A density adjustment method for finding an optimal coding density size

Abstract

The present application relates to the field of sparse network coding, and particularly relates to a density adjustment method for finding optimal coding density size, comprising obtaining original packet quantity of a source node and link packet loss rate of a legal receiver and an eavesdropper; calculating state transition probability between each state in a coding packet transmission process based on an absorbing Markov chain model, calculating the probability of the legal receiver decoding all original packets and the total number of coding packets required to be transmitted in the system from the state transition probability; calculating the total number of coding packets expected to be received by the eavesdropper and the rank of a decoding matrix when the system reaches an absorbing state, calculating the probability of the eavesdropper decoding at least x original packets; if the decoding matrix of the legal receiver is not full rank and the probability of the eavesdropper decoding at least x original packets is greater than the eavesdropper partial decoding probability threshold, then density adjustment is performed; otherwise, original packets are generated into coding packets for transmission according to the original coding density size; the present application can ensure the security of data transmission while ensuring a relatively low decoding complexity.

Description

Technical Field

[0001] This invention relates to the field of sparse network coding in wireless reliable transmission technology, and particularly to a density adjustment method for finding the optimal coding density. Background Technology

[0002] In 2000, Ahlswede et al. first proposed the concept of Network Coding (NC). Unlike the traditional "store-and-forward" transmission mode of network relay nodes, network coding endows intermediate nodes with computational capabilities, enabling them to linearly combine information streams received from different links before forwarding. Research shows that network coding technology can enable end-to-end network transmission to reach the network's maximum flow capacity, improving data transmission efficiency and link utilization. Random Linear Network Coding (RLNC), in particular, is based on the idea of ​​using a finite field F... q RLNC randomly selects coding coefficients to linearly combine with the original packet to form a coded packet. When the destination node receives enough linearly independent coded packets, it can decode and recover the original data. RLNC can be used when the network topology is unknown and has significant advantages in improving data transmission reliability and robustness. However, it also suffers from high encoding / decoding complexity and high packet header overhead. The decoding time complexity of RLNC is O(n^2). 3 ), where n is the number of original data packets, and its decoding complexity increases rapidly as the number of original data packets n increases.

[0003] To address the aforementioned issues, Sadeghi P et al. proposed the concept of Sparse Network Coding (SNC) in 2009. SNC primarily reduces the number of original packets involved in constructing the encoded packet, resulting in a sparse matrix at the receiver. This leads to a large number of zero coding coefficients in the decoded matrix at the receiver, thus reducing the decoding complexity when using Gaussian elimination. Simultaneously, since only a portion of the original packets participate in encoding, the proportion of original packets in the encoded packet is reduced, and the overhead of the data packet header carrying the coding coefficients is also reduced. The most significant feature of SNC is its ability to perform partial decoding, meaning that a portion of the original packets is recovered before decoding the entire data packet after receiving a sufficient number of encoded packets. This feature significantly reduces decoding latency. However, compared to RLNC, SNC offers some reduction in data transmission security.

[0004] Due to the broadcast nature of wireless networks, data transmission security is a critical security concern. Firstly, N. Cai and RWYeung proposed the concept of secure network coding (SNC), and to prevent information leakage, they put forward a security requirement: the mutual information between the source information and the information received by the eavesdropper must be zero. Zero mutual information means that the eavesdropper cannot understand the original message information based on the information already intercepted, thus ensuring secure communication. This problem was studied under random linear network coding schemes; however, related work mainly achieved network topology security by proposing a precoding mechanism. Precoding mechanisms introduce additional computational complexity at the sending end, increasing performance overhead. Recent research has shown that both RLNC and SNC achieve high security, with the probability of an eavesdropper obtaining all original data packets being negligible. However, the partial decoding characteristic of SNC provides the possibility for an eavesdropper to recover a portion of the original data packets. Recovering a small portion of the original data packets could leak relevant information, thus reducing data transmission security. ASKhan et al. pointed out that in the presence of an eavesdropper, the security of a wireless network is usually measured by the probability that the eavesdropper can recover all the original data packets; this probability is called the interception probability. Furthermore, under a transmission scheme based on random linear network coding, an exact expression for the probability that an eavesdropper can intercept enough coded packets to recover the original data packet is derived. A.Tassi et al., under a transmission scheme based on sparse network coding, proposed a general approximation of the interception probability, applicable to unreliable feedback channels.

