CN116633483A - Regular variable node degree fountain coding method - Google Patents
Regular variable node degree fountain coding method Download PDFInfo
- Publication number
- CN116633483A CN116633483A CN202310133911.0A CN202310133911A CN116633483A CN 116633483 A CN116633483 A CN 116633483A CN 202310133911 A CN202310133911 A CN 202310133911A CN 116633483 A CN116633483 A CN 116633483A
- Authority
- CN
- China
- Prior art keywords
- coding
- information
- symbol
- degree
- node
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 238000000034 method Methods 0.000 title claims abstract description 73
- 230000005540 biological transmission Effects 0.000 claims abstract description 34
- 238000005315 distribution function Methods 0.000 claims abstract description 24
- 230000006854 communication Effects 0.000 claims description 33
- 238000009826 distribution Methods 0.000 claims description 31
- 239000011159 matrix material Substances 0.000 claims description 8
- 238000012937 correction Methods 0.000 claims description 6
- 230000000750 progressive effect Effects 0.000 claims description 6
- 238000004458 analytical method Methods 0.000 claims description 3
- 238000004891 communication Methods 0.000 description 26
- 238000005562 fading Methods 0.000 description 7
- 238000001228 spectrum Methods 0.000 description 5
- 238000010586 diagram Methods 0.000 description 3
- 238000012163 sequencing technique Methods 0.000 description 3
- 125000004122 cyclic group Chemical group 0.000 description 2
- 230000006866 deterioration Effects 0.000 description 2
- 230000000694 effects Effects 0.000 description 2
- 238000005516 engineering process Methods 0.000 description 2
- 230000008054 signal transmission Effects 0.000 description 2
- 238000012795 verification Methods 0.000 description 2
- 230000000007 visual effect Effects 0.000 description 2
- 229920002430 Fibre-reinforced plastic Polymers 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000004364 calculation method Methods 0.000 description 1
- 239000002131 composite material Substances 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 230000001934 delay Effects 0.000 description 1
- 238000012217 deletion Methods 0.000 description 1
- 230000037430 deletion Effects 0.000 description 1
- 239000011151 fibre-reinforced plastic Substances 0.000 description 1
- 238000012423 maintenance Methods 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000013507 mapping Methods 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
- 238000011946 reduction process Methods 0.000 description 1
Classifications
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L1/00—Arrangements for detecting or preventing errors in the information received
- H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
- H04L1/0056—Systems characterized by the type of code used
- H04L1/0057—Block codes
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L1/00—Arrangements for detecting or preventing errors in the information received
- H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
- H04L1/0041—Arrangements at the transmitter end
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
- Y02D30/00—Reducing energy consumption in communication networks
- Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks
Landscapes
- Engineering & Computer Science (AREA)
- Computer Networks & Wireless Communication (AREA)
- Signal Processing (AREA)
- Error Detection And Correction (AREA)
Abstract
A regular variable node degree fountain coding method comprises the steps of firstly constructing a coding node symbol degree distribution function, accelerating a decoding process by improving the probability of occurrence of small degree value coding symbols, and generating a degree value according to the degree distribution function; then selecting an original information symbol to participate in the coding according to the information symbol selection probability, and splicing the degree information field and the coding information field to construct a transmission data packet; secondly, the probability of selecting the information nodes is updated by recording the participation coding times of all original information nodes; finally, the received data is decoded at the destination node by a belief propagation algorithm. The invention improves the probability of occurrence of the small-scale value coding symbol by optimizing the coding node degree distribution function, adopts the information node selection strategy of the coding participation times, realizes regularization of the symbol variable node degree value, selects the information node with small degree value during coding, achieves the purposes of reducing error code platform and saving decoding cost in the fountain coding process, and reduces coding complexity at the source node.
Description
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to a regular variable node degree fountain coding method.
Background
Fountain codes are used as a coding mode without fixed code rate, and are initially used for solving the problems of large-scale data distribution, reliable multicasting, multicasting and the like in binary deletion channels, and simultaneously can cope with the phenomenon of overlong waiting time of a transmitting end caused by a feedback retransmission mechanism under a long transmission distance, effectively avoid 'feedback storm' occurring in the traditional linear block codes and ensure the reliability of data transmission, so that the fountain codes are also applied to severe transmission environments with extremely high requirements on communication reliability, such as deep space communication, high-speed aircraft plasma sheath communication, beyond-line-of-sight communication and the like. In the above transmission environment, since the communication link distance is long, the electromagnetic signal is affected by free space propagation loss, the useful signal transmission component at the receiver is low, and meanwhile, factors such as external noise interference in the transmission process are considered, so that the communication quality is rapidly deteriorated, and the communication process is interrupted.
In order to ensure the reliability of communication, the current common technical means include spread spectrum communication and diversity combining technology. In spread spectrum communication, after original information is processed by a spread spectrum code word sequence, the frequency bandwidth occupied by signal transmission is far larger than the minimum frequency bandwidth required by the information, and the effects of resisting narrowband interference and multipath are realized by acquiring the spread spectrum gain, but the influence caused by noise cannot be overcome by the spread spectrum, and the problem of rapid deterioration of communication quality still cannot be solved under the environment of extremely low signal to noise ratio. The diversity receiving technology is that several signals carrying the same information and transmitted on independent fading channels are provided to a receiver, the receiver combines the received independent signals which are not related to each other according to a certain rule, so that the energy of the received useful signal is maximum, and the signal to noise ratio of the received signal is further improved, thereby achieving the purpose of resisting fading.
