CN108055108B - Encoding method of LT code - Google Patents
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Abstract
The divisional application relates to an encoding method of an LT code, which belongs to the field of satellite channel encoding and solves the problems that the complexity of encoding and decoding in the LT code is higher, and the decoding performance is obviously reduced when the number of input symbols is smaller, and the like, and has the technical key points that: dividing original data into k data packets according to equal length l; randomly selecting a degree d according to a truncated robust solitary wave fixed degree distribution function phi (d); d data packets are selected with medium probability in the k data packets; carrying out exclusive OR on the d selected data packets, and recording an operation result as a coding packet; and repeating the steps until the receiving end receives enough coded packets.
Description
The application is a divisional application with application number 2017105807665, application date 2017-07-17 and invention name 'algorithm and equipment for optimizing degree distribution in LT code'.
Technical Field
The invention belongs to the field of satellite channel coding, researches emerging digital fountain codes, and provides a new degree distribution optimization algorithm, namely a truncated Robust solution static distribution (C _ RSSD). The algorithm effectively improves the coding and decoding performance of the LT code in the fountain code.
Background
With the rapid development of information technology and the increasing abundance of information applications, people put higher and higher requirements on the quality and capacity of satellite communication systems, which directly pushes the development of satellite communication channel coding. The satellite link has the characteristics of being easily interfered by space environment, being long in time delay, being limited in bandwidth and the like, and influences the overall performance of the satellite communication system. To ensure the communication quality, it is necessary to use the corresponding channel coding under certain power conditions to achieve the purpose of error detection and error correction. Commonly used channel codes in satellite communications are: convolutional codes, RS codes, serial concatenated codes, Turbo codes, LDPC codes, fountain codes, and the like. The digital fountain code is a new forward error correcting code based on grouping, and has the characteristics of strong channel adaptability, low coding and decoding complexity and the like. In addition, the method does not need the characteristic of feedback, thereby avoiding the long time delay of the network caused by the long-time waiting of the feedback confirmation of the sending end, and particularly, under the condition that the transmission time delay of the satellite network is very large, the feedback retransmission mechanism can introduce larger time delay. Another important characteristic of the fountain code is that the fountain code has no rate, and the code rate can be adjusted at any time along with the change of the channel state to adapt to the change of the fountain code. The characteristic can make the satellite network transmission system fully utilize the channel capacity, effectively improve the problems of high error code and the like caused by the complexity and the changeability of the satellite channel, so that the fountain code has obvious advantages and very wide development prospect when being used as the satellite channel code.
At present, LT codes and Raptor codes are widely applied to fountain codes, wherein Raptor codes are generated by cascading traditional error correcting codes and LT codes, and are adopted by the MBMS standard of 3GPP at present. The research on digital fountain codes mainly includes degree distribution design, coding method design, decoding method design and the like, wherein degree distribution functions are directly related to the performance of the digital fountain codes and determine decoding success rate, decoding cost, coding and decoding complexity and the like, and the key point of designing the fountain codes lies in constructing proper degree distribution functions. The LT code may be described by the number of source input symbols, k, and a degree distribution, Ω (d), denoted LT (k, Ω (d)), which is a probability distribution (Ω) defined over an integer set {1,2, …, k }1,Ω1,…,Ωk) Wherein Ω isdRepresenting the probability of a coded symbol being encoded by d input symbols and resulting in one encoded symbol, it is also possible to use a generator polynomial to represent the degree distribution in the form of a generator polynomial, i.e. to represent the degree distribution in the form of a generator polynomial
Luby gives two common degree Distribution forms when proposing the design of LT codes, namely Ideal Soliton Distribution (ISD) and improved Robust Soliton Distribution (RSD) based on the Ideal Soliton Distribution (ISD). Theoretically, ISD distribution enables each code symbol to be released with the same probability in each decoding iteration, and only one code symbol with 1 degree exists in each iteration, and in practical work, the ISD distribution is easy to realize in decoding iterationThe decoding fails due to the lack of the coded symbol with the degree of 1. RSD degree distribution, which is currently the most commonly used degree distribution function, introduces 2 parameters to change the size of the translatable set value during decoding, which makes the decoding process more stable. However, the probability of the small value in the RSD degree distribution is small, and the decoding process may be interrupted; when RSD degree distribution coding is adopted, the average coding degree is increased along with the increase of the code length, so that the coding and decoding complexity is increased; meanwhile, when the code length is small, the decoding failure rate is high.
Disclosure of Invention
Aiming at the problems that the most practical robust soliton distribution has higher coding and decoding complexity in LT codes and obviously reduces decoding performance when the number of input symbols is small, a novel truncated robust soliton fixed degree distribution (C _ RSSD) is provided.
