A method for fountain coding of the degree of a rule variable node

Abstract

A regular variable node degree fountain coding method first constructs a coding node symbol degree distribution function, accelerates the decoding process by increasing the probability of occurrence of small degree value coding symbols, and generates a degree value according to the degree distribution function; then, based on the information symbol selection probability, selects the original information symbol to participate in this encoding, and splices the degree information field with the coding information field to construct a transmission data packet; secondly, by recording the number of times all original information nodes participate in the encoding, the information node selection probability is updated; finally, the received data is decoded at the destination node using a belief propagation algorithm. The present invention optimizes the coding node degree distribution function, increases the probability of occurrence of small degree value coding symbols, adopts an information node selection strategy based on the number of coding participations, realizes the regularization of symbol variable node degree values, selects information nodes with small degree values during encoding, achieves the purpose of reducing the error platform and saving decoding overhead during the fountain coding process, and reduces the coding complexity at the source node.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communications, and in particular relates to a rule variable node degree fountain coding method. Background Art

[0002] Fountain codes, as a non-fixed-rate coding scheme, were initially developed to address large-scale data distribution, reliable multicast, and multicast in binary erasure channels. They can also address the long wait times at the sender caused by feedback and retransmission mechanisms over long transmission distances, effectively avoiding the "feedback storms" that occur in traditional linear block codes and ensuring data transmission reliability. Consequently, fountain codes have also been applied to harsh transmission environments such as deep space communications, plasma sheath communications for high-speed aircraft, and beyond-horizon communications, which require extremely high reliability. In these transmission environments, due to the long communication link distances, electromagnetic signals are affected by free-space propagation losses, resulting in a low useful signal transmission component at the receiver. Furthermore, factors such as external noise interference during transmission can lead to rapid deterioration in communication quality and even interruptions.

[0003] To ensure communication reliability, currently commonly used technical means include spread spectrum communication and diversity combining technology. In spread spectrum communication, after the original information is processed by the spread spectrum codeword sequence, the bandwidth occupied by the signal transmission is much larger than the minimum bandwidth required by the information itself. By obtaining the spread spectrum gain, it can achieve the functions of resisting narrowband interference and multipath. However, spread spectrum itself cannot overcome the impact of noise, and it still cannot solve the problem of rapid deterioration of communication quality in extremely low signal-to-noise ratio environments. Diversity reception technology refers to providing several signals carrying the same information sent on independent fading channels to the receiver. The receiver combines the received independent signals according to certain rules to maximize the energy of the received useful signal, thereby improving the signal-to-noise ratio of the received signal and achieving the purpose of resisting fading. The diversity gain is directly related to the diversity order. However, as the diversity order continues to increase, there are multiple demodulation branches at the receiver, which leads to increased hardware implementation complexity and cost.

[0004] Traditional fountain coding processes mostly use robust soliton distribution, randomly selecting original information nodes for encoding. This makes it very likely that a certain information node will never participate in encoding or participate in encoding only a few times. Furthermore, considering packet loss during transmission, the amount of information in this information symbol node at the receiving end is zero, impacting the decoding process and resulting in a high error rate and high decoding cost. Currently, an existing solution to this problem is to use a degree lookup table to regularize the degree values of information symbols on the encoding end. However, this requires traversing and sorting the degree lookup table during each encoding operation, and the table must be continuously maintained during the encoding process. As the number of original information nodes K increases, the degree lookup table sorting process becomes more complex. While reducing the error rate, it also causes a delay in the decoding waterfall region on the decoding end, increasing the decoding cost.

[0005] The existing patent, CN201910613926.0, derives and analyzes the optimal degree distribution function that can achieve regularization of the node degree values of the coding symbols, but does not consider the problems of slower decoding speed and increased decoding cost caused by the fountain coding of the rule variable node degree itself.

[0006] During communication transmission processes such as deep space communication and beyond-line-of-sight communication, due to the combined influence of multiple factors such as large-scale fading, small-scale fading, external noise, and interference, the communication quality deteriorates rapidly in extremely low signal-to-noise ratio environments and the communication process is interrupted.

[0007] Based on this, it is of great significance to consider how to optimize the existing fountain coding algorithm to improve the communication service rate performance in a harsh transmission environment with obvious fading characteristics and low useful signal power. Summary of the Invention

[0008] In order to overcome the shortcomings of the above-mentioned existing technologies, the purpose of the present invention is to provide a regular variable node degree fountain coding method. This method takes into account the impact of harsh transmission environments on communication performance, optimizes the coding node degree distribution function, improves the probability of occurrence of small-degree coding symbols, adopts an information node selection strategy based on the number of coding participations, and realizes the regularization of symbol variable node degrees, so as to achieve the purpose of reducing the error platform and saving decoding overhead in the fountain coding process, thereby improving the service transmission rate while ensuring communication reliability.

