] The present invention meets this objective.

[0023] Main features of the invention

[0024] The present invention relates to a method for transmitting a frame carrying messages intended for an OMAMRC telecommunications system to M sources s, ie{l, M}, possibly L relays r^ r L and a destination, N > M > 2, L > 0, the nodes operating in half-duplex mode, according to an orthogonal multiple access scheme of the transmission channel between the N nodes with a maximum number of M + T max time intervals per transmitted frame distributed between a l ere phase and a 2 nde phase, 1 < T max , the message from a source having been coded before transmission using an incremental redundancy type coding which generates several redundancies, the l ere phase includes M intervals allocated respectively to successive transmissions from the M sources and the 2 ndephase comprises at least one retransmission interval for a transmission of nodes having correctly decoded the same source s, such that these nodes simultaneously transmit during the same retransmission interval the same redundancy of the message from the same source not yet correctly decoded by the destination, called the source to be helped. The method is such that it comprises: at least one decoding control exchange between the destination and the nodes, this exchange allowing the destination to determine, for each of the sources, a quality of an equivalent channel based on a quality of the channels between the nodes having correctly decoded a source i and the destination, an estimation of a number of retransmission intervals (x, (0)) sufficient for the destination to decode a source (s,) not yet correctly decoded and correctly decoded by at least one node on the basis of the quality of an equivalent channel for this source between this at least one node and the destination and a flow rate (R;) assigned to this source (s;), a selection by the destination of the sources to be helped taking into account the estimated numbers (Xj (0)) of retransmission intervals sufficient for the destination to decode the sources not yet correctly decoded and a sum of flow rates (Ri) assigned to the sources, a number of retransmission intervals per source defining a so-called authorized duration to help a source during this authorized duration limited by a time remaining until T, maxeven if the estimated number of sufficient retransmission intervals for this source is greater than the remaining time. During a decoding control exchange between the source and the nodes, the nodes communicate to the destination their set of correctly decoded sources. If the destination has previously communicated its own set of correctly decoded sources, the transmission by the nodes may contain only their set of correctly decoded sources minus those already correctly decoded by the destination. The transmission by the nodes allows the destination to evaluate the quality of the node-destination channels to estimate per source a sufficient number of retransmission intervals for the destination to correctly decode this source.Knowing these sufficient interval numbers, the destination can then successively select the sources to be helped either randomly or in an ordered manner from among those whose sufficient interval number is less than the time remaining before reaching T. max . The ordering can be done by successively selecting the sources according to the increasing number of sufficient intervals.

[0025] Thus, while limiting the number of control exchanges between the source and the nodes during which the nodes communicate to the destination their set of correctly decoded sources, the invention gives an opportunity to the destination to decode a source even if the remaining time is less than the number of sufficient retransmission intervals estimated for this source. The destination successively selects this source for the authorized duration and at most for the remaining time until it decodes it correctly.

[0026] According to one embodiment of the invention, the method further comprises, if the remaining time is not zero, an exchange of decoding control between the destination and the nodes so that the destination reestimates a number of retransmission intervals sufficient for the destination to decode a source i, this source having been assisted for the authorized duration but not yet decoded correctly by the destination.

[0027] Help from a source for the allowed time without decoding success by the destination triggers a new decoding control exchange to update the estimated number of intervals provided there is time remaining before reaching T max The process is stopped when all sources are correctly decoded by the destination or when the maximum time Tmax est reached.

[0028] According to one embodiment of the invention, only the nodes having correctly decoded the source i transmit a decoding indicator of this source i.

[0029] According to one embodiment of the invention, only the nodes having correctly decoded the source i transmit their set of correctly decoded sources.

[0030] According to one embodiment of the invention, the nodes transmit at least their set of sources correctly decoded and not yet correctly decoded by the destination. According to one embodiment of the invention, at least one decoding control exchange comprises a transmission by the nodes of at least their set of sources correctly decoded and not yet correctly decoded by the destination carried out at the beginning of the 2 nde phase.

[0031] According to one embodiment of the invention, the method further comprises a comparison between a sum of estimated numbers of retransmission intervals to help the destination to decode sources not yet correctly decoded and a number of time intervals remaining during the 2 nde phase to help the destination correctly decode one or more sources.

[0032] In this mode, the method adds at least two estimated numbers and compares the result to the remaining time. If the result of the addition is less than the remaining time, all sources involved in the addition can be helped during the 2 nde phase.

[0033] According to one embodiment of the invention, the comparison is updated after the correct decoding of a source by the destination.

[0034] Since correct decoding by the destination of a source may occur before the end of the estimated number of sufficient retransmission intervals, this mode allows another source to benefit from the unused time.

[0035] According to one embodiment of the invention, the at least one decoding control exchange comprises a transmission by the nodes of at least their set of sources correctly decoded and not yet correctly decoded by the destination and a transmission by the source of its set of sources correctly decoded.

[0036] According to one embodiment of the invention, a node sends only its set of sources correctly decoded and not yet correctly decoded by the destination during the at least one decoding control exchange,

[0037] According to one embodiment of the invention, a node sends its set of correctly decoded sources during the at least one decoding control exchange.

[0038] According to one embodiment of the invention, the method further comprises a comparison between the estimated numbers of retransmission intervals sufficient for the selection to take into account an ordering of these estimated numbers of sufficient retransmission intervals. According to this mode, the estimated numbers of sufficient retransmission intervals are classified according to their value. And, preferably, the method first selects the source for which the estimated number of sufficient retransmission intervals is the smallest. The same source is helped for the duration corresponding to this estimated number or for a shorter duration if its correct decoding by the destination occurs before the end of the estimated number. The method thus successively considers the sources remaining to be correctly decoded.According to one embodiment of the invention, the method further comprises determining a set of sources to be assisted taking into account the estimated numbers of sufficient retransmission intervals and a time remaining before the end of the 2. nde phase.

[0039] According to one embodiment of the invention, the set of sources to be helped contains all the undecoded sources when none of the sufficient number of retransmission intervals is less than the remaining time.

[0040] The invention further relates to a communication device suitable for implementing a transmission method according to the invention.

[0041] The invention further relates to a system comprising M sources s Xi ... , s M , L relay r^ ... , r L and a destination d, M > 2, L > 0, for an implementation of a transmission method according to the invention.

[0042] The invention further relates to each of the specific software applications on one or more information media, said applications comprising program instructions adapted to the implementation of the transmission method when these applications are executed by processors.

[0043] The invention further relates to configured memories comprising instruction codes corresponding respectively to each of the specific applications.

[0044] Memory can be incorporated into any entity or device capable of storing the program. The memory can be of the ROM type, for example a CD-ROM or a microelectronic circuit ROM, or of the magnetic type, for example a USB key or a hard disk.

[0045] Furthermore, each specific application according to the invention can be downloaded from a server accessible on an Internet-type network.

[0046] The optional features presented above in the transmission method may optionally be applied to the software application and memory mentioned above.

[0047] List of figures

[0048] Other characteristics and advantages of the invention will appear more clearly on reading the following description of embodiments, given as simple illustrative and non-limiting examples, and the appended drawings, among which:

[0049] [Fig 1] Figure 1 is a diagram of an example of a so-called Cooperative OMAMRC (Orthogonal Multiple Access Multiple Relays Channel) system described with regard to the prior art, [Fig 2] Figure 2 is a diagram of a transmission cycle of a frame according to an example implementation of the invention, [Fig 3] Figure 3 is a diagram illustrating an exchange of decoding control between the destination and the nodes, sources and relays, according to the invention.