In the traditional fountain coding process, robust soliton distribution is mostly adopted, and original information nodes are randomly selected to participate in coding, so that the phenomenon that certain information nodes are not involved in coding all the time or participate in coding for a small number of times is quite likely to occur, meanwhile, the packet loss factor in the transmission process is considered, the information quantity of the information symbol nodes at a receiving end is 0, the decoding process is influenced, and the problems of high error code platform and high decoding cost occur. Aiming at the problem, the existing solution is to adopt a degree value lookup table to realize regularization of the degree value of the information symbol of the coding end, but the degree value lookup table needs to be traversed and sequenced in each coding process, the table is maintained continuously in the coding process, the sequencing process of the degree value lookup table is more complex along with the increase of the number K of the original information nodes, and the decoding cost is increased after the delay of the decoding waterfall area of the decoding end is caused while the error code platform is reduced.
In the prior art, the CN201910613926.0 derives and analyzes the optimal degree distribution function capable of realizing the regularization of the node degree value of the code symbol, but the problems of slow decoding speed, high decoding cost and the like caused by the regular variable node degree fountain code are not considered.
In the communication transmission process like deep space communication, beyond visual range communication and the like, the communication quality is rapidly deteriorated under the environment with extremely low signal to noise ratio due to the common influence of various factors such as large-scale fading, small-scale fading, external noise, interference and the like, and the communication process is interrupted.
Based on the method, how to optimize the prior fountain coding algorithm to obtain the improvement of the communication service rate performance in the severe transmission environment with obvious fading characteristics and small useful signal power is considered to have important significance.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention aims to provide a regular variable node degree fountain coding method, which considers the influence of a severe transmission environment on communication performance, improves the occurrence probability of a small value coding symbol by optimizing a coding node degree distribution function, adopts an information node selection strategy based on coding participation times, realizes the regularization of the symbol variable node degree, achieves the purposes of reducing an error code platform and saving decoding cost in the fountain coding process, and improves the service transmission rate on the premise of ensuring the communication reliability.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
a regular variable node degree fountain coding method comprises the following steps of;
step 1: defining a transmitting end as a source node in the communication process, wherein K original information symbols exist at the source node as information nodes to wait for transmission, and randomly selecting a degree value d according to a symbol degree distribution function, namely, d original information symbols participate in the coding process;
step 2: the source node selects d original information symbols with least participation in coding times according to the selection probability, carries out modulo double addition operation to obtain coded information symbols, the length of a degree information field is K bits, the corresponding K original information symbols are 1 if a certain original information symbol is selected to participate in coding in the coding process, otherwise, the corresponding degree information bit is 0, and the coded information symbols and the degree information field are spliced to obtain a transmission data packet;
step 3: recording the original information symbol nodes participating in the coding process of the K original symbol nodes, adding one operation to the total number of times of selecting the codes of the symbol nodes, and calculating the selection probability of the original information symbol nodes used for the next fountain coding;
step 4: and defining a receiving end as a destination node in the communication process, obtaining a generating matrix at the destination node according to the degree information field of the received data packet, decoding by using a belief propagation algorithm, recovering an original information symbol, and sending feedback to a source node when the destination node successfully completes decoding, and terminating the encoding operation at the source node.
The step 1 specifically comprises the following steps:
the code node symbol degree distribution function polynomial Ω (x) is defined asWherein K represents the number of nodes of the original information and is also the maximum value of the code, Ω d The probability of the selection value d is further expressed asWherein the probability mass function ρ (d) and the correction function τ (d) respectively satisfy:
wherein the method comprises the steps ofc is a constant greater than 0, delta is the maximum decoding failure probability, ++>Representing a rounding down, beta 1 、β 2 The correction factor is used for improving the occurrence probability of the coded data packet with the degree value of 1 and 2.
The step 2 specifically comprises the following steps:
assume that there are K original information symbols at the source node, denoted s= [ S ] 1 ,S 2 ,S 3 ,,S K ]Wherein the original information symbol node with less participation in coding is selected with large probability, d symbols are selected from K original information symbols according to probability for modulo double addition operation to obtain coding symbol, and the ith coding time information field is assumed to be represented as vector G i The length of the code is K, the code corresponds to K original information symbols respectively, and if one original information symbol participates in the coding process, the code is a vector G of a degree information field i If the corresponding value in the code symbol is 1, otherwise, the code symbol is 0, and the code symbol and the degree information field are spliced to obtain a transmission data packet;
the regularization of variable symbol nodes is realized through an original information node selection scheme based on coding participation times, and the specific implementation mode of analyzing the performance of the current fountain coding by using a progressive analysis method is as follows;
setting the channel as random packet loss channel, defining the number of nodes of original information as K, and the total number of transmitting symbols of the coding section asN, the lost symbol in the transmission process is N e The number of symbols successfully received by the receiving end is N r The packet loss rate of the channel is as followsThe coding overhead is gamma=n r /K。