[0009] In order to achieve the above object, the technical solution adopted by the present invention is:

[0010] A rule variable node degree fountain encoding method includes the following steps:

[0011] Step 1: Define the sender as the source node in the communication process. There are K original information symbols at the source node as information nodes waiting to be transmitted. A degree value d is randomly selected according to the symbol degree distribution function. That is, d original information symbols are involved in the encoding process.

[0012] Step 2: The source node selects d original information symbols that have participated in the least number of encodings based on the selection probability, performs a modulo-2 addition operation, and obtains the coded information symbol. The degree information field is K bits long, corresponding to K original information symbols. If an original information symbol is selected for encoding during this encoding process, the corresponding degree information bit is 1, otherwise it is 0. The coded information symbol and the degree information field are concatenated to obtain the transmission data packet.

[0013] Step 3: Among the K original symbol nodes, record the original information symbol node that participated in the encoding process, add one to the total number of times the symbol node was selected for encoding, and calculate the probability of selecting the original information symbol node used in the next fountain encoding;

[0014] Step 4: Define the receiving end as the destination node in the communication process. At the destination node, the generator matrix is obtained based on the degree information field of the received data packet, and the belief propagation algorithm is used for decoding to restore the original information symbols. When the decoding is successfully completed at the destination node, feedback is sent to the source node, and the encoding operation is terminated at the source node.

[0015] The step 1 is specifically as follows:

[0016] The coding node symbol degree distribution function polynomial Ω(x) is defined as Where K represents the number of original information nodes, and is also the maximum degree of encoding, Ω d It represents the probability of selecting the degree value d, which is further expressed as The probability mass function ρ(d) and the correction function τ(d) satisfy:

[0017]

[0018]

[0019] in c is a constant greater than 0, δ is the maximum decoding failure probability, It represents rounding down, β1 and β2 are correction factors used to increase the probability of occurrence of coded data packets with degree values of 1 and 2.

[0020] The step 2 is specifically as follows:

[0021] Assume that there are K original information symbols at the source node, represented by S = [S1, S2, S3,, S K], where the original information symbol node that participates in the encoding fewer times is selected with a high probability. According to the probability, d symbols are selected from the K original information symbols for modulo-two addition operation to obtain the encoding symbol. Assume that the information field of the i-th encoding is represented by the vector G i , whose length is K, corresponding to K original information symbols. If an original information symbol participates in the encoding process, the degree information field vector G i The corresponding value in is 1, otherwise it is 0. The coding symbol and the degree information field are concatenated to obtain the transmission data packet;

[0022] The specific implementation method of implementing variable symbol node regularization by selecting original information nodes based on the number of coding participations and analyzing the performance of current fountain coding using the progressive analysis method is as follows;

[0023] Assume that the channel is a random packet loss channel, define the number of original information nodes as K, the total number of symbols sent in the coding segment as N, and the number of symbols lost during transmission as N e , the number of symbols successfully received by the receiver is N r , the channel packet loss rate is The decoding overhead is γ = N r / K.

[0024] When the packet loss rate ε is 0, the degree of all information node symbols at the sender is equal under the rule variable node degree fountain coding method, and the coded symbols obtained by the receiver are the same as those at the sender; the average degree of the information symbol node at the receiver is defined as α. Since the degree value is a positive integer, the actual degree value of the information symbol is or Indicates rounding up, the node degree distribution of information symbols is Λ(x)=Λ h-1 x h-1 +Λ h x h , where the parameters Coefficient Λ h-1 and Λ h They represent the probability that the receiving end information symbol value is h and h-1, respectively, and satisfy:

[0025]

[0026] Define the information symbol edge distribution function polynomial as λ(x)=λ h-2 x h-2 +λ h-1 x h-1 , coefficient λ h-2 and λ h-1 satisfy:

[0027]

[0028] Since the coding node degree distribution function Ω(x) used in the rule variable node degree fountain coding is predefined, when the number of original information nodes K→∞, the asymptotic bit error rate y at the receiving end is expressed as where y l is the bit error rate after l iterative decoding, further expressed as:

[0029]

[0030] The coding symbol edge degree distribution ω(x) can be calculated from the coding node degree distribution function Ω(x), ω(x) = Ω′(x) / Ω′(1);