[0050] [Fig 4] Figure 4 is a diagram illustrating a conditional decoding control exchange between the destination and the nodes, sources and relays, according to the invention if the duration allowed to help a source i among the several not yet decoded is not sufficient for a correct decoding by the destination and the maximum time T max is not reached.

[0051] Description of particular embodiments

[0052] A channel use is the smallest granularity in time-frequency resource defined by the system that allows the transmission of a modulated symbol. The number of channel uses is related to the available frequency band and the transmission duration. An OMAMRC system is illustrated in Figure 1 already described.

[0053] An OMAMRC system according to the invention comprises M sources which belong to the set of sources 5 = {s 1; , s M], possibly L relays which belong to the relay set = {r x , ... , r L ] and a destination d. By convention, it is considered that Sj = i Vi E {1, ... , M} and

[0054] = M + t Vt £ {1, ... , L}, in other words, we can confuse a source and its index, and a relay and its index (shifted by the value M of the number of sources). Each source of set 5 communicates with the unique destination with the help of the other sources (user cooperation) and the cooperating relays.

[0055] Transmission cycle of a frame according to the invention

[0056] A transmission cycle of a frame according to an exemplary implementation of the invention is illustrated in Figure 2.

[0057] The method according to the invention distinguishes two phases for each frame to be transmitted, one ère phase and a 2 ndephase. The transmission of a frame is possibly preceded by an additional phase called initial during which the flow rates are allocated.

[0058] The M sources access the transmission channel according to a time orthogonal multiple access scheme during the l ere phase. During the 2 nde phase, access to the transmission channel of the N nodes which include the M sources and possibly the L relays is considered orthogonal because at each retransmission interval the active nodes transmit in parallel the same redundancy of the same message from the same source i.

[0059] The N nodes operate in a half-duplex mode that allows them to listen to the transmissions of other nodes without interference. The sources can act as a relay when they are not transmitting only their own message.

[0060] The CSI of the links is assumed to be constant (slow fading assumption) during the transmission of a frame. From time to time, the destination allocates rates to sources knowing the distribution of all channels (CDI: Channel Distribution Information). The rate allocation is assumed not to change for several hundred frames, it only changes with CDI changes.

[0061] Each of the allocated bit rates unambiguously determines a modulation and coding scheme (MCS) and conversely each MCS determines a bit rate. The allocated bit rates are transmitted from the destination to the sources via very limited bit rate control channels (shown in dotted lines in Figure 1).

[0062] For the sake of simplification of the description, the following assumptions are subsequently made about the OMAMRC system:

[0063] - the sources, relays and destination are equipped with a single transmit antenna (or transmit antenna port);

[0064] - sources, relays and destination are equipped with a single receiving antenna (or receiving antenna port);

[0065] - sources, relays and destination are perfectly synchronized;

[0066] - the sources are statistically independent (there is no correlation between them);

[0067] - all nodes transmit with the same power;

[0068] - use is made of a CRC code supposedly included in the K L information bits from each source i to determine whether the message associated with the information bits is correctly decoded or not, i ES;

[0069] - links between different nodes suffer from additive noise and fading. Fading gains are fixed during the transmission of a frame carried out for a maximum duration of M + T max time intervals, but can change independently from frame to frame. T max > 1 is a system parameter;

[0070] - the instantaneous quality of a direct channel / link in reception (CSIR Channel State Information at Receiver) is available at the destination, sources and relays;

[0071] - returns are error-free (no errors on control signals / channels).

[0072] The following notations are used:

[0073] • R t = K L / N ± is a discrete variable representing the throughput of source i provided by a link adaptation method implemented before the transmission of frames,

[0074] • T usedis the number of retransmission intervals used during the 2 nde phase, T used E

[0075] {1, ... , T max}, it corresponds to the number of transmissions during this phase, the remaining time is defined by T max - T used ,

[0076] • a = N2 / N r is the ratio of the number of channel uses available at each time interval (slots) of the 2 nde phase and the number of channel uses available at each time interval (slots) of the l ere phase, • S d i is the set of sources not correctly decoded by the destination at the end of the retransmission interval l, l E {1, T used ],

[0077] • S ai is the set of sources correctly decoded by node a ESU 3Î at the end of the retransmission interval l, l E {1, ... , T used},

[0078] • O i tis the outage indicator which takes the value one when an individual default event occurs and the value zero in other cases. O,- T represents the source failure event i ie the source is not decoded correctly after sending a frame given that the maximum number of retransmission intervals T max was reached without this source i being correctly decoded. The individual fault event O i t depends at each retransmission interval t (slot) on the mutual information of the nodes having correctly decoded the source i,

[0079] • L[ id represents the mutual information between the source i E {1, ... , M] and the destination d,

[0080] • J î.dXJ-) represents the mutual information between all the nodes helping the source i and the destination at the retransmission interval l (it is considered an equivalent channel formed by the different channels between these nodes and the destination). By convention, J i d (0) is equal to I i d .

[0081] Transmission of a frame according to the invention

[0082] During the first phase of the process, the sources i ES successively transmit their message u after coding L including K t information bits u L E F2 l , F2 being the two-element Galois field. The message u Lincludes a CRC-type code that allows the integrity of the tq message to be verified. The tq message is coded according to the MCS determined by the allocated bit rate. Given that the MCSs may be different between sources, the lengths of the coded messages may be different between sources. The coding uses an incremental redundancy-type code. The resulting code word is segmented into successive redundancies. The incremental redundancy code may be of a systematic type, in which case the information bits are included in the first redundancy. Whether or not the incremental redundancy code is of a systematic type, it is such that the first redundancy can be decoded independently of the other redundancies.The incremental redundancy type code can be implemented for example by means of a finite family of rate-compatible punctured linear codes or rate-free codes modified to operate with finite lengths: raptor code (RC), rate-compatible punctured turbo code (RCPTC rate-compatible punctured turbo code), rate-compatible punctured convolutional code (RCPCC rate-compatible punctured convolutional code), rate-compatible LDPC (RCLDPC rate-compatible low-density parity check code). Transmission by a source conventionally comprises one or more reference signals. The destination estimates in a known manner the channel and therefore its quality between each of the sources and the destination by exploiting for example the received reference signal(s).

[0083] Whether during the first phase or the second phase, when a node transmits, especially a source, the destination and other nodes listen.

[0084] The destination, sources, and relays attempt to decode the received redundancies at the end of a time interval. The success of decoding at each node is decided using the CRC. The destination and nodes thus determine their set of successfully decoded sources at each interval.

[0085] The 2 nde transmission phase of the process includes t = {1, ... , T used \ retransmission intervals with the convention that t = 0 corresponds to the last transmission interval of the first phase. The term retransmission associated with an interval is used in connection with the 2 nde phase to clearly indicate that any transmission during this phase of a n lème redundancy of the message from a source i occurs when this source i has already transmitted the l ere redundancy of this same message during the l ere phase.

[0086] Unlike the prior art, there is no exchange of decoding control between the destination and the nodes at each retransmission interval: the destination does not systematically send back its set of correctly decoded sources at each retransmission interval or any indication of correct or incorrect decoding, the nodes do not systematically transmit their set of correctly decoded sources at each retransmission interval or any indication of correct or incorrect decoding. The exchange of decoding control for updating the destination's knowledge of the sets of sources correctly decoded by the nodes occurs at least once when t = 1, i.e. at the start of the second phase. This exchange can occur in an equivalent manner at the end of the first phase.During such an exchange, the nodes transmit to the destination their set of correctly decoded sources or at least their set of correctly decoded sources not yet correctly decoded by the destination. The transmission by a node typically includes one or more reference signals. The destination estimates in a known manner the channel and therefore its quality between each of the nodes and the destination by exploiting, for example, the reference signal(s) received during this exchange.

