Forward erasure coding design method based on Markov arrival process queue analysis

Abstract

The invention discloses a forward erasure coding design method based on Markov arrival process queue analysis, and the method comprises the steps: obtaining actual measurement star chain data, carrying out the modeling of a low earth orbit loss trajectory, and obtaining a feature matrix of a corresponding Markov arrival process through an expectation maximization algorithm; establishing an elastic FEC (Forward Error Correction) transmission scheme for sending a repair packet at a fixed interval d; describing FEC decoding time delay for the busy period of the decoder based on the MAP / D / 1 queue; based on an embedded Markov update process MRP, decoding time delay is solved through a matrix analysis method, and an expected busy period under constant service time is obtained; the MAP / D / 1 queue busy time is subjected to fitting of low earth orbit satellite communication FEC decoding time delay, and the decoding time delay is analyzed; according to the invention, while the transmission reliability is ensured, the throughput of the system is effectively improved, the head-of-queue blocking effect is reduced, and the overall performance of the low-orbit satellite network in the high-dynamic environment is finally obviously improved.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, and in particular relates to a forward erasure coding design method based on Markov arrival process queue analysis. Background Technology

[0002] Low-Earth orbit (LEO) satellite communication plays a crucial role in the future evolution of 6G integrated air-space-ground-sea communication. LEO constellations, represented by Starlink, have entered large-scale deployment and application. However, due to factors such as the high-speed movement and switching of LEO satellites, current measured end-to-end Starlink connections exhibit frequent packet loss. The core challenge facing existing LEO satellite networks stems from their highly dynamic characteristics, leading to significant latency fluctuations and packet loss in end-to-end connections. Traditional reliable transmission mechanisms relying on retransmissions will cause severe head-of-line (HoL) congestion in this environment, resulting in significant throughput fluctuations. On the other hand, current FEC (Focused Interceptor Coding) schemes are primarily designed for terrestrial networks and fail to effectively adapt to two key characteristics of satellite links: dynamic topology changes and intermittent connectivity. This mismatch causes coding redundancy settings to often deviate from the actual network state—insufficient redundancy compromises transmission reliability, while excessive redundancy wastes valuable inter-satellite bandwidth resources. Summary of the Invention

[0003] Objective: This invention aims to provide a forward erasure coding (FEC) design method based on Markov arrival process queue analysis. The invention focuses on approximating the decoding delay characteristics by establishing a MAP / D / 1 hypothetical queue busy period, and then optimizing the FEC scheme based on this analysis. Specifically, this invention uses the MAP / D / 1 hypothetical queue busy period to model the FEC decoding delay, and numerically solves for the decoding delay using matrix analysis. Furthermore, based on the delay analysis results, targeted optimizations are performed on key parameters such as coding redundancy and packet length to design an FEC scheme that matches the dynamic characteristics of low-Earth orbit (LEO) satellite networks. This method achieves closed-loop optimization from delay theory analysis to coding scheme design, effectively improving system throughput and reducing head-of-queue congestion while ensuring transmission reliability, ultimately significantly improving the overall performance of LEO satellite networks in highly dynamic environments.

[0004] Technical solution: The present invention provides a forward erasure coding design method based on Markov arrival process queue analysis, comprising the following steps:

[0005] Step 1: Obtain measured Starlink data through satellite network. Based on the packet loss modeling method of low Earth orbit satellite communication, model the low Earth orbit loss trajectory by treating each loss event as an arrival. Use the expectation-maximization algorithm to obtain the feature matrix of the corresponding Markov arrival process.

[0006] Step 2: Establish a flexible FEC transmission scheme that sends repair packets at fixed intervals d;

[0007] Step 3: Characterize FEC decoding latency during busy periods of the decoder based on MAP / D / 1 queues;

[0008] Step 4: Based on the embedded Markov update process MRP, the decoding delay is solved by matrix analysis to obtain the expected busy period under constant service time;

[0009] Step 5: Fit the low-Earth orbit satellite communication FEC decoding delay to the busy time of the MAP / D / 1 queue, and analyze the decoding delay of the MAP / D / 1 queue.

[0010] Step 6: Based on the decoding delay analysis results, design a coding scheme that matches the characteristics of low-Earth orbit satellite networks.