[0031] When the packet loss rate ε is not 0, take any information symbol as an example, and use s to represent the information symbol. The number of coded symbols with information symbol s as neighbor nodes in N coded symbols is h. H represents the set of h coded symbols, then h = card(H), card(A) represents the cardinality of set A, and the value range of the receiving end information symbol degree d is 0≤d≤h, and d is an integer; use N e Represents the set of lost coding symbols, let I==HN e , when the set I is an empty set, the degree value of the receiving end information symbol s does not change; when I is not an empty set and card(I)=i, the degree value of the receiving end information symbol s is reduced to di; use p h (i) represents the probability of card(I) = i, which means the probability of missing i symbols in the set H of coded symbols with s as neighbor node. All sets N that satisfy card(I) = i e The number of Set N e All the numbers of Therefore, p h (i) is expressed as:

[0032]

[0033] The probability that the receiving end coding symbol degree value is h is the probability that all coding symbols of neighboring nodes with information symbols with coding end degree value h are not lost, that is, p h (0), the probability that the receiving end information symbol value is h is Λ h p h (0); Similarly, the receiving end information symbol degree value is h-1, which includes two possible situations. The first is that all the coded symbols of the neighboring nodes with the information symbol of the coding end degree value h are lost, and the second is that all the coded symbols of the neighboring nodes with the information symbol of the coding end degree value h-1 are not lost. Therefore, the probability that the receiving end information symbol degree value is h-1 is Λ h p h (1)+Λh- 1p h-1 (0); Similarly, when the packet loss rate ε is not 0, the node degree distribution of the information symbol at the receiving end is expressed as:

[0034]

[0035] The edge degree distribution of the coding symbol and the information symbol is obtained by the formula ω(x) = Ω′(x) / Ω′(1) and λ(x) = Λ′(x) / Λ′(1). Therefore, the error rate y of the rule variable node degree fountain coding after l iterations of decoding is l Expressed as:

[0036]

[0037] In the traditional fountain coding process, the original information nodes participating in the coding are randomly selected. When the number of original information nodes K→∞, the degree distribution of the information symbol node is Poisson distribution, that is, Λ(x)=exp(α(x-1)), where α represents the average degree of the information symbol node. The Taylor series expansion of the information symbol node degree distribution polynomial is obtained:

[0038] Λ(x)=exp(α(x-1))

[0039] =exp(-α)+αexp(-α)x+α 2 exp(-α)x 2 +…

[0040] The constant term exp(-α) represents the probability that an information symbol is not encoded when the average degree of the information symbol node is α, that is, the probability that the receiver cannot decode the information symbol. Therefore, the error floor of traditional fountain coding is exp(-α).

[0041] For regular variable node degree fountain coding, when the channel packet loss rate ε = 0, all information symbols participate in the coding process, which can effectively reduce the error floor. When ε ≠ 0, when all the coding symbols with a certain information symbol as the neighbor node are lost, the node degree distribution of the receiving end information symbol also has a constant term. At this time, the probability that the receiving end information symbol degree is equal to 0 is Λ0 = Λ h-1 p h-1 (h-1)+Λ h p h (h) The error platform of regular variable node degree fountain coding is related to the average degree of coded symbols and the channel packet loss rate. When Λ0<exp(-α), the error platform of regular variable node degree fountain coding is lower than that of traditional fountain coding.

[0042] The step 3 is specifically as follows:

[0043] Step 3.1: Define P(k) as the probability of selecting the kth information node, where k = 1, 2, K. In the initialization phase of encoding, the probability of selecting all original information nodes P(k) is the same, which is set to 1 / K, where K represents the number of original information nodes. For each original information node, set the number of encoding times s k All are 1;

[0044] Step 3.2: After each fountain coding is completed, the original information nodes involved in the coding are recorded and the corresponding coding times s is recorded. k Add 1;

[0045] Step 3.3: After completing the update of the encoding times of all information nodes, recalculate the selection probability P(k) of each information node, where

[0046] Step 3.4: If the source node receives the decoding success feedback information sent by the destination node, it returns to step 3.1 to complete the initialization operation; otherwise, it returns to step 3.2.

[0047] The step 4 is specifically as follows:

[0048] Step 4.1: Assume that the degree information field in the i-th received data packet received at the destination node is G i , then the generator matrix can be expressed as G=[G1,G2,…,G i ,…], get the corresponding bipartite graph and start the decoding process;

[0049] Step 4.2: Select a coding symbol with a degree of 1 from the bipartite graph, directly recover the original information symbol that is uniquely connected to it, and delete the connection between the original information symbol and the coding symbol in the bipartite graph;

[0050] Step 4.3: Use the generator matrix to find the coded symbols connected to the original symbol, XOR the values of these coded symbols with the original symbol values, and delete the corresponding connections in the bipartite graph;

[0051] Step 4.4: Repeat steps 4.2 and 4.3 until all original symbols are restored and decoding is completed, or there is no coded symbol with a degree value of 1 and the decoding is stopped.

