Classifications

• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L5/00—Arrangements affording multiple use of the transmission path
  • H04L5/0001—Arrangements for dividing the transmission path
  • H04L5/0003—Two-dimensional division
  • H04L5/0005—Time-frequency
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L1/00—Arrangements for detecting or preventing errors in the information received
  • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
  • H04L1/0076—Distributed coding, e.g. network coding, involving channel coding
  • H04L1/0077—Cooperative coding
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L1/00—Arrangements for detecting or preventing errors in the information received
  • H04L1/0001—Systems modifying transmission characteristics according to link quality, e.g. power backoff
  • H04L1/0002—Systems modifying transmission characteristics according to link quality, e.g. power backoff by adapting the transmission rate
  • H04L1/0003—Systems modifying transmission characteristics according to link quality, e.g. power backoff by adapting the transmission rate by switching between different modulation schemes
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L1/00—Arrangements for detecting or preventing errors in the information received
  • H04L1/0001—Systems modifying transmission characteristics according to link quality, e.g. power backoff
  • H04L1/0006—Systems modifying transmission characteristics according to link quality, e.g. power backoff by adapting the transmission format
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L1/00—Arrangements for detecting or preventing errors in the information received
  • H04L1/0001—Systems modifying transmission characteristics according to link quality, e.g. power backoff
  • H04L1/0009—Systems modifying transmission characteristics according to link quality, e.g. power backoff by adapting the channel coding
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L1/00—Arrangements for detecting or preventing errors in the information received
  • H04L1/0001—Systems modifying transmission characteristics according to link quality, e.g. power backoff
  • H04L1/0023—Systems modifying transmission characteristics according to link quality, e.g. power backoff characterised by the signalling
  • H04L1/0026—Transmission of channel quality indication
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L5/00—Arrangements affording multiple use of the transmission path
  • H04L5/003—Arrangements for allocating sub-channels of the transmission path
  • H04L5/0048—Allocation of pilot signals, i.e. of signals known to the receiver

Definitions

• TITLE OMAMRC method and system of transmission with variation of the number of uses of the channel
• 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 two nodes which can be relays or sources.
• a relay has no message to transmit.
• a relay is a node dedicated to relaying messages from sources while a source has its own message to be transmitted and can also in certain cases relay messages from other sources i.e. the source is said to be cooperative in this case.
• 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 networks of sensors.
• Such a network of sensors is a multi-user network, consisting of several sources, several relays and a recipient using a time-orthogonal multiple access scheme of the transmission channel between the relays and the destination, denoted OMAMRC (“Orthogonal Multiple- Access Multiple-Relay Charnel ”according to Anglo-Saxon terminology).
• OMAMRC Orthogonal Multiple- Access Multiple-Relay Charnel
• An OMAMRC telecommunication system has M sources, possibly L relays and a destination, M ⁇ 2, L ⁇ 0 and a time-orthogonal multiple access scheme of the transmission channel which applies between the nodes taken from among the M sources and the L relays.
• the maximum number of time slots per transmitted frame is M + T max with M slots allocated during a first phase to the successive transmission of the M sources and T used ⁇ T max slots 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.
• the OMAMRC transmission system considered comprises at least two sources, each of these sources being able to operate at different times either as a source or as a relay node.
• the system may optionally further include relays.
• the system considered is such that the sources can themselves be relays.
• a relay differs from a source because it has no message to transmit which is specific to it, ie it only retransmits messages from other nodes.
• the links between the different nodes of the system are subject to slow fading and Gaussian white noise.
• Knowledge of all system links (CSI: Channel State Information) by the destination is not available. Indeed, the links between the sources, between the relays, between the relays and the sources are not directly observable by the destination and their knowledge by the destination would require an excessive exchange of information between the sources, the relays and the destination. .
• CDI Channel Distribution Information
• CDI Channel Distribution Information
• the link adaptation is of the 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).
• CDI Channel Distribution Information
• the transmissions of the messages from the sources are divided into frames during which the CSIs of the links are assumed to be constant (assumption of slow fading). Rate allocation is assumed not to change for several hundred frames, it only changes with CDI changes.
• the transmission of a frame takes place in two phases which are optionally preceded by an additional so-called initial phase.
