Deflatable set-oriented rateless coding degree distribution design method

Abstract

The invention discloses a translatable set-oriented rateless coding degree distribution design method, which relates to the technical field of error correction code coding and decoding in communication, and comprises the following steps: S100, calculating a translatable set; s200, determining a selected interpretable set; s300, constructing a degree distribution explicit expression; and S400, determining the maximum degree value of the optimal degree distribution. According to the method, the decoding success rate is improved, the block error rate is reduced, the coding and decoding complexity is low, the application range of the code length is large, the obvious advantages compared with the prior art are shown, and a more efficient and reliable solution is provided for practical application.

Description

Technical Field

[0001] The present invention relates to the technical field of error correction code encoding and decoding in communication, and in particular to a method for designing rateless coding degree distribution guided by a translatable set. Background Art

[0002] Rateless coding is a popular forward error correction (FEC) code in reliable communication over erasure channels. Rateless coding was first proposed by Byers et al. in 1998 as a new broadcast protocol, and subsequently attracted great attention in digital video broadcasting and cellular mobile communications. Compared with fixed-rate coding such as Turbo codes and low-density parity check (LDPC) codes, rateless coding has no fixed rate, which means that the input symbol can generate any number of coded symbols, and the decoder can recover the input symbol from enough coded symbols, which makes rateless coding have unique advantages in certain transmission scenarios. For example, in the coding design of data packet transmission on the network, the transmission channel can be abstracted as a binary erasure channel (BEC). The erasure rate is difficult to obtain for the sender and receiver. However, the erasure rate needs to be accurately estimated when designing the coding parameters. When using fixed coding, if the erasure rate of the channel changes frequently and transiently, the error correction performance of the coding will be greatly reduced due to the inaccurate channel estimation. Designing codes based on a predetermined worst-case scenario is a common solution, but this leads to unnecessary overhead. Rateless coding is suitable for packet transmission over BECs with unknown erasure rates. In addition, rateless coding requires very little feedback, making it more attractive in feedback-constrained applications. Based on the above advantages, rateless codes are also used in in-vehicle communications, storage systems, wireless sensor networks, distributed computing, industrial cloud control systems, and other fields.

[0003] The LT codes (Luby Transform codes) proposed by Luby are the first practical implementation of rateless coding. The design of LT codes is based on the classic ball-box model, and the analysis of the confidence propagation decoding of LT codes uses the density evolution method introduced by Luby, which is called tree analysis. Both are asymptotic with respect to code length and are inaccurate for finite code lengths. Therefore, LT codes cannot provide good performance under finite code lengths. Especially for short code applications, the efficiency of LT codes is significantly reduced, including overhead and block error rate (BLER).

[0004] In the existing analysis, the state generating function of the degree distribution of each step of the decoding process has been derived to analyze the performance of LT codes with finite code length. In addition, a closed expression for the expectation of the translatable set size is given, which has a wide range of applications in degree distribution optimization. Ghid et al. generalized the analysis results of finite code length and gave an analytical expression for the variance of the translatable set size. However, finite code length inevitably reduces the coding gain or increases the lower bound of the bit error rate of the coding. Designing a rateless code with good performance under finite code length to improve the efficiency and reliability of data transmission is still an open problem that needs further study.

[0005] The rateless coding process is to input symbols SC = {s i |i=1,2,...,k} generates the check code symbol EC={e i |i=1,2,3,...,n}. During the encoding process, the encoder will randomly select d input symbols for XOR encoding, where the degree value d is generated by the degree distribution function Ω(x). Therefore, the degree distribution function has a crucial impact on the performance of rateless coding. However, the existing commonly used degree distributions, such as Robust Soliton distribution (RSD), Poisson Robust Soliton Distribution (PRSD) and Modified Robust Soliton Distribution (MRSD), have a limited range of code length applications, and the improvement of decoding success rate or block error rate performance under limited code length is not satisfactory. In addition, most research results lack theoretical explanations from the coding perspective.