[0052] Beneficial effects of the present invention:

[0053] In the transmission process with extremely high reliability requirements such as deep space communication, high-speed aircraft plasma sheath communication, and beyond-horizon communication, the effective distance of the communication link reaches thousands of kilometers. The actual electromagnetic signal is affected by both large-scale fading and small-scale fading during the propagation process, resulting in a significant reduction in the number of coded data packets successfully received at the destination node during the communication process. As a result, a huge decoding overhead is required to complete the decoding operation, which greatly reduces the effective communication rate. Therefore, it is necessary to consider ensuring communication quality in an extremely low signal-to-noise ratio transmission environment, seek coding performance gain, and achieve reliable communication.

[0054] The present invention applies fountain coding to solve the problem of rapid deterioration of communication quality in harsh transmission environments, optimizes the node degree distribution function of coding symbols, and updates the probability of selecting information nodes based on the number of times the information nodes participate in coding, thereby realizing node variable regularization. Compared with the existing fountain coding algorithm, it achieves performance improvements in bit error rate and decoding cost in a packet loss channel environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 The flowchart of a rule variable node degree fountain encoding method according to an embodiment of the present invention is shown.

[0056] Figure 2 This is a schematic diagram comparing the decoding cost performance of the algorithm in the embodiment of the present invention and the traditional fountain LT coding algorithm under different channel transmission error probabilities.

[0057] Figure 3 This is a schematic diagram comparing the bit error rate performance of the algorithm in the embodiment of the present invention and other algorithms when the channel transmission error probability is 0.5.

[0058] Figure 4 This is a system processing flow chart of a rule variable node degree fountain encoding method according to an embodiment of the present invention. DETAILED DESCRIPTION

[0059] The present invention will be described in further detail below with reference to the accompanying drawings.

[0060] The embodiment of the present invention provides a rule variable node degree fountain encoding method, the flow chart is as follows Figure 1 As shown, please follow the steps below:

[0061] Step 1 is as follows:

[0062] The coding node symbol degree distribution function polynomial Ω(x) is defined as Where K represents the number of original information nodes, and is also the maximum degree of encoding, Ω d It represents the probability of selecting the degree value d, which can be further expressed as Where ρ(d) and τ(d) satisfy:

[0063]

[0064]

[0065] in c is a constant greater than 0, δ is the maximum decoding failure probability, It represents rounding down, β1 and β2 are correction factors used to increase the probability of occurrence of coded data packets with degree values of 1 and 2.

[0066] Step 2 is as follows:

[0067] By selecting original information nodes based on the number of times they participate in encoding, the degree values of variable symbol nodes are regularized. In traditional LT encoding, original information nodes are randomly selected, and all original data packets participate in the encoding process with equal probability. Combined with packet loss during transmission, this can cause some original information nodes to participate in encoding only a few times or not at all. Consequently, the receiver cannot obtain valid information from these nodes, making decoding impossible. This keeps the system's bit error rate at a constant level, making it difficult to reduce.

[0068] To mitigate the error platform phenomenon and ensure that all original information nodes can participate in the encoding process, the degrees of information nodes are counted at the encoding end. When a certain information node is used for encoding transmission significantly more times than other information nodes, the receiver can be considered to have obtained the information from that node. Continuing to use this node for encoding not only increases the complexity of the decoding process but also has no effect on successful decoding. Therefore, in subsequent encoding processes, this information node's priority decreases, and the probability of selecting it for encoding decreases. Similarly, if an original information node has never participated in encoding or has participated in encoding only a few times, it is difficult for the receiver to obtain useful information from this node, resulting in the occurrence of an error platform. Therefore, such information nodes should be preferred in subsequent encoding processes. The specific implementation method for analyzing the performance of regular variable node degree fountain coding using the asymptotic analysis method is as follows.

[0069] Assume that the channel is a random packet loss channel, define the number of original information nodes as K, the total number of symbols sent in the coding segment as N, and the number of symbols lost during transmission as N e , the number of symbols successfully received by the receiver is N r , the channel packet loss rate is The decoding overhead is γ = N r / K.