The technical scheme is as follows:
an algorithm for optimizing degree distribution in an LT code, comprising the steps of: combining the improved truncated robust solitary wave degree distribution with the adjusted fixity degree distribution and carrying out normalization processing to form a truncated robust solitary wave fixity degree distribution phi (d), wherein the expression is as follows:
wherein d is a value, α and β are proportionality coefficients, 0 is more than α and less than 1, and 0 is more than β and less than 1;
the adjusted fixing degree distribution expression:
Z(x)＝0.107174x+0.444213x2+0.149598x3+0.065381x4+0.074302x5+0.050452x8+0.033506x9+0.050031x19+0.022521x65+0.002822x66expression of the improved truncated RSD degree distribution:
μ (d): RSD degree distribution expression; d: maximum value of the truncation distribution.
Further, the improvement method for the fixity distribution comprises the following steps: the expression of the distribution of the degree of fixation is first noted as s (x), the probability values of the values other than the degree of 1 are all reduced by 10% of themselves, the reduced probability values are all assigned to the degree of 1, the sum of the probabilities of all the values in the distribution of the degree of fixation is equal to 0.999998, and the remaining 0.000002 is also assigned to the degree of 1 for the expression of the distribution of accuracy.
Further, the method for truncating the RSD degree distribution to obtain the truncated degree distribution expression is as follows:
1) comparing k/R with the maximum value d in the fixed degree distribution;
2) if k/R is larger than or equal to D, making D equal to k/R; if k/R is less than D, making D equal to D;
3) truncating the value of D > D in RSD degree distribution;
4) and carrying out normalization processing on the truncation degree distribution to obtain the truncation robust solitary wave degree distribution which is marked as C _ RSD.
The invention also relates to a device for optimizing degree distribution in LT codes, storing a plurality of instructions, which are loaded and executed by a processor:
combining the improved truncated robust solitary wave degree distribution with the adjusted fixity degree distribution and carrying out normalization processing to form a truncated robust solitary wave fixity degree distribution phi (d), wherein the expression is as follows:
wherein d is a value, α and β are proportionality coefficients, 0 is more than α and less than 1, and 0 is more than β and less than 1;
the adjusted fixing degree distribution expression:
Z(x)＝0.1113591x+0.49357x2+0.16622x3+0.002764x4+0.082558x5+0.056058x8+0.0037229x9+0.05559x19+0.025023x65+0.003135x66expression of the improved truncated RSD degree distribution:
wherein: μ (d) is the RSD degree distribution; d: maximum value of the truncation distribution.
Further, the improvement method for the fixity distribution comprises the following steps: the expression of the distribution of the degree of fixation is first noted as s (x), the probability values of the values other than the degree of 1 are all reduced by 10% of themselves, the reduced probability values are all assigned to the degree of 1, the sum of the probabilities of all the values in the distribution of the degree of fixation is equal to 0.999998, and the remaining 0.000002 is also assigned to the degree of 1 for the expression of the distribution of accuracy.
Further, the method for truncating the RSD degree distribution to obtain the truncated degree distribution expression is as follows:
1) comparing k/R with the maximum value d in the fixed degree distribution;
2) if k/R is larger than or equal to D, making D equal to k/R; if k/R is less than D, making D equal to D;
3) truncating the value of D > D in RSD degree distribution;
4) and carrying out normalization processing on the truncated RSD distribution to obtain a truncated RSD degree distribution which is marked as C _ RSD.
Has the advantages that: the invention uses the adjusted fixed degree distribution and the improved truncated RSD degree distribution, and combines the fixed degree distribution and the improved truncated RSD degree distribution as normalization processing, thereby increasing the probability of the small degree value, reducing the possibility of interruption in the decoding process, simultaneously reducing the average degree value of the degree distribution, reducing the overall redundant operation of decoding, reducing the complexity of coding and decoding and improving the performance of the coding and decoding.
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The invention is described in detail below with reference to the accompanying drawings;
FIG. 1 is a flow chart of an optimization degree distribution algorithm;
fig. 2 shows probability distribution diagrams of three degree distribution functions when k is 70, c is 0.05, and δ is 0.05;
fig. 3 k is a graph showing the relationship between the decoding success rate and the decoding overhead when encoding and decoding are performed respectively by using three degree distributions when the k is 500;
fig. 4 a process of encoding the LT code;
fig. 5 is a satellite network channel coding and transmission scheme based on concatenation of LT codes and LDPC codes.