[0006] Therefore, those skilled in the art are committed to developing a method for designing rate-free coding degree distribution that is translatable set-oriented. Summary of the invention

[0007] In view of the above-mentioned defects of the prior art, the technical problem to be solved by the present invention is how to improve the decoding success rate and block error rate performance under limited code length.

[0008] In a communication system, the encoder at the transmitting end encodes the input symbols to form coded symbols. After the coded symbols are transmitted, the decoder at the receiving end decodes the input symbols to complete the communication. The process of belief propagation (BP) decoding depends on the translatable set. The translatable set is represented by R(L), which is the set of input symbols connected to the coded symbols with a degree value of 1. The input symbol is the original symbol before encoding, and the coded symbol is the symbol generated after rateless encoding. Each restored input symbol is called a step in the decoding process. In each step of decoding, the input symbol in the translatable set is restored, and then the input symbol is removed from all the coded symbols connected to it. This removal may cause the degree value of the coded symbol to be reduced to 1, thereby adding the input symbols adjacent to it to the translatable set, that is, the release of the coded symbol.

[0009] The present application designs a translatable set evolution based on the probability of releasing coding symbols (hereinafter referred to as translatable set evolution). The beginning of decoding is taken as the starting point, and the probability of the degree value being 1 in the degree distribution is adjusted by selecting an initial value. The initial value is the square root of the code length (the length of the input symbol) multiplied by a constant of 1.0 to 2.0. In actual simulations, it is relatively rare for the decoding process to release 3 or more coding symbols, so the present application considers the release of two coding symbols, that is, each step of the decoding process considers the release of 1 or 3 coding symbols. Specifically, the probability of releasing 0 coding symbols in each step of the decoding process is p 0 , the probability of releasing 1 coded symbol is p 1 , the probability of releasing 2 coded symbols is p 2 , the probability of releasing 3 coded symbols is p 3 Initialize p 0 =0.5, p 2 =0.5, p 1 =0, p 3 = 0. Then increase p 1 and p 3 , and let p 0 =0.5-p 1 -p 3 By increasing the mean value of the translatable set and reducing the variance of the translatable set, the optimal p 1 , p 3 . Mapping the translatable set to a degree distribution, that is, given a translatable set, achieving the corresponding degree distribution, the obtained degree distribution is called the translatable set-oriented rateless coding degree distribution.

[0010] In one embodiment of the present invention, a method for designing rateless coding degree distribution guided by a translatable set is provided, comprising:

[0011] S100, calculate the translatable set, and release probability p for different coding symbols 1 and p3 , and calculate the translatable set;

[0012] S200, determine the selected translatable set, calculate the mean and variance of the translatable set, determine the objective function, and determine the optimal coding symbol release probability p 1 and p 3 , and determine the selected translatable set;

[0013] S300, constructing an explicit expression of degree distribution, obtaining the number of coded symbols released in each step of the decoding process from the selected translatable set, calculating the explicit expression of degree distribution corresponding to the selected translatable set, and designing the maximum degree value of the degree distribution;

[0014] S400, determining the maximum degree value of the optimal degree distribution, calculating the theoretical value of the decoding failure probability under different maximum degree values, and determining the maximum degree value of the optimal degree distribution.

[0015] Optionally, in the translatable set-oriented rateless coding degree distribution design method in the above embodiment, step S100 includes:

[0016] S110, determine the coding symbol release probability p 1 and p 3 The value of (p 1 ,p 3 ) is defined as:

[0017] dom(p 1 ,p 3 )={(p 1 ,p 3 )|0≤p 1 ≤0.5,0≤p 3 ≤0.5,p 1 +p 3 ≤0.5},

[0018] (p 1 ,p 3 ) points are discretized, that is, p 1 and p 3 is a pair of discrete data points that increases with a fixed step size starting from 0;

[0019] S120, calculate the translatable set, for (p 1 ,p 3 ) points, and calculate the corresponding translatable set:

[0020] Let the initial value c is a non-negative constant ranging from 1.0 to 2.0, and k is the code length;

[0021] Use the following recursive formula:

[0022] R(L-1)=R(L)+Δ L ,

[0023] Where Δ L =p 1 +3p 3 -(p 1 +3p 3 +1)p r,L-1 , L is the number of undecoded input symbols. As decoding proceeds, L gradually decreases from the code length k to 0. L is the change in the size of the translatable set when L input symbols are not translated during the decoding process, p r,L-1 It is the probability that the released coded symbol is already in the translatable set when there are L input symbols not translated during the decoding process, that is, the probability that the released coded symbol is redundant. The translatable set R(L) is calculated by the recursive formula, 0≤L≤k;

[0024] S130, storing the probability of releasing the coding symbol, storing (p 1 ,p 3 ) points and the corresponding translatable sets.