[0005] Balancing decoding complexity with data transmission security remains a pressing issue that needs to be addressed in this field. Summary of the Invention

[0006] To balance decoding complexity and data transmission security, this invention proposes a density adjustment method for finding the optimal coding density. This invention finds the optimal coding sparsity while ensuring that the probability of interception by an eavesdropper is below an ideal value. Each data packet is encoded and transmitted with this optimal coding sparsity. Specifically, the method includes the following steps:

[0007] S1. Obtain the number of original packets from the source node and the packet loss rate of the legitimate receiver and eavesdropper links;

[0008] S2. Set the partial decoding probability threshold T for the eavesdropper, calculate the state transition probability between each state during the transmission of the encoded packet based on the absorption Markov chain model, and calculate the probability of the legitimate receiver decoding the entire original packet and the total number of encoded packets to be transmitted in the system based on the state transition probability.

[0009] S3. Calculate the total number of encoded packets that the eavesdropper expects to receive and the rank of the decoding matrix after the system reaches the absorption state, and use this to calculate the probability that the eavesdropper decodes at least x original packets.

[0010] S4. If the decoding matrix of the legitimate receiver is not full rank and the probability of the eavesdropper decoding at least x original packets is greater than the threshold T, then density adjustment is performed; otherwise, the original packets are selected according to the original coding density to generate encoded packets for transmission.

[0011] Furthermore, based on the absorbed Markov chain model, the state transition probabilities between each state during the transmission of the encoded packet are calculated. That is, before the sender sends the encoded packet, the decoding matrix of the legitimate receiver node is initialized to be empty. After each transmission of the encoded packet, the node state changes from (r... b ,r e ,t) is transferred to (r) b +1,r e ,t+1),(r b +1,r e +1,t+1),(r b ,r e +1,t+1) or (r b ,r e The calculation process for the probability of transitioning to each state (t+1) specifically includes:

[0012] When r' b =r b +1,r' e =r e +1,t'=t+1, the node state is determined by (r b ,r e ,t) is transferred to (r' b ,r' e The transition probability of ,t') is expressed as:

[0013] P S (r b ,r e ,t)=(1-ε b )(1-ε e )p' b (i,n)p' e (i,n)

[0014] When r' b =r b +1,r' e =r e ,t'=t+1, the node state is determined by (r b ,r e ,t) is transferred to (r' b ,r' e The transition probability of ,t') is expressed as:

[0015] P S (r b ,re ,t)=(1-ε b )p' b (i,n)(ε e +(1-ε e )p' e (i,n))

[0016] When r' e =r e +1,r' b =r b ,t'=t+1, the node state is determined by (r b ,r e ,t) is transferred to (r' b ,r' e The transition probability of ,t') is expressed as:

[0017] P S (r b ,r e ,t)=(1-ε e )p' e (i,n)(ε b +(1-ε b )p' b (i,n))

[0018] When r' e =r e ,r' b =r b ,t'=t+1, the node state is determined by (r b ,r e ,t) is transferred to (r' b ,r' e The transition probability of ,t') is expressed as:

[0019] P S (r b ,r e ,t)=ε b ε e +(1-ε b )(1-ε e )p b (i,n)p e (i,n)

[0020] +ε b (1-ε e )p' e (i,n)+ε e (1-ε b )p' b (i,n)