[0011] Further, step 1 specifically involves: establishing an end-to-end connection model of the LEO satellite network to obtain measured Starlink data; modeling the low Earth orbit loss trajectory by treating each loss event as an arrival based on the packet loss modeling method of low Earth orbit satellite communication; and using the expectation-maximization algorithm to obtain the corresponding m-dimensional feature matrix {D0,D1} of the Markov arrival process.

[0012] Furthermore, step 2 specifically involves: sending source data packets in order, each data packet containing K finite field elements; inserting a repair data packet after every d-1 source data packets, the repair packet being a random linear combination of the out-of-order source data packets within its encoding window; and during the decoding process, using the dynamic Gaussian elimination method OF-GE to incrementally solve the linear equation system A based on the input data packets. c ×S=C;Matrix A c The rows of matrix C are composed of coding coefficients, where S represents the sequence of source data packets that were not successfully received, and the information symbols are stored in the rows of matrix C. After the decoder is activated, the input source data packet is treated as a special repair packet, with only one non-zero coding coefficient 1 corresponding to the source data packet itself. Throughout the decoding process, A is maintained. c The upper triangle form.

[0013] Furthermore, step 3 specifically involves: Let s j j = 0, 1, 2, ... represents the source packet being sent, and i ord Indicates the index of the latest source data packet delivered in an ordered manner, starting from [time period]. Starting from the expected reception time, subsequent received repair packets are in decoding matrix A. cThe code provides a linearly independent row; the busy period ends when the number of received repair packets equals the number of source packets lost during the busy period; assuming the repair sending process is independent of the packet loss process, this process is considered as a simulation of providing service to customers in a virtual queue; the source packets that trigger the decoder busy period are considered as customers arriving at an empty virtual queue, and all packets lost after their arrival are processed before the recovery is delivered in order; the sending of each repair packet is considered as one service, and the insertion interval is the service time; the queue becomes empty again when the number of services equals the number of arriving customers; therefore, the duration of the decoder busy period, denoted by B, is approximated by the busy period of the queue; for the FEC scheme that sends repair packets at fixed intervals d on the connection, where packet loss follows a MAP characterized by an m-dimensional matrix {D0, D1}, the average loss rate is... Where R c Representing the packet transmission rate, the decoder's expected busy period E{B} is equal to the expected busy period of a MAP / D / 1 queue with the same arrival rate and constant service rate μ, denoted by μ. BP express.

[0014] Furthermore, step 4 specifically involves: for the expected busy period μ BP The derivation of the calculation formula begins with the counting process of MAP; let N(t) be the number of arrivals in [0, t), and J(t) be the phase at time t; define the (i,j)th element of matrix P(n,t) as:

[0015]

[0016] P(n,t) represents the probability of n arrivals within the range [0,t). Let the bottom-level CTMC transition from stage i to stage j. Using the Chapman-Kolmogorov equation, we obtain:

[0017]

[0018] Where I represents an m×m identity matrix, the generating function of P(n,t) is defined as:

[0019]

[0020] Verification of the Chapman-Kolmogorov equation yields:

[0021]

[0022] in:

[0023]

[0024] Therefore, P * (z,t)=e D(z)t|z|≤1,t≥0; The busy period is described by studying the embedded Markov update process (MRP) at the queue departure time; ζ(t) is defined as the number of customers in the system at time t, including customers in service; let θ τ Let θ be the time of the τth departure, where θ0 = 0; and the interval θ be... τ+1 -θ τ Corresponding to the duration of the (τ+1)th service; when τ≥0, the triplet {ζ(θ)} τ ),J(θ τ ),θ τ+1 -θ τ A semi-Markov process Ω = {(i,j): i≥0,1≤j≤m} is formed in the state space, meaning there are i customers in the queue, and the underlying CTMC is in stage j; i = {(i,1),...,(i,m)} is defined, containing all states with the same i but different j; a matrix is ​​defined. Among them, yuan It is a conditional probability, meaning that the last departure from the queue at time 0 is busy at the bottom CTMC in stage i, the next departure is no later than time t, the CTMC is seen in stage j, and there are n arrivals during the customer's service period; the matrix representation is a function of P(n,t) and the service time distribution F(·), i.e.

[0025]

[0026] steady state Represented as

[0027]

[0028] The last equation is defined because of the constant service time d = 1 / μ.

[0029]

[0030] And thus obtain

[0031]

[0032] The expected number of arrivals during the service period starting when the underlying CTMC is in stage j is represented by the j-th element of vector β, and is determined as follows.