[0025] Preferably, in the translatable set-oriented rateless coding degree distribution design method in the above embodiment, the fixed step size in step S110 is 0.05.

[0026] Preferably, in the translatable set-oriented rateless coding degree distribution design method in the above embodiment, c in step S120 is 1.3.

[0027] Optionally, in the translatable set-oriented rateless coding degree distribution design method in the above embodiment, step S200 includes:

[0028] S210, calculate the average value of the translatable set, for each (p 1 ,p 3 ) points, calculate the average value of the translatable set, the formula is as follows:

[0029]

[0030] Where M is the average value of the translatable set;

[0031] S220, calculate the variance of the translatable set, for each (p 1 ,p 3 ) points, calculate the variance of the translatable set, the formula is as follows:

[0032]

[0033] Where V is the variance of the translatable set;

[0034] S230, determine the objective function. To increase the average value of the translatable set and reduce the variance of the translatable set, the objective function used is as follows:

[0035]

[0036] Where α is a non-negative constant, ranging from 0.1 to 10, M i and V i Each (p 1 ,p 3 ) point pair values, and calculate the mean and variance of the translatable set under each (p 1 ,p 3 ) The objective function of the point pair ψ i , ψ i The largest value (p 1 ,p 3 ) point pair as the optimal (p 1 ,p 3 );

[0037] S240, determine the selected translatable set, and select the optimal (p 1 ,p 3 ) is determined as the selected translatable set.

[0038] Preferably, in the translatable set-oriented rateless coding degree distribution design method in the above embodiment, α in step S230 is 2.5.

[0039] Optionally, in the translatable set-oriented rateless coding degree distribution design method in any of the above embodiments, step S300 includes:

[0040] S310, calculate the number of coded symbols at the start time of decoding, use d to represent the different degree values, 1≤d≤k, use the proportion to represent the number of coded symbols with a degree value of d, when d=1, calculate the proportion τ(d) that has not been normalized, the formula is as follows:

[0041]

[0042] S320, determine the proportion of each degree value, and take the maximum degree value D as an integer. When 2≤d≤D-1, the calculation process of the proportion of each degree value is as follows:

[0043] For each k-D+1≤L≤k, calculate Q(L)=R(L)-R(L+1)+1;

[0044] For each 2≤d≤D-1, calculate in L is the number of undecoded input symbols, Q(L) represents the number of released coded symbols when L input symbols are undecoded during the decoding process, and ρ(d) represents the ideal solitary wave distribution;

[0045] S330, determine the proportion of the maximum degree value in the degree distribution, when d=D:

[0046]

[0047] Where δ is a non-negative constant, ranging from 0.01 to 0.5;

[0048] S340, normalization processing, normalizing the proportion τ(d) that has not been normalized when d=1, and obtaining an explicit expression of the degree distribution:

[0049]

[0050] where Ω(d) is an explicit expression for the degree distribution.

[0051] Preferably, in the translatable set-oriented rateless coding degree distribution design method in the above embodiment, δ in step S330 is 0.1.

[0052] Optionally, in the translatable set-oriented rateless coding degree distribution design method in any of the above embodiments, step S400 includes:

[0053] S410, set the lower bound and upper bound of the maximum value, and set the lower bound of the maximum value to The value to round down Set the upper bound of the maximum degree value to k;

[0054] S420, calculate the theoretical value of decoding failure probability, Each maximum value in Ω D Denotes the degree distribution with different maximum degree values, and calculates the theoretical value of the decoding failure probability P according to the explicit expression Ω(d) of the degree distribution err (Ω D );

[0055] S430, determine the maximum value of the optimal degree distribution, and select the theoretical value of the probability of decoding failure P err (Ω D )The smallest maximum degree value is taken as the maximum degree value of the optimal degree distribution.