[0021] Where, r bLet r represent the rank of the decoding matrix for the legitimate receiver. e P represents the rank of the eavesdropper's decoding matrix, t represents the total number of encoded packets transmitted in the current system; S (r b ,r e ,t) represents the state (r) b ,r e ,t) transitions to the next state (r' b ,r' e The transition probability of ,t'); εb is the packet loss rate of the legitimate receiver link, and εe is the packet loss rate of the eavesdropper link; p' b (i,n) represents the probability that a legitimate receiver will receive another linearly independent coded packet when the original packet size is n and the rank is i; p' e (i,n) represents the probability that the eavesdropper receives another linearly independent coded packet when the original packet number is n and the rank is i; p b (i,n) represents the probability that a legitimate receiver will receive another linearly correlated coded packet when the original packet count is n and the rank is i; p e (i,n) represents the probability that the eavesdropper receives another linearly correlated coded packet when the original packet number is n and the rank is i.

[0022] Furthermore, if there are n original packets, the probability p(i,n) that the sink receives a linearly dependent coded packet after receiving i linearly independent coded packets is expressed as:

[0023]

[0024] Where p0 is the system sparsity, representing the probability that the coding coefficients in the system are 0; q represents the size of the finite field; p a' As an intermediate parameter, it is represented as

[0025] Furthermore, when the system reaches the absorption state, that is, when r b When n = n, the probability that a legitimate receiver decodes the entire original packet can be calculated based on the state transition probability. The probability of a legitimate receiver decoding the entire original packet in this case is expressed as:

[0026]

[0027] Wherein, P(r) b ,r e (t) represents the decoding matrix with rank r that reaches the valid receiver after passing through system t. b The rank of the eavesdropper's decoding matrix is ​​r. e The probability of P S (n,r e(m) represents the state transitioning from the previous state to the legitimate receiver's decoding matrix after m transmissions in a Markov chain. The rank of the decoding matrix for the legitimate receiver is n, and the rank of the decoding matrix for the eavesdropper is r. e The probability; n represents the total number of original packets, and m represents the number of encoded packets transmitted in the current system.

[0028] Furthermore, the total number of encoded packets required to be transmitted in the system is expressed as follows:

[0029]

[0030] Where E(m) represents the total number of encoded packets required to be transmitted in the system; P S (n,r e (m) represents the transition from the previous state to the right state in a Markov chain after m transmissions, where the rank of the decoding matrix for the legitimate receiver is n and the rank of the decoding matrix for the eavesdropper is r. e The probability of P(r) b -i,r e -j,t-1) represents the decoding matrix with rank r that reaches a valid receiver after t-1 transmissions. b -i, the rank of the eavesdropper's decoding matrix is ​​r e -j is the probability; n represents the total number of original packets, and m represents the total number of encoded packets transmitted in the current system.

[0031] Furthermore, calculating the probability that the eavesdropper decodes at least x original packets includes:

[0032]

[0033] Wherein, E(r) e E(m) represents the expected rank of the eavesdropper's decoding matrix when the system reaches the absorption state, x represents the minimum number of original packets decoded, and X represents the total number of data packets received by the eavesdropper. e This represents the number of encoded packets that the eavesdropper expects to receive when the system reaches the absorption state; This means randomly selecting np from n original packets. i+j The number of combinations that can be obtained from the original package, p represents the sparsity of the system; q represents the size of the finite field; Γ(x+1) represents the factorial of x; N is an intermediate parameter, denoted as n represents the original number of packets; This indicates that when the decoding matrix has E(m) e The rank of the row is E(r) e The probability of ), where m represents the total number of encoded packets transmitted in the current system.

[0034] Furthermore, the number of encoded packets that the eavesdropper expects to receive when the system reaches the absorption state is expressed as:

[0035] E(m e )=(1-εe E(m)

[0036] The expected rank of the eavesdropper's decoding matrix when the system reaches the absorption state is represented as:

[0037]

[0038] Where, ε e To set the packet loss rate for the eavesdropper link; E(m) is the total number of encoded packets required to be transmitted in the system; r e P represents the rank of the decoding matrix used by the eavesdropper. S (n,r e (m) represents the transition from the previous state to the right state in a Markov chain after m transmissions, where the rank of the decoding matrix for the legitimate receiver is n and the rank of the decoding matrix for the eavesdropper is r. e The probability of P(r) b -i,r e -j,t-1) represents the decoding matrix with rank r that reaches a valid receiver after t-1 transmissions. b -i, the rank of the eavesdropper's decoding matrix is ​​r e The probability of -j.