[0033]

[0034] in,

[0035]

[0036] The final equality is due to the constant service time, with peak periods related to the first transit time from any state in level i+1 to level i; define a matrix G(n,t), whose (j,j′)th element g j,j′ (n,t), 1≤j,j'≤m,n≥1,t≥0 corresponds to the first time reaching state (i,j') from state (i+1,j) through exactly n transitions within time t; define the transformation of G(nt). The fundamental equation relating the arrival process to G(nt) is:

[0037]

[0038] in

[0039]

[0040] The expected number of transitions from state (i+1,j) to level i is the j-th element of the vector. By differentiating G * (z,0), verification in Vector g is the steady-state vector of matrix G, satisfying gG = g, When ρ < 1, G is a random matrix;

[0041] Finally, the busy period of the queue begins when a customer arrives at an empty queue, i.e., the probability of jumping from level 0 to level 1 is g(-D0). -1 D1; The expected number of services during the peak period, corresponding to the expected first transit time from Level 1 to Level 0 under the condition of the start of the peak period, denoted as μ. N =g(-D0) -1 D1·μ G Therefore, the expected busy period under constant service hours is: Written

[0042]

[0043] Further, step 5 specifically involves: modeling the delay as the busy period of the MAP / D / 1 queue, using a fitted matrix {D0,D1} of m=16, simulating the link using the original Starlink tracking, running real streaming FEC transmission on the link, and measuring the average decoding delay. The measured FEC decoding delay and the numerically calculated busy period are compared for different repair packet insertion intervals d within different time periods. Finally, the busy period of the M / D / 1 queue is plotted, where the arrival rate is set to be equal to the average loss rate of the Starlink tracking, corresponding to a Bernoulli decoding delay for the loss process.

[0044] The present invention also discloses a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method of the present invention.

[0045] The present invention also discloses a computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implements the steps of the method of the present invention.

[0046] The present invention also discloses a computer program product, including a computer program / instructions that, when executed by a processor, implement the steps of the method of the present invention.

[0047] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0048] 1. This invention analyzes the decoding delay of low-Earth orbit (LEO) satellite communication based on the busy period analysis of the MAP / D / 1 hypothetical queue, establishing benchmark performance indicators. Based on these theoretical analysis results, the redundancy strategy and parameter configuration of forward erasure coding are scientifically optimized. While ensuring transmission reliability, this effectively alleviates the HoL congestion problem, thereby significantly improving the throughput stability and bandwidth utilization of LEO satellite networks in highly dynamic environments. This method achieves closed-loop optimization from delay theory analysis to coding scheme design, designing a forward erasure coding scheme suitable for LEO satellite communication based on specific communication transmission environments.

[0049] 2. This invention employs a matrix analytical method to numerically solve for the MAP / D / 1 queue busy period, thereby obtaining an approximate numerical solution for the decoding delay. FEC transmission simulation is performed based on measured Starlink data, and the average decoding delay is measured. The MAP / D / 1 busy period shows good consistency with the simulated FEC decoding delay. Comparative experiments demonstrate that if this invention incorrectly simulates the loss mode in a LEO scenario (e.g., Bernoulli), it may significantly underestimate the delay of the same repair packet transmission interval. This intuitively demonstrates the effectiveness of using the MAP / D / 1 queue busy period to analyze LEO network decoding delay.

[0050] 3. This invention approximates and analyzes the FEC decoding delay based on the busy period of the Markov arrival process queue. On this basis, a targeted forward erasure coding scheme is designed, achieving closed-loop optimization from theoretical analysis of FEC decoding delay to coding scheme design. This ensures transmission reliability while effectively improving system throughput and reducing head-of-line blocking effects. This invention uses the MAP / D / 1 hypothetical queue busy period to model the FEC decoding delay and numerically solves for the decoding delay using matrix analysis. Furthermore, based on the delay analysis results, targeted optimizations are performed on key parameters such as coding redundancy and packet length, designing an FEC scheme that matches the dynamic characteristics of low-Earth orbit satellite networks. This method achieves closed-loop optimization from delay theory analysis to coding scheme design, effectively improving system throughput and reducing head-of-line blocking effects while ensuring transmission reliability, ultimately significantly improving the overall performance of low-Earth orbit satellite networks in highly dynamic environments. Attached Figure Description

[0051] Figure 1 This is a diagram of the actual measured system of low-Earth orbit satellite communication data based on Starlink, as described in this invention.