[0070] When the packet loss rate ε is 0, the degree of all information node symbols at the sender is equal under the rule variable node degree fountain coding method, and the coded symbols obtained by the receiver are the same as those at the sender. The average degree of the information symbol node at the receiver is defined as α. Since the degree value is a positive integer, the actual degree value of the information symbol is or Indicates rounding up, the node degree distribution of information symbols is Λ(x)=Λ h-1 x h-1 +Λ h x h , where the parameters Coefficient Λ h-1 and Λ h They represent the probability that the receiving end information symbol value is h and h-1, respectively, and satisfy:

[0071]

[0072] Define the information symbol edge distribution function polynomial as λ(x)=λ h-2 x h-2 +λ h-1 x h-1 , coefficient λ h-2 and λ h-1 satisfy:

[0073]

[0074] Since the coding node degree distribution function Ω(x) used in the rule variable node degree fountain coding is predefined, when the number of original information nodes K→∞, the asymptotic bit error rate y at the receiving end can be expressed as where y l is the bit error rate after l iterative decoding, which can be further expressed as:

[0075]

[0076] The coding symbol edge degree distribution ω(x) can be calculated from the coding node degree distribution function Ω(x), ω(x) = Ω′(x) / Ω′(1).

[0077] When the packet loss rate ε is not 0, take any information symbol as an example, and use s to represent the information symbol. The number of coded symbols with information symbol s as neighbor nodes in N coded symbols is h. Use H to represent the set of h coded symbols, then h = card(H), card(A) represents the cardinality of set A, and the value range of the receiving end information symbol degree d is 0≤d≤h, and d is an integer. e Represents the set of lost coding symbols, let When the set I is an empty set, the degree of the information symbol s at the receiving end does not change; when I is not an empty set and card(I) = i, the degree of the information symbol s at the receiving end is reduced to di. h (i) represents the probability of card(I) = i, which means the probability of missing i symbols in the set H of coded symbols with s as neighbor node. All sets N that satisfy card(I) = i e The number of Set N e All the numbers of Therefore, p h (i) can be expressed as:

[0078] The probability that the receiving end coding symbol degree value is h is the probability that all coding symbols of neighboring nodes with information symbols with coding end degree value h are not lost, that is, p h (0), the probability that the receiving end information symbol value is h is Λ h p h (0); Similarly, the receiving end information symbol degree value is h-1, which includes two possible situations. The first is that all the coded symbols of the neighboring nodes with the information symbol of the coding end degree value h are lost, and the second is that all the coded symbols of the neighboring nodes with the information symbol of the coding end degree value h-1 are not lost. Therefore, the probability that the receiving end information symbol degree value is h-1 is Λ h p h (1)+Λ h- 1p h-1 (0). Similarly, when the packet loss rate ε is not 0, the node degree distribution of the information symbol at the receiving end can be expressed as:

[0079]

[0080] The edge degree distribution of the coding symbol and the information symbol can be obtained by the formula ω(x) = Ω′(x) / Ω′(1) and λ(x) = Λ′(x) / Λ′(1). Therefore, the error rate y of the rule variable node degree fountain coding after l iterations of decoding is l It can be expressed as:

[0081]

[0082] In the traditional fountain coding process, the original information nodes participating in the coding are randomly selected. When the number of original information nodes K→∞, the degree distribution of the information symbol node is a Poisson distribution, that is, Λ(x)=exp(α(x-1)), where α represents the average degree of the information symbol node. The Taylor series expansion of the information symbol node degree distribution polynomial can be obtained:

[0083] Λ(x)=exp(α(x-1))

[0084] =exp(-α)+αexp(-α)x+α 2 exp(-α)x 2 +…

[0085] The constant term exp(-α) represents the probability that an information symbol is not encoded when the average degree of the information symbol node is α, that is, the probability that the receiver cannot decode the information symbol. Therefore, the error floor of traditional fountain coding is exp(-α).

[0086] For regular variable node degree fountain coding, when the channel packet loss rate ε = 0, all information symbols participate in the coding process, which can effectively reduce the error floor. When ε ≠ 0, when all the coding symbols with a certain information symbol as the neighbor node are lost, the node degree distribution of the receiving end information symbol also has a constant term. At this time, the probability that the receiving end information symbol degree is equal to 0 is Λ0 = Λ h-1 p h-1 (h-1)+Λ h p h (h) The error platform of regular variable node degree fountain coding is related to the average degree of coded symbols and the channel packet loss rate. When Λ0<exp(-α), the error platform of regular variable node degree fountain coding is lower than that of traditional fountain coding.