[0056] Preferably, in the translatable set-oriented rateless coding degree distribution design method in the above embodiment, the lower bound of the maximum degree value in step S410 is set to The value rounded down is 13.

[0057] Preferably, in the translatable set-oriented rateless coding degree distribution design method in the above embodiment, the upper limit of the maximum degree value in step S410 is set to k=100.

[0058] Optionally, in the translatable set-oriented rateless coding degree distribution design method in the above embodiment, step S420 includes:

[0059] S421, determine the initial value, the formula of the initial value is as follows:

[0060] p k+1 =Ω 1 ,P k+1 (x,y)=x n

[0061] Where n is an integer greater than the code length k, p k+1 is the state generating function P of the degree distribution L The parameter P in the recursive formula of (x,y) L The initial value of P k+1 The state generating function P of the (x,y) degree distribution L Initial value of (x,y), Ω 1 is the value of Ω(d) in the explicit expression of degree distribution when d=1, that is, Ω(1), x, y are the independent variable parameters in the state generating function of the degree distribution of the decoding process, and their values ​​are all real numbers;

[0062] S422, obtain the theoretical value of the probability of decoding failure, and calculate the state generation function P of the degree distribution of each step of the decoding process according to the recursive formula of the state generation function of the degree distribution L (x, y), thereby obtaining the theoretical value of decoding failure probability P err (Ω D ):

[0063]

[0064] Among them, Ω D Refers to the degree distribution of different maximum degree values, P L (1,1) is P L (x,y), both x and y are 1.

[0065] Furthermore, in the translatable set-oriented rateless coding degree distribution design method in the above embodiment, in step S421, n is 1.1 to 1.3 times the value of k.

[0066] Furthermore, in the translatable set-oriented rateless coding degree distribution design method in the above embodiment, the state generation function P of the degree distribution in step S4221 is L The (x,y) formula is as follows:

[0067]

[0068] Where R is the number of coded symbols whose value is 1 when L input symbols are not decoded, C is the number of coded symbols whose value is strictly greater than 1 when L input symbols are not decoded, L is the number of input symbols that are not decoded during the decoding process (i.e., it is a representation of the decoding process), and p C,R,L It is the probability that when L input symbols are not decoded, the number of coded symbols with a degree value of 1 is R, and the number of coded symbols with a degree value strictly greater than 1 is C.

[0069] Furthermore, in the translatable set-oriented rateless coding degree distribution design method in the above embodiment, the state generation function recursive formula of the degree distribution in step S422 is as follows:

[0070]

[0071] where p L for:

[0072]

[0073] Where [] indicates the number of permutations.

[0074] The present invention is based on the evolution of a translatable set. In each step of the decoding process of multiple coding symbols, one or three coding symbols are released, an initial translatable set is set, and the derivation is performed with the beginning of decoding as the starting point. A translatable set-oriented rateless coding degree distribution design method is proposed, which improves the decoding success rate, reduces the block error rate, has a low encoding and decoding complexity, and has a wide range of application of the code length. It shows obvious advantages over the existing technology and provides a more efficient and reliable solution for practical applications.

[0075] The concept, specific structure and technical effects of the present invention will be further described below in conjunction with the accompanying drawings to fully understand the purpose, characteristics and effects of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 is a flow chart illustrating a translatable set-oriented rateless coding degree distribution design method according to an exemplary embodiment;

[0077] Figure 2 is a diagram illustrating a comparison of the decoding success rate between the translatable set-oriented rateless coding degree distribution design method according to an exemplary embodiment and the prior art;

[0078] Figure 3 is a diagram illustrating a comparison of a translatable set-oriented rateless coding degree distribution design method according to an exemplary embodiment and the prior art in terms of decoding block error rate (BLER);

[0079] Figure 4 3 is a diagram illustrating a comparison of the block error rate (BLER) of the translatable set-oriented rateless coding degree distribution design method according to an exemplary embodiment when the code length k=1024 and the robust soliton distribution (RSD) at different parameters (c and δ). DETAILED DESCRIPTION

[0080] The following describes several preferred embodiments of the present invention with reference to the drawings in the specification, so that the technical content is clearer and easier to understand. The present invention can be embodied in many different forms of embodiments, and the protection scope of the present invention is not limited to the embodiments mentioned in the text.