[0087] Thus, the nodes transmit to the destination their set of correctly decoded sources or at least their set of correctly decoded sources not yet correctly decoded by the destination at least once, i.e. at least during the last transmission interval, t = 0 or equivalently during the 1 erretransmission interval, t = 1. On the other hand, the destination selects at each retransmission interval a source called source to help by using a broadcast control channel from the destination to the nodes. The nodes having correctly decoded this source then transmit the same redundancy of the message from this source during this interval using a data channel. Helping a source means helping the destination to decode this source by transmitting by the nodes having correctly decoded this source a redundancy of the message from this source during the 2 nde phase.

[0088] Selection according to the invention

[0089] The selection by the destination of a source to be assisted at each retransmission interval is explained below with the support of Figure 3 which illustrates an exchange of decoding control between the destination and the nodes according to one embodiment. According to this mode, the destination sends back to the nodes its set of correctly decoded sources and the nodes transmit their set of correctly decoded sources. According to another mode, the destination sends back to the nodes its set of correctly decoded sources and the nodes transmit their set of correctly decoded sources and not yet correctly decoded by the destination. According to another mode, the destination sends back to the nodes a signal indicating a lack of correct decoding, NACK and the nodes transmit their set of correctly decoded sources.

[0090] During the 2 ndephase, the destination schedules in turn the sources not yet correctly decoded for a given number of successive transmissions in order to maximize the received sum throughput. A transmission, during a retransmission interval, to assist a source i corresponds to the transmission of the same redundancy version of its message by all the nodes having correctly decoded this source. Transmissions to assist a source i begin at the retransmission interval t s i and end when the source is decoded. The individual fault event of source i, for which the retransmission intervals start at t s i , at the end of the retransmission interval t — 1, can be expressed in the form:

[0091] This expression reflects the fact that source i is not decoded correctly at retransmission interval t — 1 if the rate R Lof the source is greater than the sum of the transmission capacities. This transmission capacity includes the capacity of the channel between this source i and the destination which occurs during the l ere phase and a weighted sum by a of the capacities of the equivalent channels which occur during the second phase from t s i up to retransmission interval t — 1. At retransmission interval l > t s i of the second phase, an equivalent channel is considered for source i. The equivalent channel considered at a retransmission interval l groups the channels between each of the nodes helping source i during this interval and the destination. The capacity of the channel between this source i and the destination is deduced from the quality of the channel i.e. the mutual information between source i E {1, ... , M} and destination d. The capacity of the equivalent channel considered when source i is assisted during interval l is evaluated by the mutual information J L: a(J-) between the set of nodes that help source i at retransmission interval l and the destination. This capacity depends on time l since a node can benefit from transmissions to help a source i during the 2 nde phase and correctly decode this source i from a retransmission interval of the 2 nde phase when he had not decoded it at the end of the l ere phase.

[0092] X(t) is defined as the number of retransmission intervals elapsed up to (but not including) the current interval during the second phase since the last decoding control exchange between the destination and the nodes.

[0093] X m(t) defines the value of X(t) that triggers a new exchange of decoded source sets. For example, X m (t) = 2 Vt E {1, ... , T max ] triggers an exchange of decoded source sets

[0094] By convention, X m (l) = 0 triggers an exchange of decoded source sets at the start of the 2 nde transmission phase.

[0095] It is assumed that a source i is aided over one or more consecutive retransmission intervals starting with retransmission interval t s i E {1, ... , T max}. At each retransmission interval (time slot) t > t s i , and for the selected source i not yet correctly decoded by the destination, i ES ati, the variable %j(t) is defined according to the invention. This variable %j(t) is defined as being the maximum number (i.e. sufficient number) of retransmission intervals for the destination to decode this source i (starting from and counting the retransmission interval t s ), that is, source i is decoded at the latest at the end of the retransmission interval t + %j(t) — 1. This variable %j(t) is estimated by the destination based on its knowledge of J i d (!) IE {t s i , ... t}. Let the set S' = {t' o , t\, t' N} determined by X m (t) retransmission intervals starting with an exchange of sets of decoded sources. Let the set S = {t0, ... , t M ] retransmission intervals starting with an exchange of decoded source sets coinciding with transmissions to assist source i, i.e., t s i < t0 < ■■■ < t M .

[0096] In the event that an exchange of decoded source sets took place before t s that is, before the start of the selection of source i to help during the 2 nde phase, the destination knows h,d(ts,i) = Ji,d(ts,i) It should be noted that an exchange of sets of decoded sources at the beginning of the 2 nde transmission phase allows the destination to know for all sources. Indeed, the transmissions preceding t s i being linked to another source they do not impact the number of nodes having decoded source i nor

[0097] Otherwise, the destination only knows Ji d to estimate %j(t) for t s i < t < t0. For simplicity of notation, the source index i of t s i is omitted when it is obvious.

[0098] For retransmission intervals t s < t < t0the invention considers: the number of sufficient retransmission intervals estimated by the destination from the retransmission interval t is:

[0099] Xi(t) = [yi(t)l (4) where |q] represents the upper integer function (ceiling function) which takes the integer value just greater than or equal to q, eg, [2.3] = 3.

[0100] For t = t0, an exchange of decoded source sets takes place, which allows the destination

[0101] More generally, for tq < t < t / +1 j = 0, ... , M — 1, it is possible to recursively construct y t (t) as: with always:

[0102] Xi(t) = [yi(01- Note:

[0103] Between two decoding control exchanges the number of retransmission intervals sufficient to decode source i is decremented at each transmission helping source i. For t > t M , he comes:

[0104] Finally, in the case where no exchange of decoded source sets is carried out either before or after t s , he comes:

[0105] In the case where a single exchange of decoded source sets is carried out at the beginning of the 2 nde transmission phase then:

[0106] Xi(t) is the number of retransmission intervals to assist source i from and including retransmission interval t sufficient for error-free decoding of source i which is estimated by the destination based on its knowledge of Ji :d (T) Vl G ■■■ > t + %j(t) — !}■ The destination uses as an approximation of J i d ( / ) a previous (closest known) value J iid (l) = J iid (l') with l' < l therefore J i d (!) < ] i d (l) Vl E {t s i , .... t + %j(t) - 1}-

[0107] The number of retransmission intervals needed in practice x“(t) requires knowledge of Ji :d (l') Vl G {t s i , t + x“(t) — 1}. It is given by the smallest value of x such that:

[0108] The estimate %j(t) is the smallest value of x such that:

[0109] In case Ji :d (T) = Ji,a(XR it comes:

[0110] Indeed, the smallest positive integer such that: East :

[0111] Thus, it is certain that the fault event (outage) does not occur at t + Xjft) — 1. The source i is systematically decoded correctly by the destination at — 1 if it is helped %j(t) times from the interval t included.

[0112] The generalization of this demonstration in the case of several decoding exchanges is immediate.

[0113] It should be noted that the evaluation of the number of retransmission intervals sufficient for a source i is the same regardless of t s i its retransmission interval chosen for the first transmission intended to help this source during the 2 nde phase. At a given retransmission interval t, %j(t) depends only on the number of transmissions îtj = t — t s i helping source i during the 2 nde phase and before t. Thus, the notation denotes the necessary number of transmissions helping source i knowing the number of transmissions Hj having helped source i (already carried out) during the 2 nde phase. Subsequently, we denote x Lthe counter of the number of transmissions remaining to help source i, this counter being initialized to %j(0) and being decremented each time source i is helped without decoding exchange. This counter is updated at each decoding control exchange at the retransmission interval l = tj j = 0, ... , M — 1 which makes it possible to know

[0114] If the estimate of X[ is such that there has been no previous transmission to help source i or such that %j(0) relies solely on knowledge of direct links and that for all sources i E {1,

[0115] T'max — HiES (i t-1 x i then all sources can be decoded without exchanging sets of decoded sources. Since all sources can be decoded correctly by the destination in the remaining time, the method chooses, for example, successively the sources to be helped and randomly. The method according to the invention is particularly interesting when T max x i since it allows the destination to correctly decode an optimal number of sources by optimizing spectral efficiency while very strongly limiting the signaling overhead by performing the selection of the source to be helped according to a certain strategy.