[0087] Step 3 is as follows:

[0088] Step 3.1, define P(k) as the probability of selecting the kth information node, where k = 1, 2, K. In the initialization phase of encoding, the probability of selecting all original information nodes P(k) is the same, which is set to 1 / K, where K represents the number of original information nodes. For each original information node, set the number of encoding times s k All are 1;

[0089] Step 3.2: After each fountain coding is completed, the original information nodes involved in the coding are recorded and the corresponding coding times s is recorded. k Add 1;

[0090] Step 3.3: After completing the update of the encoding times of all information nodes, recalculate the selection probability P(k) of each information node, where

[0091] Step 3.4: If the source node receives the decoding success feedback information sent by the destination node, it returns to step 3.1 to complete the initialization operation; otherwise, it returns to step 3.2.

[0092] In each encoding process, the two processes of generating the encoded data packet and updating the probability of selecting the original information node are processed in parallel. That is, the update of the record of the number of encoding times and the update of the calculation of the selection probability will not affect the normal encoding process, ensuring the efficient encoding of the source node.

[0093] Step 4 is as follows:

[0094] Step 4.1: The destination node reconstructs the generator matrix based on the degree information field in the received data packet, obtains the corresponding bipartite graph, and starts the decoding process;

[0095] Step 4.2: Select a code symbol with a degree of 1 from the bipartite graph, directly recover the original information symbol that is uniquely connected to it, and delete the corresponding edge;

[0096] Step 4.3: Find the coded symbols connected to the original symbol by generating the matrix, XOR the values of these coded symbols with the original symbol values, and delete the corresponding connected edges in the bipartite graph;

[0097] Step 4.4: Repeat steps 4.2 and 4.3 until all original symbols are restored and decoding is completed, or there is no coded symbol with a degree value of 1 and the decoding is stopped.

[0098] The method of the embodiment of the present invention was verified, assuming that the number of original information symbol nodes was 128, the length of each information node symbol was 3520 bits, and the packet loss rate in the deletion channel was set to 0.3 to 0.8, simulating different channel transmission environments.

[0099] like Figure 2 As shown in the figure, the comparison methods adopted by the present invention are as follows: (1) Traditional fountain LT coding algorithm: The coding symbol node degree distribution function selects robust soliton distribution, and the original information node is randomly selected during each coding. (2) The rule variable node degree fountain coding algorithm proposed by the present invention: The coding symbol node degree distribution uses an optimized degree distribution function to increase the probability of the occurrence of small-degree coding symbols. At the same time, a strategy for selecting original information nodes based on the number of coding times is adopted to calculate the selection probability, and selects information nodes with small degrees to participate in the coding process during each coding process.

[0100] like Figure 2 As shown, the proposed algorithm achieves decoding cost performance gains compared to traditional fountain LT coding under different channel error probabilities. This performance gain becomes increasingly apparent as the error probability increases and the transmission environment quality degrades. While achieving decoding cost performance gains, the proposed algorithm effectively reduces the number of code transmissions, improving the actual service transmission rate.

[0101] like Figure 3As shown in the figure, the channel transmission error probability is fixed at 0.5. Under the above comparison method, the existing regularized variable-node Luby Transform (RLT) algorithm is included in the performance comparison. The algorithm adopts a robust soliton degree distribution function and a degree lookup table to regularize the degree values of the coded segment information symbols. Each time encoding is performed, the degree lookup table needs to be traversed and sorted, and the information node with the smallest degree value is selected to participate in the encoding. The table needs to be maintained during the encoding process. As the number of original information nodes K increases, the sorting process of the degree lookup table becomes more complicated.

[0102] like Figure 3 As shown in the figure, the RLT coding algorithm increases the coverage of information nodes during the coding process due to the use of a regular variable node degree coding method. Compared with the traditional fountain LT coding, it can reduce the bit error rate at the same decoding cost. However, while the RLT coding algorithm realizes the regularization of the information node degree value, the "waterfall area" is delayed during the decoding process, resulting in a slow decoding process. The algorithm proposed in the present invention adopts an optimized coding symbol node degree distribution function to effectively increase the probability of small and medium degree values appearing in the coding symbols. The coding symbol with a degree value of 1 can be directly decoded at the destination node, and the coding symbol with a degree value of 2 can be decoded with only one removal operation, thereby speeding up the decoding speed. At the same time, in each coding process, the original signal node with a smaller degree value is selected according to the selection probability to realize the regularization of the variable node degree value. It can be clearly seen from the figure that the algorithm proposed in the present invention improves the bit error rate at the same decoding cost. Compared with the RLT coding algorithm, the bit error rate reduction process is faster and more obvious, which reflects that the algorithm of the present invention has good performance in a packet loss channel environment.