[0081] In the drawings, components with the same structure are indicated by the same numerical reference numerals, and components with similar structures or functions are indicated by similar numerical reference numerals. The size and thickness of each component shown in the drawings are arbitrarily shown, and the present invention does not limit the size and thickness of each component. In order to make the illustration clearer, the thickness of the components is schematically exaggerated in some places in the drawings.

[0082] The inventors have designed a translatable set-oriented rateless coding degree distribution design method, such as Figure 1 As shown, including:

[0083] S100, calculate the translatable set, and release probability p for different coding symbols 1 and p 3 The value of is used to calculate the translatable set; specifically, it includes:

[0084] S110, determine the coding symbol release probability p 1 and p 3 The value of (p 1 ,p 3 ) is defined as:

[0086] dom(p 1 ,p 3 )={(p 1 ,p 3 )|0≤p 1 ≤0.5,0≤p 3 ≤0.5,p 1 +p 3 ≤0.5},

[0087] (p 1 ,p 3 ) points are discretized, that is, p 1 and p 3 is a pair of discrete data points that starts from 0 and increases with a fixed step size of 0.05;

[0088] S120, calculate the translatable set, for (p 1 ,p 3) points, and calculate the corresponding translatable set:

[0089] Let the initial value c is a non-negative constant, c=1.3, k is the code length, k=100;

[0090] Use the following recursive formula:

[0091] R(L-1)=R(L)+Δ L ,

[0092] Among them, Δ L =p 1 +3p 3 -(p 1 +3p 3 +1)p r,L-1 ,

[0093] L is the number of undecoded input symbols. As decoding proceeds, L gradually decreases from the code length k to 0. L is the change in the size of the translatable set when L input symbols are not translated during the decoding process, p r,L-1 is the probability that the released coded symbol is already in the translatable set when there are L input symbols left untranslated during the decoding process, that is, the release probability of the coded symbol

[0094] is the probability of redundancy; the translatable set R(L) is calculated by the recursive formula, 0≤L≤k;

[0095] S130, storing the probability of releasing the coding symbol, storing (p 1 ,p 3 ) points and the corresponding translatable sets.

[0096] S200, determine the selected translatable set, calculate the mean and variance of the translatable set, determine the objective function, and determine the optimal coding symbol release probability p 1 and p 3 , and determine the selected translatable set; specifically including:

[0097] S210, calculate the average value of the translatable set, for each (p 1 ,p 3 ) points, calculate the average value of the translatable set, the formula is as follows:

[0098]

[0099] Where M is the average value of the translatable set;

[0100] S220, calculate the variance of the translatable set R(L), for each (p 1 ,p 3 ) points, calculate the variance of the translatable set, the formula is as follows:

[0101]

[0102] Where V is the variance of the translatable set;

[0103] S230, determine the objective function. To increase the average value of the translatable set and reduce the variance of the translatable set, the objective function used is as follows:

[0104]

[0105] Where α is a non-negative constant, α = 2.5, M i and V i Each (p 1 ,p 3 ) point pair values, and calculate the mean and variance of the translatable set under each (p 1 ,p 3 ) The objective function of the point pair ψ i , ψ i The largest value (p 1 ,p 3 ) point pair as the optimal (p 1 ,p 3 ); Table 1 shows each pair (p 1 ,p 3 ) i Values, of which there are 4 pairs (p 1 ,p 3 ) i The maximum values ​​are (0.05, 0.15), (0.20, 0.10), (0.35, 0.05), (0.50, 0.00), so we take this as (p 1 ,p 3 ) values, these four pairs (p 1 ,p 3 ) is consistent with the translatable set curve.