[0052] Figure 2 This is a decoding example with a decoding window width of 6;

[0053] Figure 3 This is a diagram illustrating the decoding delay.

[0054] Figure 4 For the comparison of FEC decoding delay and MAP / D / 1 busy cycle analysis, the packet transmission interval of the MAP model is 10ms, and m=16.

[0055] Figure 5 For the comparison of FEC decoding delay and MAP / D / 1 busy cycle analysis, the packet transmission interval of the MAP model is 10ms, and m=16. Detailed Implementation

[0056] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0057] This invention discloses a forward erasure coding design method based on Markov arrival process queue analysis. This method models the decoding process of erasure coding as a hypothetical queue system, and then uses the busy period of the hypothetical queue to characterize the decoding delay. For scenarios where packet loss can be characterized by the MAP arrival process and repair packets are inserted at fixed intervals, the decoding delay is analyzed based on the busy period of the MAP / D / 1 queue, and an approximate numerical solution for the decoding delay is obtained using matrix analysis. Compared with traditional analysis methods based on Poisson processes, this method can more accurately predict the decoding delay performance in actual satellite communication environments. Furthermore, based on delay analysis, the redundancy and repair interval of the erasure coding are optimized, and a forward erasure coding scheme more suitable for low-Earth orbit satellite communication networks is designed.

[0058] The forward erasure coding design method based on Markov arrival process queue analysis disclosed in this invention specifically includes the following steps:

[0059] S1. Preparation: Establish an end-to-end connection model of the LEO satellite network, obtain measured Starlink data, and model the low Earth orbit loss trajectory by treating each loss event as an arrival based on the packet loss modeling method of low Earth orbit satellite communication. Use the expectation-maximization algorithm to obtain the corresponding m-dimensional feature matrix {D0,D1} of the Markov arrival process.

[0060] S2. Establish a flexible FEC transmission scheme that sends repair packets at fixed intervals d. Source data packets are sent in order (each packet contains K finite field elements). After every d-1 source data packets, a repair packet is inserted. The repair packet is a random linear combination of the out-of-order source data packets within its encoding window. During decoding, dynamic Gaussian elimination (OF-GE) is used to incrementally solve the linear equation system A based on the input data packets. c ×S=C. Matrix A c The rows of matrix C are composed of coding coefficients, while the information symbols are stored in the rows of matrix C. After the decoder is activated, the input source data packet is treated as a special repair packet, with only one non-zero coding coefficient 1 corresponding to the source data packet itself. Throughout the decoding process, A is maintained. c The upper triangle shape allows the decoder to immediately know when enough repair packets have been received to complete the decoding.

[0061] S3. Characterizing FEC decoding delay based on busy periods of MAP / D / 1 queues. The key to characterizing FEC delay lies in analyzing the duration of busy periods in the decoder. Let s j j = 0, 1, 2, ... represents the source packet being sent, and i ord Indicates the index of the latest source data packet delivered in an ordered manner. Busy periods start from... Starting from the expected reception time, subsequent received repair packets are in decoding matrix A. cThe system provides a linearly independent row. The busy period ends when the number of received repair packets equals the number of source packets lost during the busy period. Assuming the repair transmission process is independent of the packet loss process, this process can be viewed as a simulation of providing services to customers in a virtual queue. This invention treats the source packets that trigger the decoder's busy period as customers arriving at an empty virtual queue, and processes all packets lost after their arrival before delivering the recovery in order. The transmission of each repair packet is considered a service, and the insertion interval is the service time. When the number of services equals the number of arriving customers, the queue becomes empty again. Therefore, the duration of the decoder's busy period, denoted by B, can be approximated by the busy period of the queue. Formally, this invention has the following proposition: For an FEC scheme that transmits repair packets at fixed intervals d on a connection, where packet loss follows a MAP characterized by an m-dimensional matrix {D0, D1}, the average loss rate is... Where R c Representing the packet transmission rate, the decoder's expected busy period E{B} is approximately equal to the expected busy period of a MAP / D / 1 queue with the same arrival rate and constant service rate μ, denoted by μ. BP express.