[0103] A system processing flow chart of a rule variable node degree fountain encoding method according to an embodiment of the present invention is as follows: Figure 4 As shown, the destination node completes regular variable node degree fountain coding using the algorithm proposed in this invention. After completing the outer erasure coding, cyclic redundancy check bits are added to the encoded data. Then, inner turbo coding is performed to add redundant information to improve error correction performance. Rate matching is used to match service resources with actual system physical resources. Interleaving is then used to convert a series of burst errors that occur during transmission into random errors. Finally, the signal is transmitted through symbol modulation. After the transmitted data passes through the wireless channel, it reaches the destination node. The destination node obtains the encoded data through a series of inverse operations: demodulation, deinterleaving, rate matching, and turbo decoding. A cyclic redundancy check is used to determine the correctness of the data packet. Correct packets are then decoded, while incorrect packets are discarded.

Claims

1. A rule variable node degree fountain encoding method, characterized in that: The following steps are included: Step 1: Define the sender as the source node in the communication process. There are K original information symbols at the source node as information nodes waiting to be transmitted. A degree value d is randomly selected according to the symbol degree distribution function. That is, d original information symbols are involved in the encoding process. Step 2: The source node selects d original information symbols that have participated in the least number of encodings based on the selection probability, performs a modulo-2 addition operation, and obtains the coded information symbol. The degree information field is K bits long, corresponding to K original information symbols. If an original information symbol is selected for encoding during this encoding process, the corresponding degree information bit is 1, otherwise it is 0. The coded information symbol and the degree information field are concatenated to obtain the transmission data packet. Step 3: Among the K original symbol nodes, record the original information symbol node that participated in the encoding process, add one to the total number of times the symbol node was selected for encoding, and calculate the probability of selecting the original information symbol node used in the next fountain encoding; Step 4: Define the receiving end as the destination node in the communication process. At the destination node, the generator matrix is obtained based on the degree information field of the received data packet, and the belief propagation algorithm is used to decode and restore the original information symbols. When the destination node successfully completes the decoding, it sends feedback to the source node, and the source node terminates the encoding operation. The step 1 is specifically as follows: The coding node symbol degree distribution function polynomial Ω(x) is defined as Where K represents the number of original information nodes, and is also the maximum degree of encoding, Ω d It represents the probability of selecting the degree value d, which is further expressed as The probability mass function ρ(d) and the correction function τ(d) satisfy: in c is a constant greater than 0, δ is the maximum decoding failure probability, It represents rounding down, β1 and β2 are correction factors used to increase the probability of occurrence of coded data packets with degree values of 1 and 2; The step 2 is specifically as follows: Assume that there are K original information symbols at the source node, represented by S = [S1, S2, S3, ..., S K ], where the original information symbol node that participates in the encoding fewer times is selected with a high probability. According to the probability, d symbols are selected from the K original information symbols for modulo-two addition operation to obtain the encoding symbol. Assume that the information field of the i-th encoding is represented by the vector G i , whose length is K, corresponding to K original information symbols. If an original information symbol participates in the encoding process, the degree information field vector G i The corresponding value in is 1, otherwise it is 0. The coding symbol and the degree information field are concatenated to obtain the transmission data packet; The specific implementation method of implementing variable symbol node regularization by selecting original information nodes based on the number of coding participations and analyzing the performance of current fountain coding using the progressive analysis method is as follows; Assume that the channel is a random packet loss channel, define the number of original information nodes as K, the total number of symbols sent in the coding segment as N, and the number of symbols lost during transmission as N e , the number of symbols successfully received by the receiver is N r , the channel packet loss rate is The decoding overhead is γ = N r / K; When the packet loss rate ε is 0, the degree of all information node symbols at the sender is equal under the rule variable node degree fountain coding method, and the coded symbols obtained by the receiver are the same as those at the sender; the average degree of the information symbol node at the receiver is defined as α. Since the degree value is a positive integer, the actual degree value of the information symbol is or Indicates rounding up, the node degree distribution of information symbols is Λ(x)=Λ h-1 x h-1 +Λ h x h , where the parameters Coefficient Λ h-1 and Λ h They represent the probability that the receiving end information symbol value is h and h-1 respectively, and satisfy: Define the information symbol edge distribution function polynomial as λ(x)=λ h-2 x h-2 +λ h-1 x h-1 , coefficient λ h-2 and λ h-1 satisfy: Since the coding node degree distribution function Ω(x) used in the rule variable node degree fountain coding is predefined, when the number of