[0039] Furthermore, the density adjustment process includes:

[0040] If the encoding density satisfies the condition that the probability of partial interception by the eavesdropper is less than the set threshold, then the original packet is selected using the encoding density to generate an encoded packet and sent to the legitimate receiver.

[0041] Otherwise, adjust the coding density and repeat the above steps until the coding density satisfies the condition that the probability of partial interception by the eavesdropper is less than the set threshold.

[0042] The process of adjusting the coding density includes:

[0043]

[0044] Where p represents the current sparsity of the system, A←B means assigning the value of B to A; P'(|X|≥x) represents the result of taking the derivative of P(|X|≥x) with respect to p; P(|X|≥x) represents the probability of decoding at least x original packets; x represents the minimum number of original packets to be decoded; |X| represents the actual number of original packets decoded, which is greater than x.

[0045] This invention comprehensively considers the phenomenon of data packet loss in actual network transmission channels. In addition to the overhead caused by the linear correlation of the data packets themselves during transmission, it also considers the overhead caused by packet loss. At the same time, this scheme uses an approximate expression of linearly independent probability as the basic formula for calculating the probability of the system being in the absorption state and the partial decoding probability of the eavesdropper, so that the final calculated density can be more accurate and can better evaluate the relevant performance of actual network data packet transmission. Attached Figure Description

[0046] Figure 1 This invention provides a network model for a density adjustment method to find the optimal coding density.

[0047] Figure 2 This is a flowchart of a density adjustment method for finding the optimal coding density according to the present invention. Detailed Implementation

[0048] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0049] This invention proposes a density adjustment method for finding the optimal coding density, which specifically includes the following steps:

[0050] S1. Obtain the number of original packets from the source node and the packet loss rate of the legitimate receiver and eavesdropper links;

[0051] S2. Set the partial decoding probability threshold T for the eavesdropper, calculate the state transition probability between each state during the transmission of the encoded packet based on the absorption Markov chain model, and calculate the probability of the legitimate receiver decoding the entire original packet and the total number of encoded packets to be transmitted in the system based on the state transition probability.

[0052] S3. Calculate the total number of encoded packets that the eavesdropper expects to receive and the rank of the decoding matrix after the system reaches the absorption state, and use this to calculate the probability that the eavesdropper decodes at least x original packets.

[0053] S4. If the decoding matrix of the legitimate receiver is not full rank and the probability of the eavesdropper decoding at least x original packets is greater than the threshold T, then density adjustment is performed; otherwise, the original packets are selected according to the original coding density to generate encoded packets for transmission.

[0054] Given that sparse network coding offers the possibility for eavesdroppers to decode parts of the original packet due to partial decoding characteristics, this embodiment proposes a density adjustment method to find the optimal coding density, in order to limit the eavesdropper from obtaining complete information. This method utilizes an absorbing Markov chain model to analyze the probability of the eavesdropper decoding parts of the original packet. The method includes the following:

[0055] S1: Obtain the number of original packets from the source node and the packet loss rate of the legitimate receiver and eavesdropper links.

[0056] like Figure 1Obtain information from source node A, legitimate receiver B, and eavesdropper E, and set the packet loss rate of the legitimate receiver link to ε. b Set the packet loss rate of the eavesdropper link to ε. e .

[0057] S2: Set the partial decoding probability threshold T for the eavesdropper; calculate the state transition probability between each state during the transmission of the encoded packet based on the absorbing Markov chain model, and further derive the probability of the legitimate receiver decoding the entire original packet and the total number of encoded packets to be transmitted in the system from the state transition probability.

[0058] Define coding coefficients {c1, c2, ..., c n In the finite field F q Above, q represents the size of the finite field, which is randomly and uniformly chosen. The selection of the coding coefficients follows the following probability distribution:

[0059]

[0060] Where p0 is the system sparsity, representing the probability that the coding coefficient in the system is 0; in the traditional RLNC scheme In sparse network coding q represents the finite field F q Size.