When the packet loss rate epsilon is 0, the symbol degrees of all information nodes of the transmitting end are equal in a regular variable node degree fountain coding mode, and the coding symbols obtained by the receiving end are the same as those of the transmitting end; defining the average degree of the information symbol nodes of the receiving end as alpha, and the actual degree value of the information symbol is as positive integerOr->Representing an upward rounding, the information symbol node degree distribution is Λ (x) =Λ h-1 x h-1 +Λ h x h Wherein parameter->Coefficient lambda h-1 Sum lambda h The probability of the receiving end information symbol degree value h and h-1 is respectively represented, and the following conditions are satisfied:
defining information symbol edge distribution function polynomial as lambda (x) =lambda h-2 x h-2 +λ h-1 x h-1 Coefficient lambda h-2 And lambda (lambda) h-1 The method meets the following conditions:
as the coding node degree distribution function omega (x) used in the regular variable node degree fountain coding is predefined, when the number of the original information nodes K & gtto & gtinfinity, the progressive error at the receiving end is causedThe code rate y is expressed asWherein y is l The error rate after l times of iterative decoding is further expressed as:
wherein the encoded symbol edge degree distribution ω (x) can be calculated from the encoded node edge degree distribution function Ω (x), ω (x) =Ω '(x)/Ω' (1);
when the packet loss rate epsilon is not 0, taking any information symbol as an example, s is used for representing the information symbol, the number of the coding symbols taking the information symbol s as a neighbor node in N coding symbols is H, H is used for representing a set of H coding symbols, h=card (H), card (A) represents the base number of the set A, the value range of the receiving end information symbol degree value d is 0-d-H, and d is an integer; by N e Representing a missing set of encoded symbols, let i= =hn e When the set I is an empty set, the degree value of the information symbol s of the receiving end is not changed; when I is not an empty set and there is a card (I) =i, the degree value of the receiving-end information symbol s is reduced to d-I; by p h (i) The probability of occurrence of card (I) =i is represented as the probability of losing I symbols in the coded symbol set H having s as the neighbor node. All sets N satisfying card (I) =i e The number of (2) isSet N e All numbers are->Thus p is h (i) Expressed as:
the probability of the code symbol degree value h of the receiving end is all codes taking the information symbol with the code symbol degree value h as the neighbor nodeProbability of none of the code symbols being lost, i.e. p h (0) At this time, the probability of the receiving end information symbol degree value h is Λ h p h (0) The method comprises the steps of carrying out a first treatment on the surface of the The same method comprises two possible cases that the information symbol degree value of the receiving end is h-1, wherein the first is that all coding symbols taking the information symbol with the coding end degree value of h as a neighbor node lose 1, and the second is that all coding symbols taking the information symbol with the coding end degree value of h-1 as the neighbor node do not lose, so that the probability that the information symbol degree value of the receiving end is h-1 is Λ h p h (1)+Λ h- 1 p h-1 (0) The method comprises the steps of carrying out a first treatment on the surface of the Similarly, when the packet loss rate epsilon is not 0, the node degree distribution of the information symbol of the receiving end is expressed as follows:
the edge degree distribution of the coding symbol and the information symbol is obtained through formulas omega (x) =omega '(x)/omega' (1) and lambda (x) =lambda '(x)/lambda' (1), so that the error rate y of the regular variable node degree fountain coding after l times of iterative decoding is obtained at the moment l Expressed as:
in the conventional fountain coding process, original information nodes participating in coding are randomly selected, when the number of the original information nodes is K & gtto & gtinfinity, the information symbol node degree distribution is poisson distribution, namely Λ (x) =exp (alpha (x-1)), wherein alpha represents the average degree of the information symbol nodes, and Taylor series expansion is carried out on an information symbol node degree distribution polynomial, so that the information symbol node degree distribution polynomial is obtained:
Λ(x)＝exp(α(x-1))
＝exp(-α)+αexp(-α)x+α 2 exp(-α)x 2 +…
when the average degree of the nodes of the information symbol is alpha, the constant term exp (-alpha) represents the probability that the information symbol does not participate in encoding, namely the probability that the receiving end cannot decode the information symbol, so that the error code platform of the traditional fountain coding is exp (-alpha);
for regular variable node degree fountain coding, when the channel packet loss rate epsilon=0, all information symbols participate in the coding process, so that an error code platform can be effectively reduced, when epsilon is not equal to 0, when the coding symbols taking a certain information symbol as a neighbor node are all lost, constant items exist in the node degree distribution of the information symbol of a receiving end, and at the moment, the probability that the information symbol degree of the receiving end is equal to 0 is lambda 0 ＝Λ h-1 p h-1 (h-1)+Λ h p h (h) Error code platform under regular variable node degree fountain coding is related to coding symbol average degree and channel packet loss rate, and when Λ 0 And when the value is less than exp (-alpha), the code error platform of the regular variable node degree fountain code is lower than the traditional fountain code.
The step 3 specifically comprises the following steps:
step 3.1: defining P (K) as the selection probability of the kth information node, wherein k=1, 2, K, wherein the selected probabilities P (K) of all the original information nodes in the coding initialization stage are the same and are set to 1/K, wherein K represents the number of the original information nodes, and setting the coding times s for each original information node k Are all 1;
step 3.2: every time fountain coding is completed, the original information nodes participating in coding are recorded, and the corresponding coding times s are recorded k Adding 1;
step 3.3: after the number of times of coding of all the information nodes is updated, recalculating the selection probability P (k) of each information node, wherein
Step 3.4, if the source node receives the decoding success feedback information sent by the destination node, returning to the step 3.1, and finishing the initialization operation; otherwise, returning to the step 3.2.