original information nodes K→∞, the asymptotic bit error rate y at the receiving end is expressed as where y l is the bit error rate after l iterative decoding, further expressed as: The coding symbol edge degree distribution ω(x) can be calculated from the coding node degree distribution function Ω(x), ω(x) = Ω′(x) / Ω′(1); When the packet loss rate ε is not 0, take any information symbol as an example, and use s to represent the information symbol. The number of coded symbols with information symbol s as neighbor nodes in N coded symbols is h. H represents the set of h coded symbols, then h = card(H), card(A) represents the cardinality of set A, and the value range of the receiving end information symbol degree d is 0≤d≤h, and d is an integer; use N e Represents the set of lost coding symbols, let I==H∩N e , when the set I is an empty set, the degree value of the receiving end information symbol s does not change; when I is not an empty set and card(I)=i, the degree value of the receiving end information symbol s is reduced to di; use p h (i) represents the probability of card(I) = i, which means the probability of missing i symbols in the set H of coded symbols with s as neighbor node; all sets N that satisfy card(I) = i e The number of Set N e All the numbers of Therefore, p h (i) is expressed as: The probability that the receiving end coding symbol degree value is h is the probability that all coding symbols of neighboring nodes with information symbols of coding end degree value h are not lost, that is, p h (0), the probability that the receiving end information symbol value is h is Λ h p h (0); Similarly, the receiving end information symbol degree value is h-1, which includes two possible situations. The first is that all the coded symbols of the neighboring nodes with the information symbol of the coding end degree value h are lost, and the second is that all the coded symbols of the neighboring nodes with the information symbol of the coding end degree value h-1 are not lost. Therefore, the probability that the receiving end information symbol degree value is h-1 is Λ h p h (1)+Λ h-1 p h-1 (0); Similarly, when the packet loss rate ε is not 0, the node degree distribution of the information symbol at the receiving end is expressed as: The edge degree distribution of the coding symbol and the information symbol is obtained by the formula ω(x) = Ω′(x) / Ω′(1) and λ(x) = Λ′(x) / Λ′(1). Therefore, the error rate y of the rule variable node degree fountain coding after l iterations of decoding is l Expressed as: In the traditional fountain coding process, the original information nodes participating in the coding are randomly selected. When the number of original information nodes K→∞, the degree distribution of the information symbol node is Poisson distribution, that is, Λ(x)=exp(α(x-1)), where α represents the average degree of the information symbol node. The Taylor series expansion of the information symbol node degree distribution polynomial is obtained: Λ(x)=exp(α(x-1)) =exp(-α)+αexp(-α)x+α 2 exp(-a)x 2 +… The constant term exp(-α) represents the probability that an information symbol is not encoded when the average degree of the information symbol node is α, that is, the probability that the receiver cannot decode the information symbol. Therefore, the error floor of traditional fountain coding is exp(-α). For regular variable node degree fountain coding, when the channel packet loss rate ε = 0, all information symbols participate in the coding process, which can effectively reduce the error floor. When ε ≠ 0, when all the coding symbols with a certain information symbol as the neighbor node are lost, the node degree distribution of the receiving end information symbol also has a constant term. At this time, the probability that the receiving end information symbol degree is equal to 0 is Λ0 = Λ h-1 p h-1 (h-1)+Λ h p h (h) The error platform of regular variable node degree fountain coding is related to the average degree of coded symbols and the channel packet loss rate. When Λ0<exp(-α), the error platform of regular variable node degree fountain coding is lower than that of traditional fountain coding. The step 3 is specifically as follows: Step 3.1: Define P(k) as the probability of selecting the kth information node, where k = 1, 2, ... K. In the initialization phase of encoding, the probability of selecting all original information nodes P(k) is the same, which is set to 1 / K, where K represents the number of original information nodes. For each original information node, set the number of encoding times s k All are 1; Step 3.2: After each fountain coding is completed, the original information nodes involved in the coding are recorded and the corresponding coding times s is recorded. k Add 1; Step 3.3: After completing the update of the encoding times of all information nodes, recalculate the selection probability P(k) of each information node, where Step 3.4: If the source node receives the decoding success feedback information sent by the destination node, it returns to step 3.1 to complete the initialization operation; otherwise, it returns to step 3.2; The step 4 is specifically as follows: Step 4.1: Assume that the degree information field in the i-th received data packet received at the destination node is G i , then the generator matrix can be expressed as G=[G1,G2,…,G i ,], get the corresponding bipartite graph and start the decoding process; Step 4.2: Select a coding symbol with a degree of 1 from the bipartite graph, directly recover the original information symbol that is uniquely connected to it, and delete the connection between the original information symbol and the coding symbol in the bipartite graph; Step 4.3: Use the generator matrix to find the coded symbols connected to the original symbol, XOR the values of these coded symbols with the original symbol values, and delete the corresponding connections in the bipartite graph; Step 4.4: Repeat steps 4.2 and 4.3 until all original symbols are restored and decoding is completed, or there is no coded symbol with a degree value of 1 and the decoding is stopped.

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