[0106] Table 1

[0107]

[0108]

[0109] S240, determine the selected translatable set, and select the optimal (p 1 ,p 3 ) is determined as the selected translatable set.

[0110] S300, constructing an explicit expression of degree distribution, obtaining the number of coded symbols released in each step of the decoding process from the selected translatable set, calculating the explicit expression of degree distribution corresponding to the selected translatable set, and designing the maximum degree value of the degree distribution; specifically including:

[0111] S310, calculate the number of coded symbols at the start time of decoding, use d to represent the different degree values, 1≤d≤k, use the proportion to represent the number of coded symbols with a degree value of d, when d=1, calculate the proportion τ(d) that has not been normalized, the formula is as follows:

[0112]

[0113] S320, determine the proportion of each degree value, and take the maximum degree value D as an integer. When 2≤d≤D-1, the calculation process of the proportion of each degree value is as follows:

[0114] For each k-D+1≤L≤k, calculate Q(L)=R(L)-R(L+1)+1;

[0115] For each 2≤d≤D-1, calculate

[0116] in L is the number of undecoded input symbols, Q(L) represents the number of released coded symbols when L input symbols are undecoded during the decoding process, and ρ(d) represents the ideal solitary wave distribution;

[0117] S330, determine the proportion of the maximum degree value in the degree distribution, when d=D:

[0118]

[0119] Where δ is a non-negative constant, δ = 0.1;

[0120] S340, normalization processing, normalizing the proportion τ(d) that has not been normalized when d=1, and obtaining an explicit expression of the degree distribution:

[0121]

[0122] where Ω(d) is an explicit expression for the degree distribution.

[0123] S400, determining the maximum degree value of the optimal degree distribution, calculating the theoretical value of the decoding failure probability under different maximum degree values ​​D, and determining the maximum degree value of the optimal degree distribution; specifically including:

[0124] S410, set the lower bound and upper bound of the maximum value, and set the lower bound of the maximum value to

[0125] The value to round down Set the upper bound of the maximum degree value to k = 100;

[0126] S420, calculate the theoretical value of decoding failure probability, (i.e., each maximum value in [13,100]) is expressed as Ω D Denotes the degree distribution with different maximum degree values, and calculates the theoretical value of the decoding failure probability P according to the explicit expression Ω(d) of the degree distribution err (Ω D ); specifically including:

[0127] S421, determine the initial value, the formula of the initial value is as follows:

[0128] p k+1 =Ω 1 ,P k+1 (x,y)=x n

[0129] Where n is an integer greater than the code length k, n is 1.2 times the value of k, p k+1 is the state generating function P of the degree distribution L The parameter P in the recursive formula of (x,y) L The initial value of P k+1 The state generating function P of the (x,y) degree distribution L Initial value of (x,y), Ω 1 is the value of Ω(d) in the explicit expression of degree distribution when d=1, that is, Ω(1), x, y are the independent variable parameters in the state generating function of the degree distribution of the decoding process, and their values ​​are all real numbers;

[0130] S422, obtain the theoretical value of decoding failure probability, and generate a recursive formula based on the state of the degree distribution function, as follows:

[0131]

[0132] where p L for:

[0133]

[0134] Where [] indicates the number of permutations;

[0135] Calculate the state generation function P of the degree distribution of each step in the decoding process L (x,y), the formula is as follows:

[0136]

[0137] Where R is the number of coded symbols whose value is 1 when L input symbols are not decoded, C is the number of coded symbols whose value is strictly greater than 1 when L input symbols are not decoded, L is the number of input symbols that are not decoded during the decoding process (i.e., it is a representation of the decoding process), and p C,R,Lis the probability that when L input symbols are not decoded, the number of coded symbols with a degree value of 1 is R, and the number of coded symbols with a degree value strictly greater than 1 is C;

[0138] Get the theoretical value of decoding failure probability P err (Ω D ), the formula is as follows:

[0139]

[0140] Among them, Ω D Refers to the degree distribution of different maximum degree values, P L (1,1) is P L (x,y), both x and y are 1.