The step 4 specifically comprises the following steps:
step 4.1: assume that the degree information field in the ith received packet obtained at the destination node is G i The generator matrix may be expressed as g= [ G ] 1 ,G 2 ,…,G i ,…]Obtaining a corresponding bipartite graph and starting a decoding process;
step 4.2: selecting a coding symbol with a degree value of 1 from the bipartite graph, directly recovering an original information symbol uniquely connected with the coding symbol, and deleting a connecting line between the original information symbol and the coding symbol in the bipartite graph;
step 4.3: searching coding symbols connected with the original symbols through the generating matrix, performing exclusive OR on the values of the coding symbols and the original symbol values, and deleting corresponding connecting lines in the bipartite graph;
step 4.4: and repeating the steps 4.2 and 4.3 until all original symbols are restored to finish decoding or the coded symbol with the absence degree value of 1 is stopped.
The invention has the beneficial effects that:
in the transmission process with extremely high requirements on reliability, such as deep space communication, high-speed aircraft plasma sheath communication, beyond visual range communication and the like, the effective distance of a communication link reaches thousands of kilometers, and an actual electromagnetic signal is influenced by large-scale fading and small-scale fading in the transmission process, so that a large amount of successfully received coded data packets at a destination node in the communication process are reduced, so that great decoding expenditure is required to finish decoding operation, the effective communication rate is greatly reduced, the communication quality is ensured under the extremely low signal-to-noise ratio transmission environment, the coding performance gain is sought, and reliable communication is realized;
the fountain coding is applied to solve the problem of rapid deterioration of communication quality in a severe transmission environment, the node degree distribution function of coding symbols is optimized, meanwhile, the probability of selecting the information nodes is updated based on the number of times of participation of the information nodes in coding, regularization of node variables is realized, and compared with the existing fountain coding algorithm, the performance of obtaining the error rate and the decoding cost in the packet loss channel environment is improved.
Drawings
Fig. 1 is a flowchart of a rule variable node degree fountain coding method according to an embodiment of the present invention.
Fig. 2 is a schematic diagram showing comparison of decoding cost performance effects of an algorithm in a verification embodiment of the present invention and a conventional fountain LT coding algorithm under different channel transmission error probabilities.
Fig. 3 is a schematic diagram showing the comparison of the performance of the algorithm and other algorithms in the verification embodiment of the present invention under the condition that the probability of channel transmission error is 0.5.
Fig. 4 is a system processing flow diagram of a rule variable node degree fountain coding method according to an embodiment of the invention.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings.
The embodiment of the invention discloses a regular variable node degree fountain coding method, wherein a flow chart is shown in fig. 1, and the method is implemented according to the following steps:
the step 1 is as follows:
the code node symbol degree distribution function polynomial Ω (x) is defined asWherein K represents the number of nodes of the original information and is also the maximum value of the code, Ω d The probability of representing the value of the selection degree as d can be further expressed asWherein ρ (d), τ (d) satisfy:
wherein the method comprises the steps ofc is a constant greater than 0, delta is the maximum decoding failure probability, ++>Representing a rounding down, beta 1 、β 2 The correction factor is used for improving the occurrence probability of the coded data packet with the degree value of 1 and 2.
The step 2 is as follows:
and realizing regularization of the node degree value of the variable symbol through an original information node selection scheme based on the coding participation times. In the conventional LT coding process, original information nodes are randomly selected, all original data packets participate in the coding process with the same probability, and meanwhile, due to the fact that some original information nodes participate in the coding less times or do not participate in the coding, the receiving end can not obtain the effective information of the information nodes all the time, decoding can not be completed, and the error rate of the system is maintained on an error platform and is difficult to reduce.
In order to improve the error platform phenomenon, all original information nodes can participate in the encoding process, statistics is carried out on the information node degree at the encoding end, when the number of times that one information node is used for encoding and transmitting is obviously more than that of other information nodes, the receiving end can be considered to obtain the information quantity of the node, if the node is used for encoding continuously, the complexity of the decoding process is increased, and no gain is caused for successful decoding, so that the priority of the information node is lowered in the subsequent encoding process, and the probability of selecting the node for encoding is reduced. Similarly, if a certain original information node does not participate in encoding at all times or participates in encoding for a small time, the receiving end has difficulty in obtaining useful information of the node, thus causing an error platform to appear, so that the information node should be preferentially selected in the subsequent encoding process. The specific implementation mode for analyzing the performance of the regular variable node degree fountain code by using the progressive analysis method is as follows.
Setting the channel as a random packet loss channel, defining the number of nodes of original information as K, setting the total number of transmitted symbols of a coding section as N, and setting the lost symbols in the transmission process as N e The number of symbols successfully received by the receiving end is N r The packet loss rate of the channel is as followsThe coding overhead is gamma=n r /K。
When the packet loss rate epsilon is 0, the rule variable node degree fountain coding mode is adopted by the transmitting endThe information nodes have equal symbol degrees, and the code symbols obtained by the receiving end are the same as those of the transmitting end. Defining the average degree of the information symbol nodes of the receiving end as alpha, and the actual degree value of the information symbol is as positive integerOr->Representing an upward rounding, the information symbol node degree distribution is Λ (x) =Λ h-1 x h-1 +Λ h x h Wherein parameter->Coefficient lambda h-1 Sum lambda h The probability of the receiving end information symbol degree value h and h-1 is respectively represented, and the following conditions are satisfied:
defining information symbol edge distribution function polynomial as lambda (x) =lambda h-2 x h-2 +λ h-1 x h-1 Coefficient lambda h-2 And lambda (lambda) h-1 The method meets the following conditions:
since the code node degree distribution function omega (x) used in the regular variable node degree fountain coding is predefined, when the number of original information nodes K-infinity, the progressive error rate y at the receiving end can be expressed asWherein y is l For the error rate after l iterative decoding, it can be further expressed as:
the encoded symbol edge degree distribution ω (x) can be calculated from the encoded node degree distribution function Ω (x), ω (x) =Ω '(x)/Ω' (1).