[0062] S4. Using the matrix analysis method first proposed by M. Neuts, the decoding delay is numerically solved. For μ BP The derivation of the calculation formula begins with the counting process of MAP. Let N(t) be the number of arrivals in [0, t), and J(t) be the phase at time t. Define the (i, j)th element of matrix P(n, t) as... P(n,t) represents the probability of n arrivals within the range [0,t), assuming the underlying CTMC transitions from stage i to stage j. Using the Chapman-Kolmogorov equation, we can obtain:

[0063]

[0064] Where I represents an m×m identity matrix. The generating function of P(n,t) is defined as... |z|≤1,t≥0. This invention can verify the Chapman-Kolmogorov equation. |z|≤1, where P * (z,0)=I, Therefore, P * (z,t)=e D(z)t |z|≤1,t≥0. The key to describing busy periods is studying the embedded Markov renewal processes (MRP) at the queue departure time. Let ζ(t) be defined as the number of customers in the system at time t (including customers already in service). Let θτ Let θ be the time of the τth departure (service completion), where θ0 = 0. The interval θ τ+1 -θ τ This corresponds to the duration of the (τ+1)th service. When τ≥0, the triplet {ζ(θ)} τ ),J(θ τ ),θ τ+1 -θ τ A semi-Markov process Ω = {(i,j): i≥0,1≤j≤m} is formed in the state space, meaning there are i customers in the queue, and the underlying CTMC is in stage j. For convenience, this invention defines a level i = {(i,1),...,(i,m)}, which contains all states with the same i but different j. A matrix is ​​defined. Among them, yuan This is a conditional probability, meaning the last departure from the queue at time 0 occurs, the underlying CTMC is busy in stage i, the next departure is no later than time t, the CTMC is seen in stage j, and there are n arrivals during the customer's service period. The matrix can be represented as a function of P(n,t) and the service time distribution F(·), i.e. n≥0, t≥0. Steady state. It can be represented as The last equation is defined because of the constant service time d = 1 / μ.

[0065]

[0066] And thus obtain

[0067]

[0068] The expected number of arrivals during the service period starting when the underlying CTMC is in stage j, represented by the j-th element of vector β, can be determined as follows:

[0069]

[0070] in, The final equality is due to the constant service time. Busy periods are closely related to the first transit time from any state at level i+1 to level i. Define a matrix G(n,t), whose (j,j')th element g j,j' (n,t), 1≤j,j'≤m,n≥1,t≥0 corresponds to the first time reaching state (i,j') from state (i+1,j) through exactly n transitions within time t. Define the transformation of G(nt). |z|≤1, Re(s)≥0. The fundamental equation relating the arrival process to G(nt) is: in

[0071] The expected number of transitions from state (i+1,j) to level i is the j-th element of the vector. By differentiating G * (z,0) can be verified in Vector g is the steady-state vector of matrix G, satisfying gG = g, When ρ < 1, G is a random matrix.

[0072] Finally, the busy period of the queue begins when a customer arrives at an empty queue, i.e., the probability of jumping from level 0 to level 1 is g(-D0). -1 D1. The expected number of services during peak hours, corresponding to the expected first transit time from Level 1 to Level 0 under peak start conditions, denoted as μ. N =g(-D0) -1 D1·μ G Therefore, the expected busy period under constant service hours is... Specifically, it can be written as

[0073]

[0074] S5. Performance analysis of the effect of fitting the busy time of the MAP / D / 1 virtual queue on the FEC decoding delay of low-Earth orbit satellite communication. By modeling the delay as the busy period of the MAP / D / 1 queue, it can be numerically solved using the matrix analysis method introduced in S4. This invention uses a fitting matrix {D0,D1} with m=16. On the other hand, this invention uses the original Starlink trace to simulate the link, then runs real streaming FEC transmission on the link and measures the average decoding delay, comparing the measured FEC decoding delay and the numerically calculated busy period for different repair packet insertion intervals d on June 14 and September 22, 2024. The MAP / D / 1 busy period and the simulated FEC decoding delay show good consistency, but there are some minor deviations. This invention points out that the deviations are mainly due to the differences between the model assumptions and the actual system behavior in the following two aspects. First, the model implicitly assumes that by assuming the queue service time is constant, all repair packets can be successfully received. Given a repair packet insertion rate f = (d-1) / d, the effective insertion probability is actually f(1-ε), where ε represents the packet loss rate, which leads to an underestimation of latency. Secondly, the model assumes that lost source packets must undergo a constant repair transmission interval, i.e., a time proportional to the number of packets sent, so that the corresponding row in the decoding matrix can be filled with repair packets. However, in reality, the corresponding row of the first lost source packet is filled by the next repair packet, which typically arrives within fewer than d packets, leading to an overestimation of latency. These two bias mechanisms coexist in the system, but their dominance varies with the repair packet insertion interval. Smaller intervals primarily lead to latency underestimation because the repair insertion rate is high (therefore ignoring repair packet losses results in more bias), while longer insertion intervals lead to a dominant overestimation of latency. Figure 4 and Figure 5 In this paper, the busy periods of the M / D / 1 queue are also plotted, where the arrival rate is set to equal the average loss rate tracked by Starlink, corresponding to the decoding delay assuming a Bernoulli loss process. The results show that if this invention incorrectly simulates the loss pattern in a LEO scenario, such as Bernoulli, it may significantly underestimate the delay of sending the same repair packet interval. This intuitively demonstrates that the busy periods of the MAP / D / 1 virtual queue can approximate the FEC decoding delay in LEO satellite networks quite well.