[0141] S430, determine the maximum value of the optimal degree distribution, and select the theoretical value of the probability of decoding failure P err (Ω D )The smallest maximum degree value is taken as the maximum degree value of the optimal degree distribution. After calculation, the maximum degree value of the optimal degree distribution is 36.

[0142] Table 2 shows the degree distribution Ω D (d) The final result.

[0143] Table 2

[0144]

[0145]

[0146]

[0147] When the code length k = 100, the applicant uses the technical solution of the present application, the translatable set-oriented rateless coding degree distribution (RODD) design method, to compare with several existing technologies, namely, the robust solitary wave distribution (RSD), the modified robust solitary wave distribution (MRSD), and the Poisson robust solitary wave distribution (PRSD) in terms of decoding success rate and decoding block error rate (BLER). Figure 2 and Figure 3 shown.

[0148] Figure 2 This is a comparison chart of the decoding success rate between the present application and the prior art. The horizontal axis Overhead is the overhead, which means the ratio of the difference between the number of coded symbols and the number of input symbols to the number of input symbols: (nk) / k, which is an important indicator for measuring coding efficiency. The vertical axis Decoding success rate is the decoding success rate, that is, the probability that all input symbols are successfully decoded. Figure 2 It can be seen that the decoding success rate of the present application (RODD) is higher than that of the robust solitary wave distribution (RSD), the modified robust solitary wave distribution (MRSD) and the Poisson robust solitary wave distribution (PRSD).

[0149] Figure 3 The block error rate (BLER) of the present application and the prior art is compared. The block error rate (BLER) is the probability of decoding error of each input symbol. Figure 3 It can be seen that the degree distribution of the present application (RODD) is lower than other prior arts when Overhead≤0.6, and lower than the robust solitary wave distribution (RSD) and the Poisson robust solitary wave distribution (PRSD) when Overhead>0.5. In addition, the average degree value of the present application (RODD) is 6.1355, which is lower than the average degree value of RSD 8.2059 and the average degree value of MRSD 6.6575, and the computational complexity of encoding and decoding is lower than the robust solitary wave distribution (RSD) and the modified robust solitary wave distribution (MRSD).

[0150] In order to verify the advantage of the wide application range of the code length of the present application, when the code length k = 1024, the applicant uses the technical solution of the present application---the translatable set-oriented rateless coding degree distribution (RODD) design method and the prior art---the robust solitary wave distribution (RSD) to compare the decoding block error rate (BLER) with different parameters (c and δ), such as Figure 4 As shown in the figure, each color of the RSD curve cluster represents the simulation results when the parameter δ takes values ​​of 0.5, 1.0, 1.5, 2.0, 3.0, 4.0, and 5.0 respectively under different parameters c (c = 0.01, c = 0.03, c = 0.05, c = 0.07, and c = 0.09). Figure 4 It can be seen that the block error rate (BLER) of the present application (RODD) is lower than the robust solitary distribution (RSD) under various parameters.

[0151] It can be seen from the above-mentioned effect verification that the present application improves the decoding success rate, reduces the block error rate, has a wide range of applicable code lengths, and shows obvious advantages over the prior art.

[0152] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A method for designing rateless coding degree distribution based on a translatable set, characterized in that: The steps include: S100, calculating a translatable set, and calculating a translatable set for different values ​​of the coding symbol release probabilities p1 and p3; S200, determining a selected translatable set, calculating the mean value and variance of the translatable set, determining an objective function, determining optimal coding symbol release probabilities p1 and p3, and determining a selected translatable set; S300, constructing an explicit expression of degree distribution, obtaining the number of coded symbols released in each step of the decoding process from the selected translatable set, calculating the explicit expression of degree distribution corresponding to the selected translatable set, and designing the maximum degree value of the degree distribution; S400, determining the maximum degree value of the optimal degree distribution, calculating the theoretical value of the decoding failure probability under different maximum degree values, and determining the maximum degree value of the optimal degree distribution.