• the destination determines an initial rate for each source by taking into account the average quality (for example SNR) of each of the links in the system.
• the average quality for example SNR
• the destination estimates the quality (for example SNR) of the direct links: source to destination and relay to destination according to known techniques based on the use of reference signals.
• the quality of the source - source, relay - relay and source - relay links is estimated by the sources and the relays by using, for example, the reference signals.
• the sources and the relays transmit to the destination the average qualities of the links. This transmission takes place before the initialization phase. Only the average value of the quality of a link being taken into account, its refreshing takes place on a long time scale, that is to say over a time which allows 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 frequency of the signal transmitted for a given speed.
• the initialization phase occurs for example every 200 to 1000 frames.
• the destination goes back to the sources via a return path the initial rates that it determined.
• the initial flow rates remain constant between two occurrences of the initialization phase.
• the M sources successively transmit their message during the M time slots using respectively modulation and coding schemes determined from the initial bit rates.
• the number N 1 of uses of the channel (channel use, ie resource element according to 3GPP terminology) is fixed and identical for each of the sources.
• the source messages are transmitted cooperatively by the relays and / or by the sources.
• This phase lasts at most T max time slots.
• the number N 2 of channel uses is fixed and identical for each of the sources.
• the sources which are independent from one another broadcast their coded information sequences in the form of messages for the attention of a single recipient.
• Each source broadcasts its messages at the initial rate.
• the destination communicates its initial rate to each source via very limited rate control channels.
• the sources each transmit their respective message in turn during time slots each dedicated to a source.
• the sources other than the one which transmits and possibly the relays, of the “Half Duplex” type receive the successive messages from the sources, decode them and, if they are selected, generate a message solely from the messages from the sources decoded without error.
• the selected nodes then access the channel orthogonally in time to each other during the second phase to transmit their generated message to the destination.
• the destination can choose which node should transmit at a given time.
• the method implements a strategy to maximize the average spectral efficiency (utility metric) within the system considered under constraint to respect an individual quality of service (QoS) per source ie an average individual BLER per source:
• R i is a variable which takes discrete values taken from a set with n MCS Ie number of flow rates corresponding to the different diagrams Modulation and Coding Scheme (MCS) available for transmission.
• MCS Modulation and Coding Scheme
• T used ⁇ T- ma x shows the number of retransmissions used during the 2 nd phase, is the average of the number of retransmissions used during the second phase
• BLERi represents the block error rate for source i.
• BLERi denotes the function with multiple variables BLERi (R 1 , ..., R M ) which depends on the current value taken by the flow variables R 1 , ..., R M.
• the QoS constraint on the individual BLER given by source is written: BLER i ⁇ BLER QoS, i , ⁇ i ⁇ ⁇ 1,, M ⁇ .
• the algorithm based on an interference-free or “Genre Aided” approach is used to solve the multidimensional allocation optimization problem (rate). This approach consists in independently determining each initial rate of a source by assuming that all the messages of the other sources are known by the destination and the relays then in iteratively determining the rates by initializing their value with the values determined according to the approach. "Kind Aided”.
• the utility metric which consists of spectral efficiency is conditioned by the node selection strategy that occurs during the second phase. Main features of the invention
• the present invention relates to a transmission method with slow link adaptation for an OMAMRC telecommunication system according to which the number of uses of the channel is determined by the destination for each source ie by time interval, on the basis of a knowledge of the statistical distribution of all channels (Channel Distribution Information according to English terminology).
• the present invention substantially improves the performance of the method.
• the number of uses of the channel for the first phase is variable, the number N 2 of uses of the channel for the second phase is fixed.
• the number N 1, i of uses of the channel by a source for the first phase can thus be adapted taking into account the distribution of the CDI channels.
• the destination selects at each time interval t ⁇ ⁇ 1, ... T used ) the node among the sources and the relays which will transmit using the N 2 uses of the channel.
• This metric is thus a function with multiple variables which depends on the current value taken by the flow variables R 1 ..., R M and by the variables of the ratio ⁇ 1 , ..., ⁇ M between the number N 2 d 'uses of the channel during the second phase and the number N 1, i of uses of the channel during the first phase:
• the uses of the channel consisting of time and / or frequency resources, a variation in the number of uses of the channel consists of a variation in the number of resources allocated to each source which takes account of the average qualities of the channels.