[0075] S6. Based on the decoding delay analysis results of forward erasure coding, a coding scheme matching the characteristics of low-Earth orbit satellite networks is designed. Based on Markov arrival process queue analysis, targeted optimizations are made on key parameters such as coding redundancy and packet length, realizing closed-loop optimization from delay theory analysis to coding scheme design. This can effectively improve system throughput and reduce head-of-queue blocking effect while ensuring transmission reliability, ultimately significantly improving the overall performance of low-Earth orbit satellite networks in high-dynamic environments.

Claims

1. A forward erasure coding design method based on Markov arrival process queue analysis, characterized in that, Includes the following steps: Step 1: Obtain measured Starlink data through satellite network. Based on the packet loss modeling method of low Earth orbit satellite communication, model the low Earth orbit loss trajectory by treating each loss event as an arrival. Use the expectation-maximization algorithm to obtain the feature matrix of the corresponding Markov arrival process. Step 2: Establish a flexible FEC transmission scheme that sends repair packets at fixed intervals d; Step 3: Characterize FEC decoding latency during busy periods of the decoder based on MAP / D / 1 queues; Step 4: Based on the embedded Markov update process MRP, the decoding delay is solved by matrix analysis to obtain the expected busy period under constant service time; Step 5: Fit the low-Earth orbit satellite communication FEC decoding delay to the busy time of the MAP / D / 1 queue, and analyze the decoding delay of the MAP / D / 1 queue. Step 6: Based on the decoding delay analysis results, design a coding scheme that matches the characteristics of low-Earth orbit satellite networks.

2. The forward erasure coding design method based on Markov arrival process queue analysis according to claim 1, characterized in that, Step 1 specifically involves: establishing an end-to-end connection model of the LEO satellite network to obtain measured Starlink data; modeling the low Earth orbit loss trajectory by treating each loss event as an arrival based on the packet loss modeling method of low Earth orbit satellite communication; and using the expectation-maximization algorithm to obtain the corresponding m-dimensional feature matrix {D0,D1} of the Markov arrival process.

3. The forward erasure coding design method based on Markov arrival process queue analysis according to claim 1, characterized in that, Step 2 specifically involves: sending source data packets in order, with each packet containing K finite field elements; inserting a repair data packet after every d-1 source data packets, where the repair packet is a random linear combination of the out-of-order source data packets within its encoding window; during decoding, the dynamic Gaussian elimination method OF-GE is used to incrementally solve the linear equation system A based on the input data packets. c ×S=C;Matrix A c The rows of matrix C are composed of coding coefficients, S represents the sequence of source data packets that were not successfully received, and the information symbols are stored in the rows of matrix C; after the decoder is activated, the input source data packet is regarded as a special repair packet, with only one non-zero coding coefficient 1 corresponding to the source data packet itself; Maintain A throughout the entire decoding process c The upper triangle form.

4. The forward erasure coding design method based on Markov arrival process queue analysis according to claim 1, characterized in that, Step 3 specifically involves: Let s j j = 0, 1, 2, ... represents the source packet being sent, and i ord Indicates the index of the latest source data packet delivered in an ordered manner, starting from [time period]. Starting from the expected reception time, subsequent received repair packets are in decoding matrix A. c The system provides a linearly independent row; the busy period ends when the number of received repair packets equals the number of source packets lost during the busy period. set up The repair transmission process is independent of the packet loss process, and this process is regarded as a simulation of providing services to customers in a virtual queue; the source packet that triggers the decoder busy period is regarded as a customer arriving in an empty virtual queue, and all packets lost after their arrival are processed before the recovery is delivered in order; the transmission of each repair packet is regarded as one service, and the insertion interval is the service time; when the number of services equals the number of arriving customers, the queue becomes empty again; the duration of the decoder busy period is denoted by B; for the FEC scheme of sending repair packets at fixed intervals d on the connection, where packet loss follows a MAP represented by an M-dimensional matrix {D0, D1}, the average loss rate is... Where R c Representing the packet transmission rate, the decoder's expected busy period E{B} is equal to the expected busy period of a MAP / D / 1 queue with the same arrival rate and constant service rate μ, denoted by μ. BP express.