When the packet loss rate epsilon is not 0, taking any information symbol as an example, s is used for representing the information symbol, the number of the coding symbols taking the information symbol s as a neighbor node in N coding symbols is H, H is used for representing a set of H coding symbols, h=card (H), card (A) represents the base number of the set A, the value range of the receiving end information symbol degree value d is 0-d-H, and d is an integer. By N e Representing a missing set of encoded symbols, letWhen the set I is an empty set, the degree value of the information symbol s of the receiving end is not changed; when I is not an empty set and there is a card (I) =i, the degree value of the receiving side information symbol s is reduced to d-I. By p h (i) The probability of occurrence of card (I) =i is represented as the probability of losing I symbols in the coded symbol set H having s as the neighbor node. All sets N satisfying card (I) =i e The number of (2) is->Set N e All numbers are->Thus p is h (i) Can be expressed as: />
The probability of the code symbol degree value h of the receiving end is the probability that all code symbols taking the information symbol with the code terminal degree value h as neighbor nodes are not lost, namely p h (0) At this time, the probability of the receiving end information symbol degree value h is Λ h p h (0) The method comprises the steps of carrying out a first treatment on the surface of the The information symbol degree value of h-1 of the receiving end in the same way comprises two possible cases, wherein the first is that 1 code symbol is lost by taking the information symbol with the code degree value of h as all code symbols of neighbor nodes, and the second is that the code is taken as the codeAll the code symbols with the end value of h-1 as neighbor nodes are not lost, so that the probability that the receiving end information symbol with the end value of h-1 is Λ can be obtained h p h (1)+Λ h- 1 p h-1 (0). Similarly, when the packet loss rate epsilon is not 0, the information symbol node degree distribution of the receiving end can be expressed as:
the edge degree distribution of the coding symbol and the information symbol can be obtained through formulas omega (x) =Ω '(x)/Ω' (1) and lambda (x) =Λ '(x)/Λ' (1), so that the error rate y of the regular variable node degree fountain coding after l times of iterative decoding can be obtained at the moment l Can be expressed as:
in the conventional fountain coding process, original information nodes participating in coding are randomly selected, when the number of the original information nodes is K & gtto & gtinfinity, the information symbol node degree distribution is poisson distribution, namely Λ (x) =exp (alpha (x-1)), wherein alpha represents the average degree of the information symbol nodes, and Taylor series expansion is carried out on an information symbol node degree distribution polynomial, so that the information symbol node degree distribution can be obtained:
Λ(x)＝exp(α(x-1))
＝exp(-α)+αexp(-α)x+α 2 exp(-α)x 2 +…
when the average degree of the nodes of the information symbol is alpha, the constant term exp (-alpha) represents the probability that the information symbol does not participate in encoding, namely the probability that the receiving end cannot decode the information symbol, so that the error code platform of the traditional fountain coding is exp (-alpha).
For the regular variable node degree fountain coding, when the channel packet loss rate epsilon=0, all information symbols participate in the coding process, so that an error code platform can be effectively reduced, when epsilon is not equal to 0, when the coding symbols taking a certain information symbol as a neighbor node are all lost, the node degree distribution of the information symbol at the receiving end also has a constant term,at this time, the probability that the receiving end information symbol degree is equal to 0 is Λ 0 ＝Λ h-1 p h-1 (h-1)+Λ h p h (h) A. The invention relates to a method for producing a fibre-reinforced plastic composite Error code platform under regular variable node degree fountain coding is related to coding symbol average degree and channel packet loss rate, and when Λ 0 And when the value is less than exp (-alpha), the code error platform of the regular variable node degree fountain code is lower than the traditional fountain code.
The step 3 is as follows:
step 3.1, defining P (K) as the probability of selecting the kth information node, wherein k=1, 2, K, wherein the probability of selecting all the original information nodes P (K) in the coding initialization stage is the same, and is set to 1/K, wherein K represents the number of original information nodes, and for each original information node, the coding times s are set k Are all 1;
step 3.2, recording the original information nodes participating in the coding every time the fountain coding is finished, and recording the corresponding coding times s k Adding 1;
step 3.3, after finishing the updating of the coding times of all the information nodes, recalculating the selection probability P (k) of each information node, wherein
Step 3.4, if the source node receives the decoding success feedback information sent by the destination node, returning to the step 3.1, and finishing the initialization operation; otherwise, returning to the step 3.2.
In each coding process, two processes of generating a coded data packet and selecting probability updating of an original information node are processed in parallel, namely, record updating of coding times and calculation updating of selecting probability cannot influence normal coding processes, and efficient coding of a source node is guaranteed.
The step 4 is as follows:
step 4.1, the destination node reconstructs the generating matrix according to the degree information field in the received data packet to obtain a corresponding bipartite graph and starts the decoding process;
step 4.2, selecting a code symbol with a degree value of 1 from the bipartite graph, directly recovering an original information symbol uniquely connected with the code symbol, and deleting a corresponding edge;
step 4.3, searching the code symbols connected with the original symbols through the generation matrix, performing exclusive or on the values of the code symbols and the original symbol values, and deleting the corresponding connected edges in the bipartite graph;
and 4.4, repeating the steps 4.2 and 4.3 until all original symbols are restored to finish decoding or the coded symbol with the absence degree value of 1 is stopped.