2. The translatable set-oriented rateless coding degree distribution design method according to claim 1, characterized in that: The step S100 includes: S110, determining the values ​​of the coding symbol release probabilities p1 and p3, the domain of (p1, p3) is: dom(p1,p3)={(p1,p3)|0≤p1≤0.5,0≤p3≤0.5,p1+p3≤0.5}, The (p1, p3) point pair is discretized, that is, p1 and p3 are discrete data point pairs that increase with a fixed step size starting from 0; S120, calculating the translatable set. For the point pair (p1, p3), calculate the corresponding translatable set: Let the initial value c is a non-negative constant ranging from 1.0 to 2.0, and k is the code length; the following recursive formula is used: R(L-1)=R(L)+Δ L ; S130, storing the coding symbol release probability, storing the (p1, p3) point and the corresponding translatable set.

3. The translatable set-oriented rateless coding degree distribution design method according to claim 2, characterized in that: The fixed step size in step S110 is 0.

05.

4. The translatable set-oriented rateless coding degree distribution design method according to claim 3, characterized in that: In step S120 , c=1.

3.

5. The translatable set-oriented rateless coding degree distribution design method according to claim 1, characterized in that: The S200 includes: S210, calculating the average value of the translatable set, for each (p1, p3) point pair, calculating the average value of the translatable set, the formula is as follows: S220, calculating the variance of the translatable set. For each (p1, p3) point pair, the variance of the translatable set is calculated using the following formula: S230, determining an objective function. To increase the average value of the translatable set and reduce the variance of the translatable set, the objective function is as follows: Calculate the objective function ψ of each (p1, p3) point pair in turn i , ψ i The point pair (p1, p3) with the largest value is regarded as the optimal (p1, p3); S240: Determine a selected translatable set, and determine the translatable set corresponding to the optimal (p1, p3) as the selected translatable set.

6. The translatable set-oriented rateless coding degree distribution design method according to claim 5, characterized in that: In the step S230 , α=2.

5.

7. The translatable set-oriented rateless coding degree distribution design method according to claim 1, characterized in that: The step S300 includes: S310, calculate the number of coded symbols at the start time of decoding, use d to represent the different degree values, 1≤d≤k, and the proportion represents the number of coded symbols with a degree value of d. When d=1, calculate the proportion τ(d) that has not been normalized, and the formula is as follows: S320, determine the proportion of each degree value, and take the maximum degree value D as an integer. When 2≤d≤D-1, the calculation process of the proportion of each degree value is as follows: For each k-D+1≤L≤k, calculate Q(L)=R(L)-R(L+1)+1; S330, determine the proportion of the maximum degree value in the degree distribution, when d=D: S340, normalization processing, normalizing the proportion τ(d) that has not been normalized when d=1, and obtaining an explicit expression of the degree distribution:

8. The translatable set-oriented rateless coding degree distribution design method according to claim 7, characterized in that: In the step S330, δ=0.

1.

9. The translatable set-oriented rateless coding degree distribution design method according to claim 1, characterized in that: The step S400 includes: S410, setting the lower bound and upper bound of the maximum value, setting the lower bound of the maximum value to The value to round down Setting the upper bound of the maximum degree value to k; S420, calculate the theoretical value of decoding failure probability, Each maximum value in Ω D Denotes the degree distribution with different maximum degree values, and the theoretical value of the decoding failure probability P is calculated according to the explicit expression Ω(d) of the degree distribution err (Ω D ); S430, determine the maximum value of the optimal degree distribution, and select the theoretical value of the decoding failure probability P err (Ω D )The smallest maximum degree value is taken as the maximum degree value of the optimal degree distribution.

10. The translatable set-oriented rateless coding degree distribution design method according to claim 9, characterized in that: The step S420 includes: S421, determine the initial value, the formula of the initial value is as follows: p k+1 =Ω1,P k+1 (x,y)=x n ; S422, obtain the theoretical value of the probability of decoding failure, and calculate the state generation function P of the degree distribution of each step of the decoding process according to the recursive formula of the state generation function of the degree distribution L (x, y), thereby obtaining the theoretical value of decoding failure probability P err (Ω D ):

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