[0061] This embodiment defines the node states (r) of the absorbing Markov process. b ,r e ,t), where rb represents the rank of the decoding matrix of the legitimate receiver, r e Let t represent the rank of the eavesdropper's decoding matrix, t represent the total number of encoded packets transmitted in the current system, and r represent the total number of encoded packets transmitted in the current system. b =n indicates that the system has reached the absorption state. Before the sender sends the encoded packet, the decoding matrix of the valid receiver node is initialized to empty. After each transmission of the encoded packet, the node state changes from (r) b ,r e ,t) is transferred to (r) b +1,r e ,t+)1、(r b +1,r e +1,t+1),(r b ,r e +1,t+1) or (r b ,r e ,t+1).

[0062] The expression for the state transition probability between any two states can be derived from the meaning of the transition from one state to another. The formula is as follows:

[0063]

[0064] Where, r b Let r represent the rank of the decoding matrix for the legitimate receiver. e P represents the rank of the eavesdropper's decoding matrix, t represents the total number of encoded packets transmitted in the current system; S (r b ,r e ,t) represents the state (r) b ,r e ,t) transitions to the next state (r' b ,r' e The transition probability of ,t'); p' b (i,n) represents the probability that a legitimate receiver will receive another linearly independent coded packet when the original packet size is n and the rank is i; p' e (i,n) represents the probability that the eavesdropper receives another linearly independent coded packet when the original packet number is n and the rank is i; p b (i,n) represents the probability that a legitimate receiver will receive another linearly correlated coded packet when the original packet count is n and the rank is i; p e (i,n) represents the probability that the eavesdropper receives another linearly correlated coded packet when the original packet number is n and the rank is i.

[0065] Assuming there are n original packets, the probability that the receiver (in this example, the receiver is either an eavesdropper or a legitimate recipient) receives a linearly dependent coded packet after having already received i linearly independent coded packets is:

[0066]

[0067] Where, p a' As an intermediate parameter, it is represented as

[0068] Once the state transition probabilities between all states are obtained, the expression for the probability of occurrence of each state in the system model can be derived based on these probabilities:

[0069]

[0070] Among them, P S (r b ,r e (t) represents a Markov chain where the state transitions from the previous state to the legitimate receiver after t transmissions, and the rank of the decoding matrix is ​​r. b The rank of the eavesdropper's decoding matrix is ​​r. e The probability of P(r) b -i,r e -j,t-1) represents the decoding matrix with rank r that reaches a valid receiver after t-1 transmissions. b -i, the rank of the eavesdropper's decoding matrix is ​​r eThe probability of -j.

[0071] Then, calculate the probability that the system reaches the absorption state, and the expected number of transmissions when the system reaches the absorption state, i.e., the total number of encoded packets transmitted in the system:

[0072]

[0073]

[0074] Where P(n,r) e P(m) represents the probability that the system reaches the absorption state; S (n,r e (m) represents the transition from the previous state to the right state in a Markov chain after m transmissions, where the rank of the decoding matrix for the legitimate receiver is n and the rank of the decoding matrix for the eavesdropper is r. e The probability of E(m) is given by E(m), which represents the total number of encoded packets that need to be transmitted in the system.

[0075] S3. Derive the total number of encoded packets that the eavesdropper expects to receive after the system reaches the absorption state and the rank of the decoding matrix, and combine the partial decoding probabilities to derive the probability that the eavesdropper decodes at least x original packets.

[0076] When the system reaches the absorption state, the number of encoded packets received by the eavesdropper Eve's decoding matrix and the rank of the decoding matrix are expressed as follows:

[0077] E(m e )=(1-ε e E(m)

[0078]

[0079] Wherein, 1-ε e E(m) represents the probability that an eavesdropper can intercept the encoded packet, and E(m) represents the total number of encoded packets that the system needs to transmit to be in the absorption state.