The method of the embodiment of the invention is verified, the number of the original information symbol nodes is assumed to be 128, the symbol length of each information node is 3520 bits, the packet loss rate in the deleted channel is set to be 0.3 to 0.8 respectively, and different channel transmission environments are simulated.
As shown in fig. 2, the comparison method adopted by the invention is as follows: (1) traditional fountain LT encoding algorithm: the code symbol node degree distribution function selects Lu Banggu sub-distribution, and the original information node is randomly selected when each code is performed. (2) The invention provides a rule variable node degree fountain coding algorithm: the node degree distribution of the coding symbol uses an optimized degree distribution function to increase the probability of the occurrence of the small-scale value coding symbol, meanwhile, an original information node selection strategy based on the coding times is adopted to calculate the selection probability, and the information nodes with small-scale values are selected to participate in coding in each coding process.
As shown in fig. 2, the algorithm provided by the invention can obtain the performance gain of decoding cost under different channel transmission error probabilities compared with the traditional fountain LT coding, and the performance gain of the algorithm is more obvious as the quality of the transmission environment is reduced with the increase of the transmission error probability. The algorithm provided by the invention can effectively reduce the coding transmission times and improve the actual service transmission rate while obtaining the performance gain of the decoding cost.
As shown in fig. 3, the channel transmission error probability is fixed to be 0.5, under the comparison method, the existing regular variable node degree fountain coding (Regularized variable-node Luby Transform, RLT) algorithm is incorporated into performance comparison, the algorithm adopts a robust soliton degree distribution function, regularization of the code segment information symbol degree value is realized by adopting a degree value lookup table mode, the degree value lookup table is required to be subjected to traversal sequencing during each coding, the information node with the minimum degree value is selected to participate in coding, maintenance is required to be carried out on the table during the coding, and the sequencing process of the degree value lookup table is more complex along with the increase of the original information node number K.
As shown in FIG. 3, the RLT coding algorithm adopts a coding mode of regular variable node degree, so that the coverage rate of information nodes in the coding process is increased, and compared with the traditional fountain LT coding, the RLT coding algorithm can reduce the bit error rate at the same coding cost. However, the RLT coding algorithm realizes regularization of the information node degree value, and delays a 'waterfall region' in the decoding process, so that the decoding process is slow. The algorithm provided by the invention adopts the optimized node degree distribution function of the code symbol, effectively increases the probability of occurrence of small degree values in the code symbol, directly decodes the code symbol with the degree value of 1 at a target node, and can realize decoding by only one dismantling operation of the code symbol with the degree value of 2, thereby accelerating the decoding speed. Meanwhile, in each encoding process, according to the original signal node with smaller selection degree value of the selection probability, the regularization of the degree value of the variable node is realized, and the error rate of the algorithm provided by the invention is improved under the same decoding cost, compared with the RLT encoding algorithm, the error rate reduction process is quicker and more obvious, so that the algorithm has good performance in the packet loss channel environment.
As shown in FIG. 4, a destination node completes regular variable node fountain coding through the algorithm provided by the invention, after outer layer erasure coding is completed, cyclic redundancy check bits are added into coded data, then inner layer Turbo coding is continued to be carried out, redundant information is added, error correction performance is improved, matching mapping of service resources and actual system physical resources is completed through rate matching, a series of burst errors occurring in the transmission process are converted into random errors through interleaving operation, and finally signals are sent through symbol modulation. The transmitted data reach the destination node after passing through the wireless channel, the destination node obtains the encoded data through a series of inverse operations of demodulation, de-interleaving, de-rate matching and Turbo decoding, judges whether the data packet is correct or not through cyclic redundancy check, and the data packet with correct check continues to carry out subsequent decoding operation, and the data packet with incorrect check is directly discarded and is not processed.
Claims (6)
1. A regular variable node degree fountain coding method is characterized by comprising the following steps of;
step 1: defining a transmitting end as a source node in the communication process, wherein K original information symbols exist at the source node as information nodes to wait for transmission, and randomly selecting a degree value d according to a symbol degree distribution function, namely, d original information symbols participate in the coding process;
step 2: the source node selects d original information symbols with least participation in coding times according to the selection probability, carries out modulo double addition operation to obtain coded information symbols, the length of a degree information field is K bits, the corresponding K original information symbols are 1 if a certain original information symbol is selected to participate in coding in the coding process, otherwise, the corresponding degree information bit is 0, and the coded information symbols and the degree information field are spliced to obtain a transmission data packet;
step 3: recording the original information symbol nodes participating in the coding process of the K original symbol nodes, adding one operation to the total number of times of selecting the codes of the symbol nodes, and calculating the selection probability of the original information symbol nodes used for the next fountain coding;
step 4: and defining a receiving end as a destination node in the communication process, obtaining a generating matrix at the destination node according to the degree information field of the received data packet, decoding by using a belief propagation algorithm, recovering an original information symbol, and sending feedback to a source node when the destination node successfully completes decoding, and terminating the encoding operation at the source node.
2. The regular variable node degree fountain coding method according to claim 1, wherein the step 1 is specifically:
the code node symbol degree distribution function polynomial Ω (x) is defined asWherein K represents the number of nodes of the original information and is also the maximum value of the code, Ω d The probability of the selection value d is further expressed asWherein the probability mass function ρ (d) and the correction function τ (d) respectively satisfy:
wherein the method comprises the steps ofc is a constant greater than 0, delta is the maximum decoding failure probability, ++>Representing a rounding down, beta 1 、β 2 The correction factor is used for improving the occurrence probability of the coded data packet with the degree value of 1 and 2.