5. The forward erasure coding design method based on Markov arrival process queue analysis according to claim 4, characterized in that, Step 4 specifically involves: for the expected busy period μ BP The derivation of the calculation formula begins with the counting process of MAP; let N(t) be the number of arrivals in [0, t), and J(t) be the phase at time t; define the (i, j)th element of matrix P(n, t) as: P(n,t) represents the probability of n arrivals within the range [0,t). Let the bottom-level CTMC transition from stage i to stage j. Using the Chapman-Kolmogorov equation, we obtain: Where I represents an m×m identity matrix, the generating function of P(n,t) is defined as: Verification of the Chapman-Kolmogorov equation yields: in: Therefore, P * (z,t)=e D(z)t |z|≤1,t≥0; The busy period is described by studying the embedded Markov update process (MRP) at the queue departure time; ζ(t) is defined as the number of customers in the system at time t, including customers in service; let θ τ Let θ be the time of the τth departure, where θ0 = 0; and the interval θ be... τ+1 -θ τ Corresponding to the duration of the (τ+1)th service; when τ≥0, the triplet {ζ(θ)} τ ),J(θ τ ),θ τ+1 -θ τ A semi-Markov process Ω = {(i,j): i≥0,1≤j≤m} is formed in the state space, meaning there are i customers in the queue, and the underlying CTMC is in stage j; i = {(i,1),...,(i,m)} is defined, containing all states with the same i but different j; a matrix is ​​defined. Among them, yuan It is a conditional probability, meaning that the last departure from the queue at time 0 is busy at the bottom CTMC in stage i, the next departure is no later than time t, the CTMC is seen in stage j, and there are n arrivals during the customer's service period; the matrix representation is a function of P(n,t) and the service time distribution F(·), i.e. steady state Represented as The last equation is defined because of the constant service time d = 1 / μ. And thus obtain The expected number of arrivals during the service period starting when the underlying CTMC is in stage j is represented by the j-th element of vector β, and is determined as follows. in, The final equality is due to the constant service time, with peak periods related to the first transit time from any state at level i+1 to level i; define a matrix G(n,t), whose (j,j')th element g j,j' (n,t), 1≤j,j'≤m,n≥1,t≥0 corresponds to the first time reaching state (i,j') from state (i+1,j) through exactly n transitions within time t; define the transformation of G(nt). If |z|≤1 and Re(s)≥0, the fundamental equation relating the arrival process to G(nt) is: in The expected number of transitions from state (i+1,j) to level i is the j-th element of the vector. By differentiating G * (z,0), verification in Vector g is the steady-state vector of matrix G, satisfying gG = g, When ρ < 1, G is a random matrix; Finally, the busy period of the queue begins when a customer arrives at an empty queue, i.e., the probability of jumping from level 0 to level 1 is g(-D0). -1 D1; The expected number of services during the peak period, corresponding to the expected first transit time from Level 1 to Level 0 under the condition of the start of the peak period, denoted as μ. N =g(-D0) -1 D1·μ G Therefore, the expected busy period under constant service hours is: Written 6. The forward erasure coding design method based on Markov arrival process queue analysis according to claim 1, characterized in that, Step 5 specifically involves: modeling the delay as the busy period of the MAP / D / 1 queue, using a fitted matrix {D0,D1} of m=16, simulating the link using the original Starlink tracking, running real streaming FEC transmission on the link, and measuring the average decoding delay. The measured FEC decoding delay and the numerically calculated busy period are compared for different repair packet insertion intervals d within different time periods. Finally, the busy period of the M / D / 1 queue is plotted, where the arrival rate is set to equal the average loss rate of the Starlink tracking, corresponding to a Bernoulli decoding delay for the loss process.

7. A computer device comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method of claim 1.

8. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method of claim 1.

9. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method of claim 1.

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