Detailed Description
An algorithm for optimizing degree distribution in an LT code, comprising the steps of:
1. improvement of fixation distribution
The fixed degree distribution is one kind of degree distribution with strong practicability summarized by people in long-term engineering practice application, and is mainly suitable for LT codes with longer code length, and for LT codes with shorter code length, because the probability of the degree of 1 is smaller, the number of code packets with the degree of 1 is too small, so that the decoding is easy to fail. The fixed distribution is abbreviated as SD (Stationarydistribution), is denoted as S (x), and is expressed by a generator polynomial form as:
in the formula (1.1), SdThe probability value of degree d is represented. The fixation distribution is then adjusted: since the probability value of the height 1 needs to be reduced, the probability values of other values need to be reduced, in order to keep the probability distribution trend of the fixed degree distribution, the probability values of other values except the value with the degree of 1 are reduced by 10 percent of the probability values, and the reduced probability values are all endowed with the degree of 1. We know that the sum of probabilities for all values in one degree distribution function should be equal to 1, but to fix the sum of probabilities for all values in the degree distribution is equal to 0.999998, 0.000002 (residual probability value) is also assigned to degree 1 in order to get the exact probability distribution function. The modified fixing degree distribution (a _ SD), denoted as z (x), is expressed in the form of a generator polynomial:
the average value of the fixed degree distribution is 5.8703, the average value of the modified fixed degree distribution is 5.3833, and the average value is reduced, so that the calculation redundancy and the encoding and decoding complexity in the encoding and decoding process can be reduced, and the overall performance of the LT code is improved.
2. Truncating RSD degree distribution
(1) First we give an expression for the RSD degree distribution, denoted μ (d):
wherein the content of the first and second substances,
wherein k is the number of input symbols, d is a value, rho (d) is an ISD degree distribution function, tau (d) is an auxiliary function, c is a constant and c is more than 0 and less than 1; and delta is the probability of decoding failure allowed by the decoder to successfully recover all the original data packets when the decoder receives n code packets, and 0 < delta < 1.
(2) Truncating RSD degree distribution
It is known that the probability values for values of d > k/R are small, and the probability of selecting values greater than k/R in the code is small, so that appropriate truncation is applied. The method comprises the following specific steps:
1) comparing k/R with the maximum value d in the fixed degree distribution;
2) if k/R is larger than or equal to D, making D equal to k/R; if k/R is less than D, making D equal to D;
3) truncating the value of D > D in RSD degree distribution;
4) the truncated RSD distribution is normalized. Modified distribution of truncation (Chopped \ u)
The Robust SolitoDistribution, C _ RSD) is denoted as Ψ (d), and the expression is:
the maximum value of the modified truncation degree distribution is D, and the larger value is removed, so that the value of the average value is reduced, and the integral redundant operation of decoding is reduced, thereby reducing the complexity of coding and decoding and improving the performance of the coding and decoding. The improved truncated RSD degree distribution is the truncated robust solitary wave degree distribution, which is marked as C _ RSD in this embodiment, and is used in the present invention.
3. Merging of two degree distributions
Combining the C _ RSD degree distribution with the adjusted fixed degree distribution and carrying out normalization processing to form a new degree distribution, psi (d) represents the optimized degree distribution, and the expression is as follows:
(7) in the formula, Φ (d) represents an optimized degree distribution, and represents a probability that a coded data packet degree is d when the degree distribution is used for coding, and is denoted as truncated Robust Soliton stationary distribution (C _ RSSD), wherein α and β are proportionality coefficients, 0 < α < 1, and 0 < β < 1, and an optimal degree distribution function can be found by adjusting the proportionality coefficients according to requirements, Ψ (d) is a truncated degree distribution C _ RSD, and z (d) is an adjusted stationary degree distribution function, and the optimized degree distribution can combine advantages of the two degree distributions, as shown in fig. 1, a flow chart of an optimized degree distribution algorithm, and fig. 2 is a probability distribution chart of the Robust Soliton degree distribution, the stationary Soliton distribution and the truncated Soliton stationary distribution.
In contrast, a binary sequence with 0 or 1 is input, the parameters of C _ RSSD and RSD degree distributions are both C ═ 0.05, δ ═ 0.05, the scaling coefficients are α ═ 0.5, β ═ 0.5, Ψ (d) and z (d) have the same weight, table 1 shows the average values of RSD, SD and C _ RSSD degree distributions, and fig. 3 is a simulation diagram of the relationship between decoding success rate and decoding overhead when encoding and decoding are performed using the three degree distributions respectively when the number of input symbols k is 500.
TABLE 1 mean values of three degree distributions at different code lengths k
| Input symbol k | Mean value of RSD | Mean value of SD | Mean value of C _ RSSD |
| 200 | 9.3339 | 5.8703 | 6.9511 |
| 500 | 10.9507 | 5.8703 | 7.3728 |
| 1000 | 12.2258 | 5.8703 | 7.6948 |
The invention provides a new degree distribution algorithm for optimizing the degree distribution in the LT code, and introduces the application of the degree distribution in the LT code.