3. The regular variable node degree fountain coding method according to claim 1, wherein the step 2 is specifically:
assume that there are K original information symbols at the source node, denoted s= [ S ] 1 ,S 2 ,S 3 ,…,S K ]Wherein the original information symbol node with less participation in coding is selected with large probability, d symbols are selected from K original information symbols according to probability for modulo double addition operation to obtain coding symbol, and the ith coding time information field is assumed to be represented as vector G i The length is K, and the K original information symbols respectively correspond toIf some original information symbol participates in the encoding process, a degree information field vector G i If the corresponding value in the code symbol is 1, otherwise, the code symbol is 0, and the code symbol and the degree information field are spliced to obtain a transmission data packet;
the regularization of variable symbol nodes is realized through an original information node selection scheme based on coding participation times, and the specific implementation mode of analyzing the performance of the current fountain coding by using a progressive analysis method is as follows;
setting the channel as a random packet loss channel, defining the number of nodes of original information as K, setting the total number of transmitted symbols of a coding section as N, and setting the lost symbols in the transmission process as N e The number of symbols successfully received by the receiving end is N r The packet loss rate of the channel is as followsThe coding overhead is gamma=n r /K。
4. The regular variable node degree fountain coding method according to claim 3, wherein when the packet loss rate epsilon is 0, the symbol degrees of all information nodes of a transmitting end are equal in the regular variable node degree fountain coding mode, and the coding symbols obtained by a receiving end are the same as the transmitting end; defining the average degree of the information symbol nodes of the receiving end as alpha, and the actual degree value of the information symbol is as positive integerOr->Representing an upward rounding, the information symbol node degree distribution is Λ (x) =Λ h-1 x h-1 +Λ h x h Wherein parameter->Coefficient lambda h-1 Sum lambda h The probability of the receiving end information symbol degree value h and h-1 is respectively represented, and the following conditions are satisfied:
defining information symbol edge distribution function polynomial as lambda (x) =lambda h-2 x h-2 +λ h-1 x h-1 Coefficient lambda h-2 And lambda (lambda) h-1 The method meets the following conditions:
as the coding node degree distribution function omega (x) used in the regular variable node degree fountain coding is predefined, when the number K & gtto & gtinfinity of the original information nodes is calculated, the progressive error rate y at the receiving end is expressed asWherein y is l The error rate after l times of iterative decoding is further expressed as:
wherein the encoded symbol edge degree distribution ω (x) can be calculated from the encoded node edge degree distribution function Ω (x), ω (x) =Ω '(x)/Ω' (1);
when the packet loss rate epsilon is not 0, taking any information symbol as an example, s is used for representing the information symbol, the number of the coding symbols taking the information symbol s as a neighbor node in N coding symbols is H, H is used for representing a set of H coding symbols, h=card (H), card (A) represents the base number of the set A, the value range of the receiving end information symbol degree value d is 0-d-H, and d is an integer; by N e Representing a missing set of encoded symbols, letWhen the set I is an empty set, the degree value of the information symbol s of the receiving end is not changedA change; when I is not an empty set and there is a card (I) =i, the degree value of the receiving-end information symbol s is reduced to d-I; by p h (i) The probability of occurrence of card (I) =i is represented as the probability of losing I symbols in the coded symbol set H having s as the neighbor node. All sets N satisfying card (I) =i e The number of (2) is->Set N e All numbers are->Thus p is h (i) Expressed as: />
The probability of the code symbol degree value h of the receiving end is the probability that all code symbols taking the information symbol with the code terminal degree value h as neighbor nodes are not lost, namely p h (0) At this time, the probability of the receiving end information symbol degree value h is Λ h p h (0) The method comprises the steps of carrying out a first treatment on the surface of the The same method comprises two possible cases that the information symbol degree value of the receiving end is h-1, wherein the first is that all coding symbols taking the information symbol with the coding end degree value of h as a neighbor node lose 1, and the second is that all coding symbols taking the information symbol with the coding end degree value of h-1 as the neighbor node do not lose, so that the probability that the information symbol degree value of the receiving end is h-1 is Λ h p h (1)+Λ h-1 p h-1 (0) The method comprises the steps of carrying out a first treatment on the surface of the Similarly, when the packet loss rate epsilon is not 0, the node degree distribution of the information symbol of the receiving end is expressed as follows:
the edge degree distribution of the coding symbol and the information symbol is obtained through formulas omega (x) =omega '(x)/omega' (1) and lambda (x) =lambda '(x)/lambda' (1), so that the error rate y of the regular variable node degree fountain coding after l times of iterative decoding is obtained at the moment l Expressed as:
in the conventional fountain coding process, original information nodes participating in coding are randomly selected, when the number of the original information nodes is K & gtto & gtinfinity, the information symbol node degree distribution is poisson distribution, namely Λ (x) =exp (alpha (x-1)), wherein alpha represents the average degree of the information symbol nodes, and Taylor series expansion is carried out on an information symbol node degree distribution polynomial, so that the information symbol node degree distribution polynomial is obtained:
Λ(x)＝exp(α(x-1))
＝exp(-α)+αexp(-α)x+α 2 exp(-α)x 2 +…
when the average degree of the nodes of the information symbol is alpha, the constant term exp (-alpha) represents the probability that the information symbol does not participate in encoding, namely the probability that the receiving end cannot decode the information symbol, so that the error code platform of the traditional fountain coding is exp (-alpha);
for regular variable node degree fountain coding, when the channel packet loss rate epsilon=0, all information symbols participate in the coding process, so that an error code platform can be effectively reduced, when epsilon is not equal to 0, when the coding symbols taking a certain information symbol as a neighbor node are all lost, constant items exist in the node degree distribution of the information symbol of a receiving end, and at the moment, the probability that the information symbol degree of the receiving end is equal to 0 is lambda 0 ＝Λ h-1 p h-1 (h-1)+Λ h p h (h) Error code platform under regular variable node degree fountain coding is related to coding symbol average degree and channel packet loss rate, and when Λ 0 And when the value is less than exp (-alpha), the code error platform of the regular variable node degree fountain code is lower than the traditional fountain code.