[0080] Once the total number of encoded packets received by the eavesdropper's decoding matrix and the rank of the decoding matrix are obtained when the system reaches the absorption state, a partial decoding probability can be introduced and substituted into the expression for the eavesdropper's partial decoding probability:

[0081]

[0082] Where X represents the total number of data packets received by the eavesdropper; This means randomly selecting np from n original packets. i+j The number of combinations that can be obtained from the original package; Γ(x+1) represents the factorial of x; N is an intermediate parameter, expressed as This indicates that when the decoding matrix has E(m) e The rank of the row is E(r)e The probability of ), where m represents the total number of encoded packets transmitted in the current system.

[0083] S4. If the decoding matrix of the legitimate receiver is not full rank and the probability of the eavesdropper decoding at least x original packets is greater than the threshold T, then density adjustment is performed; otherwise, the original packets are selected according to the original coding density to generate encoded packets for transmission.

[0084] Set a threshold T for the probability of partial interception by the eavesdropper, and initialize the coding density as follows: Determining whether the probability of partial interception by an eavesdropper at the current coding density is less than a set threshold T can be expressed as:

[0085] if P(|X|≥x)≤T

[0086] If the encoding density satisfies the condition that the probability of partial interception by the eavesdropper is less than a set threshold, then the original packet is selected using this encoding density to generate an encoded packet and sent to the legitimate receiver, which can be expressed as:

[0087] p opt =p

[0088] Otherwise, adjust the coding density and repeat the above steps until the coding density satisfies the condition that the probability of partial interception by the eavesdropper is less than a set threshold, which can be expressed as:

[0089] while P(|X|≥x)>T do

[0090]

[0091] endwhile

[0092] The coding density value obtained under the above conditions is the optimal coding density value under the current system conditions. The sender selects the original packet using this coding density value to encode it into a coding packet and sends it to the legitimate receiver. The sender stops sending coding packets when the legitimate receiver's decoding matrix reaches full rank.

[0093] like Figure 2 This embodiment also provides a density adjustment method for finding the optimal coding density, which specifically includes the following steps:

[0094] Initialization parameters include encoding batch w, finite field size q, and total number of original packets n;

[0095] Construct a formula for the state transition probability of an absorbing Markov chain, and calculate the partial interception probability of the eavesdropper based on the state transition probability;

[0096] Determine if the partial interception probability of some eavesdroppers is greater than a set threshold. If it is, adjust the coding density and recalculate the partial interception probability of eavesdroppers until the partial interception probability of eavesdroppers is less than the set threshold.

[0097] The system constructs and transmits encoded packets according to the current encoding density, determines whether the maximum encoding batch has been reached, and proceeds with the next encoding cycle if not, until the maximum encoding batch is reached.