(1) Coding principle and function of degree distribution of LT code
Suppose the input original data packet is X ═ X1,x2…xk) The LT coded packet is Y ═ (Y)1,y2…yk) LT encoding Process as illustrated in FIG. 4The algorithm flow is shown as follows:
1) dividing original data into k data packets according to equal length l (completing the insufficient 0 supplementation);
2) randomly selecting a degree d according to a truncated robust solitary wave fixed degree distribution function phi (d), wherein a probability distribution diagram of C _ RSSD degree distribution is shown in a figure 2;
3) d data packets are selected with medium probability in the k data packets;
4) carrying out exclusive OR on the d selected data packets, and recording an operation result as a coding packet;
5) and repeating the steps 2), 3) and 4) until the receiving end receives enough coded packets.
(2) Decoding algorithm of LT code
Generally, a belief propagation coding algorithm (BP decoding algorithm for short) is used as a fountain code decoding algorithm, and the algorithm flow is as follows:
1) the decoder directly restores the coded symbol with the degree of 1, and if the coded symbol with the degree of 1 does not exist, the decoding fails;
2) carrying out XOR on the recovered code symbol and the neighbor connected with the recovered code symbol respectively, updating the code symbols of the neighbor, and removing the adjacent edges of the updated code symbols and the neighbor;
3) and repeating the steps 2) and 3) until all the original input symbols are recovered, and then successfully decoding.
It can be seen from the LT coding and decoding process that if the average value of the degree distribution function is high, the number of xor operations and iterations performed in the coding and decoding process is large, thereby greatly increasing the coding and decoding time and complexity. However, if the average value is low, the original data packet may not be completely covered, thereby causing decoding failure or requiring more decoding overhead. Therefore, the degree distribution function is directly related to the performance of the digital fountain code, and determines the decoding success rate, decoding cost, encoding and decoding complexity and the like, and the key point of constructing the proper degree distribution function is the fountain code.
The LT code and the LDPC code are cascaded to be used as channel coding of a satellite network, wherein degree distribution in the LT code adopts shortened robust soliton fixed degree distribution C _ RSSD. The application scheme in satellite network channel coding is shown in figure 5.
The above description is only for the purpose of creating a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can substitute or change the technical solution and the inventive concept of the present invention within the technical scope of the present invention.
Claims (3)
1. An encoding method of an LT code, characterized in that:
1) dividing original data into k data packets according to equal length l;
2) randomly selecting a degree d according to a truncated robust solitary wave fixed degree distribution function phi (d);
3) d data packets are selected with medium probability in the k data packets;
4) carrying out exclusive OR on the d selected data packets, and recording an operation result as a coding packet;
5) repeating the steps 2), 3) and 4) until the receiving end receives enough coding packets;
wherein: combining the improved truncated RSD degree distribution and the adjusted fixity degree distribution and carrying out normalization processing on the truncated robust soliton wave fixity degree distribution function phi (d) to form the truncated robust soliton wave fixity degree distribution phi (d), wherein the expression of the truncated robust soliton wave fixity degree distribution phi (d) is as follows:
α and β are proportionality coefficients, and 0 < α < 1, 0 < β < 1;
wherein:
the adjusted fixing degree distribution expression:
Z(d)＝0.107174d+0.444213d2+0.149598d3+0.065381d4+0.074302d5+0.050452d8+0.033506d9+0.050031d19+0.022521d65+0.002822d66
expression of the improved truncated RSD degree distribution:
μ (d): RSD degree distribution expression; d: maximum value of the truncation distribution.
2. The LT code encoding method according to claim 1, wherein: the method for adjusting the fixation degree distribution comprises the following steps: the probability values of the other values except the value with the degree of 1 are all reduced by 10 percent of the value, the reduced probability values are all assigned to the degree of 1, the sum of the probabilities of all the values in the fixed degree distribution is equal to 0.999998, the residual probability value of the sum of the probabilities of all the values in the fixed degree distribution function is added to the probability value of the degree of 1 in the fixed degree distribution, and the residual probability value is assigned to the degree of 1.
3. The LT code encoding method according to claim 1, wherein:
the expression of the RSD degree distribution is noted μ (d):
wherein:
rho (d) is an ISD degree distribution function, tau (d) is an auxiliary function, k is the number of input symbols, d is a value, c is a constant and is more than 0 and less than 1; and delta is the probability of decoding failure allowed by the decoder to successfully recover all the original data packets when the decoder receives n code packets, and 0 < delta < 1.
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| CN107994974A (en) | 2018-05-04 |
| CN107395326A (en) | 2017-11-24 |
| CN107395326B (en) | 2020-06-02 |
| CN108055108A (en) | 2018-05-18 |
| CN107994974B (en) | 2020-09-22 |
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