• the mean utility metric takes into account M ratios ⁇ i which are considered to be of discrete values and belonging to a finite set of possible values.
• the values of a ratio of uses of the channel between the two phases determined for each source belong to a finite set of discrete values, preferably ⁇ 1, 0.5, 2).
• the method maximizes the average utility metric with an initialization of the ratio for each source to the closest discrete value to an average of the ratio values denoted ⁇ GA and implementing a “Genie Aided” approach.
• the "Genie Aided” approach of independently determining each bit rate from a source, assuming all messages from other sources are known to the destination and assuming a relationship for each source, leads to initial flow values for each source which are not sufficiently precise.
• an iterative calculation of the initial throughputs by the destination makes it possible to correct these initial throughput values by taking into account the selection strategy which occurs during the second phase, which the "Genie Aided” approach cannot by nature. »Only which assumes that the active node for each time interval of the second phase is chosen randomly among the nodes.
• This mode is advantageous in that it makes it possible to use a “Genie Aided” approach for the initialization of the iterative algorithm.
• the cooperative transmission of a node during the second phase results in the transmission of a redundancy based on incremental coding to the sources.
• the strategy for selecting the nodes occurring during the second phase follows a sequence known in advance by all the nodes.
• the iterative calculation of the initial flow rates takes into account a node selection strategy (strategy with random selection, strategy with cyclic selection, etc.).
• the strategy for selecting the nodes intervening during the second phase takes into account information coming from the nodes indicating their set of correctly decoded sources.
• the strategy for selecting the nodes intervening during the second phase corresponds to each time interval to the selection of the node which has correctly decoded at least one source that the destination has not decoded correctly at the end of the previous time interval and which benefits from the best instantaneous quality among the instantaneous qualities of all the links between the nodes and the destination.
• the message transmission method results from a software application divided into several specific software applications stored in the sources, in the destination and possibly in the relays.
• the destination can be for example the receiver of a base station.
• the execution of these specific software applications is suitable for implementing the transmission method.
• a further subject of the invention is a system comprising M sources, possibly L relays, and a destination, M> 1, L ⁇ 0, for implementing a transmission method according to a preceding object.
• a further subject of the invention is 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.
• a further subject of the invention is configured memories comprising instruction codes corresponding respectively to each of the specific applications.
• the memory can be incorporated into any entity or device capable of storing the program.
• the memory may be of the ROM type, for example a CD ROM or a microelectronic circuit ROM, or else of the magnetic type, for example a USB key or a hard disk.
• each specific application according to the invention can be downloaded from a server accessible on an Internet type network.
• the optional characteristics presented above in the context of the transmission method can optionally be applied to the software application and to the memory mentioned above.
• FIG. 1 is a diagram of an example of a so-called Cooperative OMAMRC (Orthogonal Multiple Access Multiple Relays Channel) system according to the invention
• FIG. 2 is a diagram of a frame transmission cycle which can be preceded by an initialization step according to the invention
• FIG. 3 is a diagram of the OMAMRC system of FIG. 1 for which all the sources except the source s-, are considered to be correctly decoded.
• 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 uses of the channel is linked to the available frequency band and the transmission time.
• the fading gains are constant during the M + T max time intervals where M + T max is the maximum number of time slots to accomplish a transmission cycle.
• FIG. 1 An embodiment of the invention is described in the context of an OMAMRC system illustrated by FIG. 1 and in support of the diagram of FIG. 2 which illustrates a transmission cycle of a frame.
• Every source in the game communicates with the single destination with the help of other sources (user cooperation) and cooperating relays.
• the relays are equipped with a single transmitting antenna
• the sources, the relays, and the destination are equipped with a single receiving antenna
• T max ⁇ 2 is a system parameter
• the instantaneous quality of the channel / direct link in reception (CSIR Channel State Information at Receiver) is available at the destination, at the sources and at the relays;
• Nodes include relays and sources that can behave like a relay when they are not sending their own message.
• the nodes access the transmission channel according to an orthogonal time multiple access scheme which allows them to listen without interference to the transmissions of the other nodes.
• the nodes operate in a half-duplex mode.