[0098] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A density adjustment method for finding the optimal coding density, characterized in that, Specifically, the following steps are included: S1. Obtain the number of original packets from the source node and the packet loss rate of the legitimate receiver and eavesdropper links; S2. Set the threshold for the probability of partial decoding by the eavesdropper. Under the premise of ensuring that the partial decoding probability of the eavesdropper is lower than the set threshold, the state transition probability between each state during the transmission of the encoded packet is calculated based on the absorption Markov chain model. The probability of the legitimate receiver decoding the entire original packet and the total number of encoded packets to be transmitted in the system are calculated from the state transition probability. S3. Calculate the total number of encoded packets the eavesdropper expects to receive and the rank of the decoding matrix after the system reaches the absorption state. Based on this, calculate the eavesdropper's decoding of at least... The probability of each original packet specifically includes: in, The expected rank of the eavesdropper's decoding matrix when the system reaches the absorption state is represented as: ; x represents the minimum number of original packets decoded, and X represents the total number of data packets received by the eavesdropper; The number of encoded packets that the eavesdropper expects to receive when the system reaches the absorption state is represented as . ; Indicates from Randomly selected from the original packages The number of combinations that can be obtained from the original package Indicates the sparsity of the system. Represents the size of a finite field. This indicates finding the factorial of x; As an intermediate parameter, it is represented as ; Indicates the original number of packets; This indicates that when the decoding matrix has Rank of the line The probability of; This indicates the total number of encoded packets currently being transmitted in the system; To set the packet loss rate for the eavesdropper link; This represents the total number of encoded packets required to be transmitted in the system. The rank of the decoding matrix for the eavesdropper; This indicates that the Markov chain passes through... The next transmission transitions from the previous state to the rank of the decoding matrix of the legitimate receiver. The rank of the eavesdropper's decoding matrix is The probability of; Indicates the process The subtransmission system achieves a rank of the decoding matrix for the legitimate receiver. The rank of the eavesdropper's decoding matrix is The probability of; S4. If the legitimate receiver's decoding matrix is ​​not full rank and the eavesdropper decodes at least one of them... The probability of a single original packet being greater than a threshold is greater than the threshold. Density adjustment is then performed, specifically including: If the encoding density satisfies the condition that the probability of partial interception by the eavesdropper is less than the set threshold, then the original packet is selected using the encoding density to generate an encoded packet and sent to the legitimate receiver. Otherwise, adjust the coding density and repeat the above steps until the coding density satisfies the condition that the probability of partial interception by the eavesdropper is less than the set threshold. The process of adjusting the coding density includes: in, Indicates the current sparsity of the system. This means assigning the value of B to A; express right Find the result of the derivative; This indicates that at least one of them is decoded. The probability of a given number of original packets; x represents the minimum number of original packets that need to be decoded; This indicates the number of original packets actually decoded; Otherwise, the original packet is selected based on its original encoding density to generate an encoded packet for transmission.

2. The density adjustment method for finding the optimal coding density according to claim 1, characterized in that, The state transition probabilities between states during the transmission of encoded packets are calculated based on the Absorbed Markov Chain model. Specifically, before the sender sends the encoded packet, the decoding matrix of the legitimate receiver nodes is initialized to empty. After each transmission of an encoded packet, the node state changes from... Transferred to , , or The specific process of calculating the probability of transitioning to each state includes: when The node state is determined by Transferred to The transition probability is expressed as: when The node state is determined by Transferred to The transition probability is expressed as: when The node state is determined by Transferred to The transition probability is expressed as: when The node state is determined by Transferred to The transition probability is expressed as: in, Denotes the rank of the decoding matrix of the legitimate receiver. This indicates the total number of encoded packets currently being transmitted in the system; Indicates the state Transition to the next state The transition probability; Packet loss rate for legitimate recipients; The original number of packets is Rank The probability that a legitimate receiver will receive another linearly independent coded packet at that time; The original number of packets is Rank The probability that the eavesdropper will receive another linearly independent coded packet at that time; The original number of packets is Rank The probability that a legitimate receiver will receive another linearly correlated coded packet at that time; The original number of packets is Rank The probability that the eavesdropper will receive another linearly correlated coded packet at that time.

3. The density adjustment method for finding the optimal coding density according to claim 2, characterized in that, If there is The original packet has been received by the receiver. Given a set of linearly independent coded packets, what is the probability of receiving a linearly dependent coded packet next? Represented as: in, The sparsity of the system represents the probability that the coding coefficient in the system is 0; Indicates the size of a finite field; As an intermediate parameter, it is represented as .

4. The density adjustment method for finding the optimal coding density according to claim 2, characterized in that, When the system reaches the absorption state, that is, when At this point, the probability that a legitimate receiver decodes the entire original packet can be calculated based on the state transition probability. The probability of a legitimate receiver decoding the entire original packet is expressed as: in, This represents the probability that a legitimate receiver decodes the entire original packet when the system reaches the absorption state.

5. The density adjustment method for finding the optimal coding density according to claim 2, characterized in that, The total number of encoded packets required to be transmitted in the system is expressed as follows: in, Indicates the process The subtransmission system achieves a rank of the decoding matrix for the legitimate receiver. The rank of the eavesdropper's decoding matrix is The probability of.

Images