[0116] Furthermore, according to invention X m (l) = 0 ie an exchange of control of correctly decoded source sets between the destination and the nodes occurs at least once ie at the beginning of the 2 nde phase.

[0117] At t = 1 ie at the beginning of the 2 ndephase, the method comprises an exchange of decoding control between the destination and the nodes. The method determines the sufficient number of retransmission intervals for the destination to decode the source i not yet decoded at the end of the l ere phase knowing its allocated flow rate with îtj the number of transmissions already made to help source i. Following the exchange of decoding control between the destination and the nodes at t = 1, the destination knows ] = Without decoding control exchange at t=l, the destination is based on Â,d(ls,i) = / t,d(0) = k,D i.e. on the knowledge of the direct link between the source i and the destination.

[0118] The estimation of the channel between source i and destination is performed, for example, on the basis of the reference signals emitted by source i when it transmits during the first phase. Since the channels are assumed to be invariant during a frame, this value is independent of the transmission or retransmission interval. This knowledge of the channel quality between source i and destination allows the destination to estimate mutual information representative of this quality and therefore of the capacity of the channel.

[0119] In the second phase, the estimation of the channel between node j E {1, ... , M + L} and the destination is performed, for example, on the basis of a reference signal emitted by node j during a control exchange during which it transmits its set or a subset of this set of correctly decoded sources. This knowledge of the quality of the channel between node j and the destination at the interval t = 1 allows the destination to estimate mutual information Ji,d(l) representative of the quality of the equivalent channel between all the nodes having decoded source i and the destination.

[0120] For t > 1 the method considers that each transmission leads to mutual information a / i,d(l) s i well q ue *i(0 decreases depending on the number of transmissions made to help source i.

[0121] The destination selects, according to the invention, for each retransmission interval t the source i to be helped.

[0122] At each retransmission interval t and before selection, the remaining number of retransmission intervals T av is . T av T-max ^used- A t ^> Tused 9. The selection is determined to maximize the spectral efficiency. The maximization of the spectral efficiency can be expressed in the form of the determination of the subset A taken from the set P(S d t-1 ') of possible subsets A of sources not yet correctly decoded by the destination at the interval preceding the current interval t leading to the largest sum of the rates of the sources and such that the sources of this subset A can be decoded in the remaining time, T av ie such that the remaining time is greater than or equal to the sum of the number of retransmission intervals sufficient to decode each of the sources of this subset A:

[0123] Â = argmax AeP( s d t-i:i X £ ieA R t such as XÎEA x t < T av(22)

[0124] P(S d t _i) is called the power game of S d

[0125] The method then successively considers each source i of this subset A.

[0126] For each source i considered in A, the destination transmits to the nodes the indication of the selection of source i at the retransmission interval t.

[0127] The nodes that have correctly decoded this source i transmit the same redundancy during this interval t to help the decoding of the source i by the destination.

[0128] The destination repeats the transmission of the indication of the selection of the same source i until the destination correctly decodes this source. The number of retransmission intervals elapsed before correct decoding is at most equal to Xj(0).

[0129] According to a particularly efficient embodiment, if the destination correctly decodes the source i before the number x has elapsed ( (0) retransmission intervals, it considers the next source of the subset A as soon as this source i is correctly decoded. This case can appear when the set of sources correctly decoded by a node changes to include source i during the %j(0) retransmission intervals. Thus, this node becomes active during the transmission at interval l of a redundancy for source i which leads to an increase in the mutual information Jt, d (l) > Ji,a <X)-

[0130] According to the invention, an authorized duration N is set maxto assist one or more sources not yet correctly decoded by the destination and for which the sufficient number of retransmission intervals is greater than the remaining time. The method may comprise a conditional decoding control exchange if the duration allowed to assist a source i among the several not yet decoded is not sufficient for correct decoding by the destination and the maximum time T max is not reached. Such a decoding control exchange is illustrated in Figure 4.

[0131] Destination d requests an update, Req_i, for source i. In response, the nodes transmit Info_i. According to a first embodiment, this decoding control exchange is such that only nodes that have correctly decoded source i transmit their set of correctly decoded sources, Info_i = S a l-r for a node a ESU 3Î under the condition that i ES a l-r .

[0132] According to another embodiment, this exchange of decoding control between the destination and the nodes is such that only the nodes having correctly decoded the source i transmit not their complete set of decoded sources but a decoding indicator Info_i of this source i. This mode consumes less bandwidth of the signaling channel than the previous mode. According to another embodiment, only the nodes having correctly decoded the source i during the second phase called retransmission transmit a decoding indicator Info_i of this source i. Indeed, the exchange of set of decoded sources at the beginning of the second phase makes it possible to know the nodes which were able to decode the source i at the end of the first phase

[0133] This mode consumes the least bandwidth of the signaling channel.

[0134] According to another embodiment, this exchange of decoding control between the destination and the nodes is such that all the nodes transmit their set of correctly decoded sources, Info_i = S ai ti for all nodes at ESU 3Î. This mode is more bandwidth-consuming for the signaling channel between the nodes and the destination than the two previous modes but simpler for the nodes.

[0135] Regardless of the embodiment, at the end of the exchange, the destination can re-estimate, i.e., update the sufficient number of retransmission intervals to decode the source i. If the re-evaluated number of retransmission intervals does not exceed T maxthen source i continues to be helped until it is decoded without error by the destination, otherwise the destination can switch to another source and remove source i from the set of sources that can be helped during the remaining retransmission intervals. At the end of the decoding control exchange, the destination can therefore update a set of sources to be helped in the remaining time. If the sufficient number updated for source i exceeds the remaining time, another source not yet decoded correctly can be favored.

[0136] Implementation example

[0137] The following description of an embodiment of the invention is illustrated with an implementation by an OMARC system with M = 4 sources, S = {1,2, 3, 4}, L = 3 relays, R = {5,6,7}, and one destination. The parameter T max is set to 8. At the beginning of the 2 ndephase, ie, t = 1, the sets of sources correctly decoded by the nodes are as follows:

[0138] 5i,o = {1}< 52, O = {2}, 5 3 0 = {3},S 40 = {4},S 5 0 = {2,3},S 6.0 = {1,2,3}, S7,0= <P, S dfi = 0.

[0139] In other words, sources 1, 2, 3, 4 and relay 7 have not yet decoded anything correctly at the end of the l ere phase but since a source knows its own message its game contains at least this message. Relay 5 correctly decoded sources 2 and 3 and relay 6 correctly decoded sources 1, 2 and 3 at the end of the l ere phase. Destination d has not yet decoded anything correctly and S d 0 #= (p at the end of the l ere phase.

[0140] During the 2 nde phase, the determination by the destination of the set of sources  to be helped takes place for example according to the algorithm in Appendix A.

[0141] During the 2nde phase, the selection of the source i to be helped from the set A at each retransmission interval takes place for example according to the algorithm of Annex B which can be used since

[0142] Sequence of the Algorithm in Appendix B:

[0143] Step 0. Initialization: t = 0, T av = T max , N; = 0 V i ES d t , N max ; F = (b

[0144] According to the example the remaining time is initialized to 8 ie T av = 8, Nj = 0 for all sources since no source has been helped yet, F = <p, N max = 3 the duration allowed for a source i even if x L exceeds the remaining time.

[0145] Step 1. The destination determines the estimate of the number of intervals required X[ for the destination to decode a source i not yet decoded based on knowledge of mutual information of the source i destination link and a rate R Lassigned to this source i. The destination therefore calculates x L for all i ES d 0 . The process moves to 2 nde phase ie t = 1.

[0146] According to the example, the variables x L have the following values ​​knowing the direct source-destination links: x t = 6, x2= 2, x3= 3, x4= 12

[0147] The flow rates have the following values:

[0148] R4= 1, R2= 2, R3= 3, R4= 4

[0149] Step 2. t = 1, initialization of the retransmission interval called the current interval. According to Appendix B this step is associated with the start of the 2 nde phase.

[0150] Step 3. If T av ie, the remaining time is less than the sum of the x t of the sources not yet correctly decoded by the destination, then the process performs steps 4-6, otherwise it goes to step 7.

[0151] According to the example, the sum of the x texceeds the remaining time: 6 + 2 + 3 -l- 12 = 23 > T av = T m ax = 8 and therefore the process performs steps 4-6 before moving on to step 7. Step 4. A decoding control exchange takes place between the destination and the nodes.

[0152] During this exchange, the nodes transmit their set of correctly decoded sources or only their set of correctly decoded sources but not yet correctly decoded by the destination.

[0153] According to the example, the sources and relays respectively send their set of correctly decoded sources: S 1 0 = {l},S2,o = {2}, S 3 0 = {3}, S 40 = {4}, S 5 0 = {2,3}, S 60 = {1,2,3}, S 7 0 = <p.

[0154] Step 5. For a source i not yet correctly decoded by the destination, the destination updates the estimate of x Lusing the quality of the equivalent channel considered as the aggregation of the channels between the nodes having correctly decoded this source and the destination.

[0155] According to the example, knowing the node-destination links, the variables become: x t = 6, x2= 1, x3= 3, x4= 12

[0156] Although x2 has decreased, the sum of %j: 6 + l -l- 3 -l- 12 = 22 remains greater than the remaining time T av — T max — 8.

[0157] Step 6. End of step 3 if.

[0158] Step 7. All sources A to help at the beginning of the 2 nde phase is determined, according to the algorithm in Appendix A, by the destination knowing the and the R flow rates L attributed to the sources.

[0159] According to the example, the possible choices for  that satisfy X[ < T avare: {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}. The set that leads to the maximum sum of the flow rates and which is determined according to the algorithm in Appendix A is  = {2, 3}. The flag returned by the call to algorithm B is equal to 1, i.e. the set A = {2, 3} is decodable since = 4 < 8 = T av .

[0160] Steps 8 to 30. l ere “while” loop. The method repeats steps 8-30 to decode the frame while t < T max , while there is time left ie T av > 0 and there remains a source i to be decoded in the set  ie  #= <p.

[0161] According to the example, at the current interval t = 1, T av = 8, Â = {2, 3}. t = 1 < T max , T av = 8 > 0 océdé goes to step 9.

[0162] According to the example, at the current interval t = 4, S d 3 = {2,3}, i = 3, x3= 1, N3= 2, N max = 3, T av = 5,  = S d 3 = {1,4}, flag = 0, Output=0. T max= 8. t = 4 < T max , T av = 5 > 0 and  = {1,4} #= 0 then the process proceeds to step 9. According to the example, at the current interval T av = 4,  = S d 4 = {1,4}, flag = 0, T max = 8, Output=0. t = 5 < T max , T av = 4 > 0 and  = {1,4} #= 0 then the process proceeds to step 9.

[0163] According to the example, at the current interval t = 6, i = 1, x4= 4, N4= 2, S d 56 = {2,3}, N max = 3, T av = 3,  = S d 5 = {1,4}, flag = 0, T max = 8. Output=0. t = 6 < T max , T av = 3 > 0 and  = {1,4} #= 0 then the process proceeds to step 9.

[0164] According to the example, at the current interval t = 7, x4= 2, N4= 3, S d 6 = {2,3}, N max = 3, T av = 2,  = S d ,6= {1,4}, flag = 0, T max = 8. Output=0. t = 7 < T max , T av = 2 > 0 and  = {1,4} 7= 0 then the process goes to step 9.

[0165] Step 9. At retransmission interval t, the destination selects source i with the smallest X[ and proceeds to step 10.

[0166] According to the example, at the current interval t = 1, T av = 8, the destination selects source 2 i.e., i = 2, x2= 1. The process proceeds to step 10.

[0167] According to the example, at the current interval t = 2, S d l = {2}, T av = 7, flag = 1, Output=0. The destination selects source 3 i.e., i = 3, x3= 3. The process proceeds to step 10.

[0168] According to the example, at the current interval t = 4, S d 3 = {2,3}, N max = 3, T av = 5, Â = S d 3 = {1,4}, flag = 0, Output=0, T max = 8. The destination selects source 1 since x x = 6 < x4= 12 ie, i = 1, x x = 6. The process proceeds to step 10.

[0169] According to the example, at the current interval t = 5, i = 1, x x= 5, N4= 1, S d 4 = {2,3}, N max = 3, T ar = 4, A = S d 4 = {1,4}, flag = 0, T max = 8, Output=0. The destination selects source 1 since x4= 5 < x4= 12 ie, i = 1, x x = 5. The process proceeds to step 10.

[0170] According to the example, at the current interval t = 6, i = 1, x4= 4, N4= 2, S d 5 = {2,3}, N max = 3, T ar = 3, A = S d 5 = {1,4}, flag = 0, T max = 8. Output=0. The destination selects source 1 since x4= 4 < x4= 12 ie, i = 1, x x = 4. The process proceeds to step 10.

[0171] According to the example, at the current interval t = 7, i = 1, x ± = 2, N4= 3, S d 6 = {2,3}, N max = 3, T av = 2, A = S d 6 = {1,4}, flag = 0, T max = 8. Output=0. The destination selects source 1 since x4= 2 < x4= 12, ie, i = 1, x x = 2. The process proceeds to step 10.

[0172] Step 10. Initialize the “Exit” exit condition of the 2 to 0 e “while” loop and the process proceeds to step IL

[0173] Steps 11-29. 2 e “while” loop. The method repeats steps 11-29 until the source i is successfully decoded by the destination, and there is time T remaining av > 0 and the maximum time is not reached i.e. t < T max and that the exit condition is not reached ie

[0174] "output" is equal to 0. According to the example, at the current interval t = 1, i = 2, N2= 0, x2= 1, T av = 8, flag = 1, Output=0, S d 0 = 0. i = 2 0 S d 0 and Output=0 and T av = 8 > 0 and t = l < T max then the process moves to step 12.

[0175] According to the example, at the current interval t = 2, Output=0, i = 3, x3= 3, S d l = {2}, T av = 7, flag = 1. i = 3 0 S d l and Output=0 and T av = 7 > 0 and t = 2 < Tmax then the process moves to step 12.

[0176] According to the example, at the current interval t = 3, i = 3, N3= 1, x3= 2 and T av = 6, N max = 3, flag = 1, Output=0. S d 2 = {2} ie, i = 3 0 S d 2 and Output=0 and T av = 6 > 0 and t = 3 < T m ax then proceeds to step 12.

[0177] According to the example, at the current interval t = 4, i = 1, x x = 6, S d 3 = {2,3}, N max = 3, T av = 5, 5 > 0 and t = 4 < T max then the process moves to step 12.

[0178] According to the example, at the current interval t = 5, i = 1, x4= 5, N3= 1, S d 4 = {2,3}, N max = 3, T av = 4, Â = S d 4 = {1,4}, flag = 0, T max = 8. Output=0. i = 1 0 S d 4 and Output=0 and T a v = 4 > 0 and t = 5 < T max then the process moves to step 12.

[0179] According to the example, at the current interval t = 6, i = 1, x4= 4, N3= 2, S d 5 = {2,3}, N max = 3, T av = 3, Â = S d 5 = {1,4}, flag = 0, T max = 8. Output=0. i = 1 0 S d 5 and Output=0 and T a v = 3 > 0 and t = 6 < T max then the process moves to step 12.

[0180] According to the example, at the current interval t = 7, i = 1, x r = 2, N3= 3, S d 6 = {2,3}, N max = 3, T av = 2, Â = S d 6 = {1,4}, flag = 0, T max = 8. Output=0. i = 1 0 S d 6 and Output=0 and T av = 2 > 0 and t = 7 < T max then the process moves to step 12.

[0181] According to the example, at the current interval t = 8, i = 1, x r = 1, N3= 4, S d 7 = {2,3}, N max = 3, T av = 1, Â = S d 7 = {1,4}, flag = 0, T max = 8. Output=0. i = 1 0 S d 7 and Output=0 and T a v = l > 0 and t = 8 < T maxthen the process moves to step 12.

[0182] Step 12. At retransmission interval t the destination forwards the number of source i to be assisted by the nodes as selected in step 9.

[0183] According to the example, at the current interval t = 1, i = 2, the destination sends back the number 2. The nodes having decoded the source 2 transmit in parallel the same redundancy. The process goes to step 13.

[0184] According to the example, at the current interval t = 2 < T max = 8, i = 3, x3= 3, S d l = {2}, T av = 7, flag = 1, Output = 0. The destination returns number 3. The nodes that decoded source 3 transmit the same redundancy in parallel. The process moves to step 13.

[0185] According to the example, at the current interval t = 3, i = 3, N3= 1, x3= 2, T av = 6, N ma x = 3, flag = 1, Output = 0. S d 2= {2}. The destination returns number 3. The nodes that decoded source 3 transmit the same redundancy in parallel. The process proceeds to step 13.

[0186] According to the example, at the current interval t = 4, i = 1, x x = 6, S d 3 = {2,3}, N max = 3, T av = 5, destination returns number 1. The nodes that decoded source 1 transmit the same redundancy in parallel. The process moves on to step 13.

[0187] According to the example, at the current interval T av = 4, A = S d 4 = {1,4}, flag = 0, T max = 8. Output=0. The destination returns number 1. The nodes that decoded source 1 transmit the same redundancy in parallel. The process proceeds to step 13.

[0188] According to the example, at the current interval t = 6, i = 1, x x = 4, N ± = 2, S d 5 = {2,3}, N max = 3, T a v = 3, A = S d 5= {1,4}, flag = 0, T max = 8. Output=0. The destination returns number 1. The nodes that decoded source 1 transmit the same redundancy in parallel. The process proceeds to step 13.

[0189] According to the example, at the current interval t = 7, i = 1, x ± = 2, N ± = 3, S d 6 = {2,3}, N max = 3, T av = 2, A = S d 6 = {1,4}, flag = 0, T max = 8. Output=0. The destination returns number 1. The nodes that decoded source 1 transmit the same redundancy in parallel. The process proceeds to step 13.

[0190] According to the example, at the current interval t = 8, i = 1, x r = 1, N r = 4, S d 7 = {2,3}, N max = 3, T av = 1, A = S d 7 = {1,4}, flag = 0, T max = 8. Output=0. The destination returns number 1. The nodes that decoded source 1 transmit the same redundancy in parallel. The process proceeds to step 13.

[0191] Step 13. The method increments the value of the current retransmission interval, t <- t + 1, decrements the remaining time, T av <- T av — 1 and decrements the value of x t since i has been helped once by the nodes and increments the counter of transmissions having helped source i. The process goes to step 14 or exits the if loop and goes to step 20.

[0192] According to the example, for i = 2, t = 2, N2= 1, x2= 0 and T av = 7. Are unchanged: flag = 1, Output=0. S d l = {2}, ie, source 2 is correctly decoded by the destination. The process proceeds to step 14.

[0193] According to the example, for i = 3, t = 3, 1V3= 1, x3= 2, T av = 6, flag = 1, Output=0.

[0194] S d 3 = {2}, 3 g S d 2 , the process proceeds to step 20.

[0195] According to the example, for i = 3, t = 4, N3= 2, x3= 1, T av = 5, flag = 1, Output=0.

[0196] S d ,3= {2,3}, 3 e S d 3 , the process proceeds to step 14. According to the example, for i = 1, t = 5, 1V X = 1, x x = 5, T av = 4, Â = S d 4 = {1,4}, flag = 0, T max = S, Output=0. process proceeds to step 20.

[0197] According to the example, for i = 1, t = 6, x x = 4, N ± = 2, S d 5 = {2,3}, T av = 3, Â = S d 5 = {1,4}, flag = 0, T max = 8. Output=0.

[0198] S d 5 = {2,3}, 1 g S d 5 , the process proceeds to step 20.

[0199] According to the example, for i = 1, t = 7, x x = 3, N ± = 3, S d 6 = {2,3}, T av = 2, Â = S d 6 = {1,4}, flag = 0, T max = 8. Output=0.

[0200] S d 6 = {2,3}, 1 g S d 6 , the process proceeds to step 20.

[0201] According to the example, for i = 1, t = 8, x± = 1, N ± = 4, S d 7 = {2,3}, N max = 3, T av = 1, Â = S d ,7= {1,4}, flag = 0, T max = 8. Output=0.

[0202] S d 78 = {2,3}, 1 0 5 d 7, the process proceeds to step 20.

[0203] According to the example, for i = 1, t = 9, x ± = 0, N ± = 5, N max = 3, T av = 0, Â = S d 8 = {4}, flag = 0, T max = 8. As x ± = 0 then 1 £ S d 8 ,

[0204] S d 8 = {1,2,3} ie source 1 is decoded correctly by the destination. Since t = 9 > T max then the process exits loop 11-29 and goes to step 29, then to step 30.

[0205] Step 14. If the destination has decoded the source i correctly then proceed to steps 15-19.

[0206] Otherwise the process goes to step 19.

[0207] According to the example, at the current interval t = 2, the source i = 2 is correctly decoded since x2= 0. S d ;1 = {2}, N2= 1, T av = 7, flag = 1, Output=0. The process proceeds to step 15. According to the example, at the current interval t = 3, i = 3, 1V3= 1, x3= 2, and T av = 6, flag = 1, Output=0, source 3 is not correctly decoded, S d 2 = {2}, the process goes to step 19, then 20.

[0208] According to the example, at the current interval t = 4, i = 3, 1V3= 2, x3= 1 and T av = 5, source 3 is correctly decoded, S d 3 = {2,3}, flag = 1, N max = 3, Output=0. The process proceeds to step 15.

[0209] Step 15. The source i correctly decoded by the destination is removed from the set Â. According to the example, at the current interval N2= 1, T av = 7, flag = 1, Output = 0. The process proceeds to step 16.

[0210] According to the example, at the current interval t = 4, i = 3, 1V3= 2, x3= 1, S d 3 = {2,3}, N max = 3 and T av = 5, flag = 1, Output=0. Â = Â \ {3} = 0 and the process proceeds to step 16. Step 16. If the x t intervals have not been consumed and that set A does not contain all the sources not decoded correctly by the destination and that flag = 1 then the method performs steps 17-18. Otherwise the method goes to step 18.

[0211] According to the example, at the current interval t = 2, i = 2, x2= 0, Â = {3}. S d l = {2}, N2= 1, T av = 7 , flag = 1, Output = 0. The condition x2 > 0 is not met although the conditions A = {3} #= S d l = {1,3,4} and flag = 1 are fulfilled, the process goes to step 18, then 19 then to step 29 then to step 30 since source 2 is correctly decoded, i.e. the process loops back to step 8 with A = {3}, t = 2, i = 2, x2= 0, S d l = {2}, N2= 1, Tav = 7, flag = 1, Output=0.

[0212] According to the example, at the current interval t = 4, i = 3, x3= 1, 1V3= 2, S d 3 = {2,3}, N max = 3 and T'a.v = flag = 1, Output=0, A = 0. The condition x3> 0 is met as well as the conditions A = 0 #= S d 3 = {1,4} and flag = 1, so the process performs steps 17-18.

[0213] Step 17. The method updates set A according to the algorithm in Appendix A with the updated set of sources not decoded correctly by the destination and returns an updated flag value.

[0214] According to the example, at the current interval t = 4, i = 3, x3= 1, 1V3= 2, S d 3 = {2,3}, N max = 3 is called the algorithm of Appendix A with (5, S d 3 ) to update A and flag.

[0215] According to the algorithm in Appendix A since Sj=i,4 x i = 6 + 12 = 18 > T av = 5 and that x d= 6 > 5 and that x4= 12 > 5 ie there is no subgame that has a sum of x t less than the remaining time then: A = S d 3 = {1,4} and flag = 0 ie A = S d 3 = {1,4} is a non-decodable set. The method proceeds to step 18, then 19, then 20 with t = 4, i = 3, x3= 1, 1V3= 2, N max = 3, T av = 5, Â = S d 3 = {1,4}, flag = 0, Output=0.

[0216] Step 18. End of step 16. The process proceeds to step 19.

[0217] Step 19. End of step 14. The process proceeds to step 20.

[0218] According to the example, at the current interval t = 3, 1V3= 1, x3= 2 and T av = 6, flag = 1, Output=0, S d 2 = {2}. The process proceeds to step 20.

[0219] Step 20. If the destination did not decode source i correctly and flag = 0 and IVj = N max then proceed to steps 21-28. Otherwise the process goes to step 28.

[0220] According to the example, at the current interval t = 3, i = 3, 1V3= 1, x3= 2, S d 2 = {2} and T av = 6, flag = 1, Output=0. i 0 S d 2 and Output=0 but / V3< N max then the process proceeds to step 28. According to the example, at the current interval t = 4, S d 3 = {1,4}, i = 3, x3= 1, N3= 2, T av = 5, A = $d,3 = {1,4}, flag = 0, Output = 0. 3 ES d 3 then the process proceeds to step 28.

[0221] According to the example, at the current interval

[0222] S d 4 = {1,4}, flag = 0, T max = 8, Output=0. 1 g S d 4 and flag = 0 but N ± #= N max then the process proceeds to step 28.

[0223] According to the example, at the current interval Sd,5 = {1,4}, flag = 0, T max = 8. Output=0. 1 g S d 5 and flag = 0 but N ± #= N max then the process proceeds to step 28.

[0224] According to the example, for i = 1, t = 7, x4= 3, N3= 3, S d 6 = {2,3}, T av = 2, Â = S d 6 = {1,4}, then the process proceeds through steps 21-28.

[0225] According to the example, for i = 1, t = 8, x r = 1, N r = 4, S d 7 = {2,3}, T av = 1, Â = S d 7 = {1,4}, flag = 0, T max = 8. Output=0. 1 g S d 7 and flag = 0 and N3 > N max then the process proceeds to step 29.

[0226] Step 21. A decoding control exchange takes place between the destination and the nodes.

[0227] During this exchange, the nodes transmit their set of correctly decoded sources or only their set of correctly decoded sources but not yet correctly decoded by the destination. The process then proceeds to step 22.

[0228] According to the example, at the current interval t = 7, there is an exchange of control and the method proceeds to step 22.

[0229] Step 22. For a source i not yet correctly decoded by the destination, the destination updates the estimate of x t using the quality of the equivalent channel considered to be the aggregation of the channels between the nodes having correctly decoded this source and the destination. The method proceeds to step 23.

[0230] According to the example, at the current interval t = 7, N ± = 3, S d 6 = {2,3}, T av = 2, Â = S d 6 = {1,4}, flag = 0, T max = 8. Output=0. After update: x r = 2, x4= 12. The process proceeds to step 23.

[0231] Step 23. If x t > T av then the process proceeds through steps 24-27.

[0232] According to the example, at the current interval t = 7, x1= 2, N1= 3, S d 6 = {2,3}, N max = 3, T av = 2, A = S d 6 = {1,4}, flag = 0, T max = 8. Output=0. x ± = 2 > T avthen the process proceeds to step 27.

[0233] Step 24. Source i is entered in list F of sources that are no longer supported.

[0234] Step 25. Update set A with the set of sources not yet decoded by the destination minus the contents of F. Step 26. Initialize to 1 the exit condition "Exit" of the 2 e “while” loop and the process proceeds to step 27.

[0235] Step 27. End of step 23, the process proceeds to step 28.

[0236] Step 28. End of step 20. The process proceeds to step 29.

[0237] Step 29. End of the while loop of step 11. The process loops back to step 11 if source i has not been decoded and output = 0 and t < T max otherwise the process proceeds to step 30. According to the example, at the current interval t = 3, i = 3, 1V3= 1, x3= 2, T av = 6, S d 2= {2}, flag = 1, Output = 0. The process loops back to step 11.

[0238] According to the example, at the current interval t = 4, S d 3 = {2,3}, i = 3, x3= 1, N3= 2, T av = 5, X = S d ,3= {1,4}, flag = 0, Output=0. 3 ES d 3 then the process proceeds to step 30.

[0239] According to the example, at the current interval t = 8, i = 1, x r = 1, N ± = 4, S d 7 = {2,3}, T av = 1, then the process loops back to step 11.

[0240] Step 30. End of the while loop from step 8.

[0241] According to the example, at the current interval t = 4, S d 3 = {2,3}, i = 3, x3= 1, N3= 2, T av = 5, then the process loops back to step 8.

[0242] According to the example, at the current interval t = 5, i = 1, x x = = 1, S d 4 = {2,3}, T av = 4,  = S d ,4= {1,4}, flag = 0, T max= 8, Output=0. t = 5 < T max = 8 and  #= 0 then the process loops back to step 8.

[0243] According to the example, at the current interval t = 6, i = 1, x x = = 2, S d 5 = {2,3}, T av = 3, Â = then the process loops back to step 8.

[0244] According to the example, at the current interval t = 7, i = 1, x r = 2, N ± = 3, S d 6 = {2,3}, T av = 2, then the process loops back to step 8.

[0245] According to the example, at the current interval t = 8, i = 1, x r = 1, N ± = 4, S d 7 = {2,3}, T av = 1, then the process loops back to step 8.

[0246] According to the example, at the current interval t = 9, Za loop 8-30 is terminated. The transmission of the frame is interrupted, there is a decoding fault (outage event) of source 4. The method moves on to the transmission of the next frame. Thus, according to the invention, the absence of correct decoding of source 1 although N max is reached (step 20) triggers a decoding control exchange (step 21) to update the determination of the x L and check if x r has become smaller or larger than the remaining time.

[0247] According to a 1 er scenario taken into account in the example above, at step 22 x r is considered equal to 2 = T av = 2, the remaining time. As a result, source 1 is not added to list F and the set A = {1,4} remains unchanged. The destination then selects the source until it is decoded or T max is reached.

[0248] According to another scenario, at step 22 x ± is considered equal to 3 > T av = 2, the remaining time. As a result, source 1 is added to list F so F = {1} and set A is updated: A = S d \F = {4} and the output variable = 1. At the end of step 30, the process loops back to step 8. The destination selects i = argmin iE ^x L = {4}. Loop 11-29 is interrupted either when source 4 is decoded correctly, or when t > T max (since N max = 3 > T av = 2). In this case:

[0249] • source 4 is helped during 7 e interval (if the decoding is correct, the transmission of the frame is interrupted),

[0250] • source 4 is helped during 8 e interval (whether the decoding is correct or not, the transmission of the frame is interrupted at the end of the interval).

[0251] Appendix A

[0252] Determination of the set A of sources to be helped:

[0253] [Table 1]

[0254] If there is no more source to decode  is the empty set

[0255] If there are enough remaining retransmission intervals (rounds) then A includes the entire set of sources not decoded by the destination. A is a "decodable" set then: flag = 1

[0256] A includes the set with the highest sum of rates and satisfying the condition of the number of remaining retransmission intervals.

[0257] A is a “decodable” game then: flag = 1

[0258] If no source subset has a sum of x L less than the remaining time, the function returns the complete set of incorrectly decoded sources.

[0259] A is a non-decodable game, i.e. no source can be decoded correctly before T max with known => flag = 0 Appendix B, Selection Strategy Algorithm: End of the l ere phase ie t initial=0, T av remaining number of intervals initialized to T max . N max est parameterized, F the list of sources that the destination cannot help is initialized to the empty set, N t counter initialized to 0 x t is estimated based on direct source-destination links at the end of the l ere phase t is initialized to 1, start of the

[0260] 2 nde phase If not enough retransmission intervals (rounds) to decode all sources then do steps 4-6 Destination requires decoding control exchange For any source not yet correctly decoded by the destination, x t is estimated based on the equivalent channel nodes - destination Determination of the set  at the start of the 2 nde phase according to Annex A Frame decoding is stopped at T maxor when A is the empty set The destination selects from set A the source i with the smallest x t .

[0261] Initializing the exit condition for 2 e "As long as" loop

[0262] The destination decodes the source i until it has been decoded correctly and the max time is not reached and the exit condition is not reached

[0263] The nodes having correctly decoded the source i transmit in parallel the same redundancy Increment of the current round t, decrement of the number of rounds remaining, decrement of Xi since i was helped once, increment of the counter N t . if i is decoded then doing steps 15-19 removes i from A

[0264] If i was decoded before x expires tand that A is different from the sources not yet decoded by the destination and that A is a decodable set (flag equal to 1) then step 17. A new determination of A with a set S d t-r update is required when A is a decodable set, according to Appendix A While exceeds T av , source i remains incorrectly decoded although it has already been helped N max times

[0265] Destination requires decoding control exchange

[0266] Update based on the equivalent channel nodes-destination if x t is always greater than the remaining time T av then: add source i to the list of sources that the destination will no longer help

[0267] The set of sources to be helped  identified by the flag = 0 as a “non-decodable” set is updated with the sources not yet correctly decoded minus those of F Exit from 2 nde“while” loop with this game  updated

Claims

CLAIMS 1. Method for transmitting a frame carrying messages intended for an OMAMRC telecommunications system, Orthogonal Multiple-Access Multiple-Relay Channel, to N nodes including M sources Sj ie{l, M] and a destination (d), N > M > 2, the nodes operating in half-duplex mode, according to an orthogonal multiple access scheme of the transmission channel between the N nodes with a maximum number of M + T max time intervals per transmitted frame distributed between a l ere phase and a 2 nde phase, 1 < T max , the message from a source having been coded before transmission according to an incremental redundancy type coding which generates several redundancies of said message, the l ere phase includes M intervals allocated respectively to successive transmissions from the M sources and the 2 ndephase comprises at least one retransmission interval for a transmission of nodes having correctly decoded the same source Sj such that these nodes simultaneously transmit during the same retransmission interval the same redundancy of the message generated according to the incremental redundancy type coding of the same source not yet correctly decoded by the destination, called the source to be helped, the method is such that it comprises: at least one decoding control exchange between the destination and the nodes, this exchange allowing the destination to determine, for each of the sources, a quality of an equivalent channel based on a quality of the channels between the nodes having correctly decoded a source i and the destination,an estimate of a number of retransmission intervals (%j(0)) sufficient for the destination to decode a source (Sj) not yet correctly decoded and correctly decoded by at least one node on the basis of the quality of an equivalent channel for this source between this at least one node and the destination and a rate (R, L ) assigned to this source (Sj), a selection by the destination of the sources to be helped taking into account the estimated numbers (%j(0)) of retransmission intervals sufficient for the destination to decode the sources not yet correctly decoded and a sum of rates (Ri) assigned to the sources, a number of retransmission intervals per source defining a so-called authorized duration to help a source during this authorized duration limited by a time remaining until T max even if the estimated number of sufficient retransmission intervals for this source is greater than the remaining time.

2. A transmission method according to claim 1, further comprising, if the remaining time is not zero, an exchange of decoding control between the destination and the nodes for the destination to reestimate a sufficient number of retransmission intervals for the destination to decode a source i, this source having been helped for the authorized duration but not yet decoded correctly by the destination.

3. Transmission method according to claim 2, such that only the nodes having correctly decoded the source i transmit a decoding indicator (Info J.) of this source i.

4. Transmission method according to claim 2 such that only the nodes having correctly decoded the source i transmit their set of correctly decoded sources.

5. Transmission method according to claim 2, such that the nodes transmit at least their set of sources correctly decoded and not yet correctly decoded by the destination.

6. Transmission method according to claim 1, such that the at least one decoding control exchange comprises a transmission by the nodes of at least their set of sources correctly decoded and not yet correctly decoded by the destination carried out at the start of the 2 nde phase.

7. Transmission method according to one of the preceding claims, further comprising a comparison between a sum of estimated numbers of retransmission intervals to help the destination to decode sources not yet correctly decoded and a number of time intervals remaining during the 2 nde phase to help the destination correctly decode one or more sources.

8. Transmission method according to the preceding claim such that the comparison is updated after the correct decoding of a source by the destination.

9. Transmission method according to one of the preceding claims such that a transmission by the nodes of at least their set of correctly decoded sources and not yet correctly decoded by the destination is part of a control exchange during which the source transmits its set of correctly decoded sources.

10. Transmission method according to the preceding claim such that during the exchange, a node sends only its set of sources correctly decoded and not yet correctly decoded by the destination.

11. Transmission method according to claim 9 such that during the exchange, a node sends its set of correctly decoded sources.

12. Transmission method according to one of the preceding claims, further comprising a comparison between the estimated numbers of retransmission intervals sufficient for the selection to take into account a sufficient ordering of these estimated numbers of retransmission intervals.

13. Transmission method according to one of the preceding claims, further comprising a determination of a set of sources to be assisted taking into account the estimated numbers of sufficient retransmission intervals and a time remaining before the end of the 2 nde phase.

14. Transmission method according to the preceding claim, such that the set of sources to be assisted contains all the undecoded sources when none of the sufficient numbers of retransmission intervals is less than the remaining time.

15. Communication device (d) adapted for implementing a method of transmitting a frame carrying messages according to one of claims 1 to 14, intended for an OMAMRC, Orthogonal Multiple- Access Multiple-Relay Channel, with N nodes including M sources Sj ie{l, M] and a destination (d), N > M > 2, said destination being said communication device.

16. System comprising N nodes including M sources Sj ie{ 1, ... , M} and a destination (d), N > M > 2, for an implementation of a transmission method according to one of claims 1 to 14.

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