• ⁇ ⁇ , b is the mean signal-to-noise ratio (SNR) which takes into account the effects of attenuation of the channel (path-loss) and of masking (shadowing), ⁇ h ⁇ , b is the attenuation gain of the channel (fading) which follows a complex circular Gaussian distribution symmetric with zero mean and of variance ⁇ ⁇ , b , the gains are independent between them,
• SNR signal-to-noise ratio
• n a, b, k are samples of an identically and independently distributed Gaussian white noise (AWGN) which follow a complex Gaussian distribution of circular symmetry with zero mean and unit variance.
• R s is a variable representing the initial flow of the source s which can take its values in the finite set
• ⁇ s is a variable representing the ratio N 2 / N 1, s which can take its values in a finite set
• the signal received at the node corresponding to the signal sent by the node can be written: (1)
• each source transmits its code words for N 1, s uses of the channel, k ⁇ ⁇ 1, ..., N 1, s ⁇ , the number N 1, s of uses of the channel depending on the source s.
• T used ⁇ T max time intervals, each selected node transmits information representative of the messages of the sources decoded without error by this node during N 2 uses of the channel, k ⁇ ⁇ 1, ...
• the destination can determine the gains (CSI Channel State Information) of the direct links: i.e. source to destination and relay links to destination and can therefore deduce the average SNRs of these links.
• gains CSI Channel State Information
• the gains of links between sources, links between relays and links between sources and relays are not known to the destination. Only sources and relays can estimate a metric of these links by exploiting reference signals in a manner similar to that used for direct links. Given that the statistics of the channels are assumed to be constant between two initialization phases, the transmission to the destination of the metrics by the sources and the relays may only take place at the same rate as the initialization phase. The channel statistic of each link is assumed to follow a circular-centered complex Gaussian distribution and the statistics are independent between the links. It is therefore sufficient to consider only the average SNR as a measure of the statistics of a link.
• the sources and the relays therefore go back to the destination of the metrics representative of the average SNRs of the links that they can observe.
• the destination thus knows the average SNR of each of the links.
• the destination transmits for each source s a representative value (index, MCS, bit rate, etc.) of an initial bit rate and a value
• Each of the initial rates unambiguously determines an initial modulation and coding scheme (MCS) or conversely each initial MCS determines an initial rate.
• MCS modulation and coding scheme
• This metric (21) is thus a function with multiple variables which depends on the current value taken by the flow variables R 1, ..., R M and by the variables of the ratio ⁇ 1 , ..., ⁇ M between the number N 2 ⁇ of uses of the channel during the second phase and the number N 1, i of uses of the channel during the first phase:
• the mean utility metric takes into account M ratios ⁇ i which are considered to be of discrete values and belonging to a finite set of possible values.
• Each source transmits its framed data to the destination with the help of other sources and relays.
• a frame occupies time slots during the transmission of the M messages from the M sources respectively.
• the transmission of a frame (which defines a transmission cycle) takes place during M + T used time intervals: M intervals for the 1 st phase of respective capacities N 1, i uses of the channel for each source i, T used intervals for the 2 nd phase.
• each source transmits after coding a message u s comprising K s information bits being the two-element Galois body.
• the message u s includes a CRC type code which allows the integrity of the message u s to be checked.
• the message u s is coded according to the initial MCS. Since the initial MCSs may be different between sources, the lengths of the encoded messages may be different between the sources.
• the encoding uses an incrementally redundant code.
• the resulting code word is segmented into redundancy blocks.
• the incremental redundancy code can be of the systematic type, the information bits are then included in the first block. Whether or not the incrementally redundant code is of the systematic type, it is such that the first block can be decoded independently of the other blocks.
• the incremental redundancy code can be achieved, for example, by means of a finite family of punched linear codes with compatible yields or of non-yielding codes modified to operate with finite lengths: raptor code (RC), punched turbo code of compatible yield ( RCPTC rate compatible punctured turbo code), rate compatible punctured convolutional code), rate compatible punctured convolutional code, LDPC rate compatible (RCLDPC rate compatible low density parity check code).
• raptor code RC
• punched turbo code of compatible yield RCPTC rate compatible punctured turbo code
• rate compatible punctured convolutional code rate compatible punctured convolutional code
• LDPC rate compatible RCLDPC rate compatible low density parity check code
• the M sources successively transmit their message during the M intervals with respectively modulation and coding schemes determined from the values of the initial bit rates.
• the selected node acts as a relay by cooperating with the sources to help the destination correctly decode messages from all sources.
• the selected node transmits ie it cooperates by transmitting the words or part of the words that it has correctly decoded.
• the second phase comprises at most T max time intervals (time slots) called rounds. Each round t ⁇ ⁇ 1, ..., T max ] has a capacity of N 2 uses of the channel.
• the destination follows a certain strategy to decide which node to transmit at each time interval (round).
• the destination informs the nodes using a limited feedback control channel to transmit a feedback message.
• This return message is based on its result of decoding received messages.
• the destination thus controls the transmission of the nodes using these return messages which improves spectral efficiency and reliability by increasing the probability of decoding of all sources by the destination.
• the return is an AC K type message.
• a cycle of transmission of a new frame begins with the erasure of the memories of the relays and of the destination and with the transmission by the sources of new messages.
• each node has ⁇ transmits its set of correctly decoded sources at the end of the previous noted time interval (round)
• the end of the time interval (round) t 0 corresponds to the end of the first phase.
• the selected node transmits parities determined from the messages of its correctly decoded source set using joint network coding and joint channel coding. This transmission takes place during a time interval of N 2 uses of the channel.
• the other nodes and the destination can improve their own decoding by exploiting the transmission of the selected node and update their correctly decoded source set accordingly.
• Spectral efficiency can be defined as the sum of individual spectral efficiencies: with the event that the source s is not decoded correctly by the destination at the end of the time interval (round) T max , hereinafter called the individual outage event of the source s at the end of the time interval (round) T max .
• the individual cut-off event from source to the outcome of the time interval (round) depends on the selected node and the game associated with decoded sources and this conditionally on knowledge of the gains direct channels and of is the game including all the nodes that have been selected at the time intervals (rounds) l ⁇ ⁇ 1, ... t - 1) preceding the time interval (round) t as well as their associated decoding set and the destination decoding set
• the common outage event at the end of the time interval (round) t is defined as being the event that at least one source is not decoded correctly by the destination at the end of the time interval (round) t.
• the probability of the individual outage event of the source s at the end of the time interval (round) t for a candidate node a t can be expressed as: with the expectation operator and such that takes the value 1 if the event V is true and the value 0 otherwise.
• the probability of the common cutoff event can be defined in the same way. In the following, the dependence on the knowledge of is omitted for the sake of simplification ratings.
• the common cut-off event of a set of sources occurs when the vector of their rate is outside the corresponding MAC capacity region.
• the common break event can be expressed in the form: such as sources that belong to are considered interference. reflects the non-respect of the MAC inequality associated with the sum rate of the sources contained in :
• I ⁇ , b the mutual information between nodes a and b and an already selected node.
• the factor 1 / a s makes it possible to standardize before addition the two terms associated respectively with the two phases for which the time intervals have respective channel use times N 1, s and N 2 .
• the individual cut-off event of the source s at the end of the time interval (round) t can be written: have the same expression as for (5).
• the destination implements a slow type link adaptation.
• the utility metric is an average spectral efficiency conditioned on the selection strategy of the nodes intervening during this second phase.
• the selection of the nodes taken from among the sources and the relays depends on the sets of the sources correctly decoded by the nodes.
• An example considered, called a preferred strategy is based on a selection of the IR-HARQ type which aims to maximize the spectral efficiency.
• the destination chooses the node with the best instantaneous quality of the link between itself and this node (for example the greatest mutual information between itself and this node) taken among all the nodes which were able to correctly decode at least one source of the game, these nodes being said to be eligible.
• This strategy makes it possible to achieve a good compromise between computational complexity and performance, but to the detriment of a large number of control signals.
• the selection of the nodes taken from among the sources and the relays does not depend on the sets of the sources correctly decoded by the nodes.
• the selection is determined and known to all nodes.
• One example considered is such that the selection sequence is cyclical and such that the selected node is selected only from among the relays.
• each relay benefits from at least one dedicated time interval (round) during the second phase to transmit. In order not to favor one relay over another, the sequence changes with each frame. According to this example, only one return bit from the destination is sufficient to send up a common ACK / NACK message.
• each source is transmitted with the initial rate R s .
• T used is a random variable which represents the number of time intervals (rounds) used during the second phase T used ⁇ T max .
• the distribution of T used depends on (R 1 ..., R M ), on (a, ..., a M ) and on what makes the optimization (7) multidimensional cardinality i.e. 91125 (2M) -tuple ..., R M , ⁇ 1 , ..., ⁇ M ) possible for 3 sources, a family of fifteen MCS and 3 possible values of a. An exhaustive search very quickly becomes impossible when the number of sources increases.
• the method according to the invention follows a so-called “Genie Aided (GA)” approach which consists in making the assumption during the initialization step that all the sources s except the source s i, of which we wants to initialize the bitrate are considered correctly decoded, All sources
• the network is a network with multiple relays denoted (1, L + M - 1,1) and no longer a network with multiple relays and multiple users.
• the search for the optimal pair for the source s under the assumptions GA and GAI can be written in the form of a one-dimensional optimization conditioned on : where is the bit rate of the source s after optimization, R s is the bit rate variable and where P (H) is the joint probability of the realizations of the channels of all the links of the network. It is clear that the rate R s depends on the selected nodes â ; and therefore the selection strategy applied by the destination.
• the approximation according to (8) with the assumptions GA, GAI, GA2 can be calculated by implementing a Monte Carlo process.
• An implementation mode is detailed by algorithm 1 (in Annex) for the source s, its principle is as follows. First, the reports are all set to Then, each bitrate value of the set of possible bitrates is considered one after the other according to a first loop on i. n MCS is the number of modulation and coding schemes.
• a second loop on cnt makes it possible to average the individual BLER or on Nb_MC draws of channels according to the statistics given by the average SNRs of all links. Thus, inside the cnt loop all the channels are known resulting from a random draw.
• equation (8) is then carried out according to a Monte-Carlo process where the integral is replaced by a sum: the out variable of algorithm 1 corresponding to:
• Algorithm 2 is based on a Monte Carlo simulation calculation of the spectral efficiency using the cutoff events given by equation (6). for everything should be evaluated in the Monte Carlo loop based on the destination active node selection strategy and the P (H) statistic similar to Algorithm 1.
• the method calculates the BLER i of the source i and the expectation of the number of retransmissions According to this mode, the method considers that the individual cut-off probability is a good approximation of individual BLER BLER i of source i.
• the individual outage probability is the average of the individual outage event given by equation (6) on PH link statistics) of the MAMRC system.
• the process relies on the evaluation of the cutoff events of equations (5) and (6) to determine the decoding set at the destination node and the relay nodes. All the sources which are not in the decoding set of the destination after T max retransmissions are declared out of service, i.e. their error counter is increased by 1.
• Agorithm 3 has a main part and two subroutines.
• the first subroutine is the check_outage (t, I list , activated_nodes_list, which takes into account the current time interval t of retransmission and the subsets for which the common outage must be calculated for .
• This function also contains two other loops, one to calculate the sum rate of the subset current as well as the mutual information included, and another loop to calculate the additional mutual information included according to the nodes activated in the retransmission phase.
• the second subroutine is the get_decoding_set (t, I list , activated_nodes_list) function which determines the decoding set at a certain time interval t by taking into account the previous parameters I list and activated_nodes_list set determined.
• the principle of this function is to find the sub games cardinality Card max up that leads to a common cutoff event zero.
• the main part has four loops.
• algorithm 1 there is the Monte-Carlo loop such that each of its iterations leads to an individual cut event as well as an expected duration of retransmission for the second phase.
• the functions defined previously are used to check the cutout event.
• the process starts a 2 nd loop, taking into account the retransmission phase and a certain allocation strategy whereby a certain node is selected to retransmit and is added to the set of activated nodes.
• the expected retransmission duration is updated.
• the method checks whether there is an outage or not and updates the individual outage event counter of each user accordingly. After the end of the Monte Carlo loop, the individual BLERs and the expected length of retransmission time slots are calculated using an average. The spectral efficiency is then calculated according to equation (3).

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