5. The regular variable node degree fountain coding method according to claim 1, wherein the step 3 is specifically:
step 3.1: defining P (K) as the probability of selecting the kth information node, wherein k=1, 2, … K, and the probability of selecting all original information nodes P (K) is the same in the encoding initialization stage, and is set to 1/K, wherein K represents the original information nodeNumber of initial information nodes, for each original information node, number of codes s is set k Are all 1;
step 3.2: every time fountain coding is completed, the original information nodes participating in coding are recorded, and the corresponding coding times s are recorded k Adding 1;
step 3.3: after the number of times of coding of all the information nodes is updated, recalculating the selection probability P (k) of each information node, wherein
Step 3.4, if the source node receives the decoding success feedback information sent by the destination node, returning to the step 3.1, and finishing the initialization operation; otherwise, returning to the step 3.2.
6. The regular variable node degree fountain coding method according to claim 1, wherein the step 4 is specifically:
step 4.1: assume that the degree information field in the ith received packet obtained at the destination node is G i The generator matrix may be expressed as g= [ G ] 1 ,G 2 ,…,G i ,…]Obtaining a corresponding bipartite graph and starting a decoding process;
step 4.2: selecting a coding symbol with a degree value of 1 from the bipartite graph, directly recovering an original information symbol uniquely connected with the coding symbol, and deleting a connecting line between the original information symbol and the coding symbol in the bipartite graph;
step 4.3: searching coding symbols connected with the original symbols through the generating matrix, performing exclusive OR on the values of the coding symbols and the original symbol values, and deleting corresponding connecting lines in the bipartite graph;
step 4.4: and repeating the steps 4.2 and 4.3 until all original symbols are restored to finish decoding or the coded symbol with the absence degree value of 1 is stopped.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310133911.0A CN116633483A (en) | 2023-02-17 | 2023-02-17 | Regular variable node degree fountain coding method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310133911.0A CN116633483A (en) | 2023-02-17 | 2023-02-17 | Regular variable node degree fountain coding method |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN116633483A true CN116633483A (en) | 2023-08-22 |
Family
ID=87637142
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202310133911.0A Pending CN116633483A (en) | 2023-02-17 | 2023-02-17 | Regular variable node degree fountain coding method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN116633483A (en) |
-
2023
- 2023-02-17 CN CN202310133911.0A patent/CN116633483A/en active Pending
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| EP1841116B1 (en) | Decoding method for tail-biting convolutional codes using a search-depth Viterbi algorithm | |
| CN1154236C (en) | Error correction coding type digital transmission method | |
| CN1104795C (en) | Interference mitigation by joint detection of cochannel signals | |
| US20070230609A1 (en) | Iterative detection and decoding apparatus and method in MIMO system | |
| CN110430009B (en) | Multi-user joint coding modulation system | |
| CN105846827B (en) | Iterative joint message source and channel interpretation method based on arithmetic code and low density parity check code | |
| CN108809518B (en) | Method for constructing cascade Spinal code for reducing error performance | |
| CN102904668A (en) | Rapid PBCH (physical broadcast channel) decoding method for LTE (long term evolution) | |
| US20130007568A1 (en) | Error correcting code decoding device, error correcting code decoding method and error correcting code decoding program | |
| CN107659318B (en) | Self-adaptive polar code decoding method | |
| US8429509B2 (en) | Apparatus and method for determining reliability of decoded data in communication system | |
| US8031792B2 (en) | Metrics calculations utilising pre-stored values | |
| US20100146371A1 (en) | Modified Turbo-Decoding Message-Passing Algorithm for Low-Density Parity Check Codes | |
| CN116633483A (en) | Regular variable node degree fountain coding method | |
| CN102832954A (en) | Turbo code iterative decoding stopping method based on soft information average minimum value | |
| CN113660064B (en) | Multi-data packet-based joint two-dimensional interleaving coding method suitable for power line communication system | |
| CN106603087B (en) | Based on the fountain codes increment decoding algorithm that can translate collection under a kind of wireless channel | |
| CN113965292B (en) | Low-complexity polarization code SC decoding method based on aggregation structure | |
| CN116418395A (en) | Relay laser communication coding method for FSO system | |
| CN112087285B (en) | Polarization code bit reversal decoding method based on code distance and polarization channel reliability | |
| JP2002026879A (en) | Data error correction system | |
| US20210203362A1 (en) | Method of interleaved polar codes and interleaved polar encoder used therein | |
| CN109245858B (en) | Improved joint network-Turbo coding method based on decoding forwarding | |
| CN117614547B (en) | Delay serial cascade pulse position modulation system, method and deep space optical communication system | |
| CN113141232B (en) | Rate-free IoT uplink transmission system and method based on 16QAM modulation |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |