An interleaved LT coding method

Abstract

The present invention discloses an interleaved LT coding method, comprising the following steps: step 1), dividing the original data into k input groups; step 2), generating odd-numbered coding groups of the coding sequence based on the robust soliton distribution (RSD) function; step 3), generating even-numbered coding groups of the coding sequence based on the improved Poisson distribution (IPD) function; step 4), repeating steps 2) and 3) to generate a coding sequence and a coding matrix; and step 5), when the degree is k / R, replacing the coding groups generated by RSD coding with the coding groups at the corresponding positions, and replacing the coding matrix columns at the corresponding positions with "adjacent" relationships. Using this novel coding method for LT coding can effectively improve the error control performance of LT codes.

Description

Technical Field

[0001] The present invention belongs to the technical field of communication channel coding, and more specifically, relates to an interleaved encoding method (IEM). Background Art

[0002] Luby Transform (LT) code is the first specific implementation of digital fountain code, which has the characteristics of no feedback retransmission, no code rate, strong compatibility, and low encoding and decoding complexity. In 2002, Michael Luby formally published the encoding and decoding algorithm and degree distribution construction of LT code, and proposed the classic Robust Soliton Distribution (RSD). It can ensure that all input packets can be covered during the encoding process, and the number of encoded packets with degree 1 is always sufficient during the decoding process to prevent decoding interruption. Therefore, as the decoding overhead increases, RSD can eventually decode all the original data.

[0003] The Improved Poisson Distribution (IPD), proposed in 2016, generates more degree-1 code blocks. While this feature significantly reduces the probability of decoding failures in the early stages of decoding, excessive degree-1 code blocks can lead to inefficient decoding, resulting in weaker decoding performance than RSD when decoding overhead is high.

[0004] Many scholars and research institutions at home and abroad have conducted extensive research on the design and optimization of coding algorithms based on degree distribution characteristics to improve the error control performance of LT codes. Although existing coding optimization schemes have achieved certain research results, there is still room for improvement. Summary of the Invention

[0005] To further improve the error control performance of LT codes, the present invention proposes an interleaved encoding method (IEM). This method takes advantage of the high decoding success rate of IPD when the decoding overhead is small and the better decoding performance of RSD when the decoding overhead is increased. By organically combining the advantages of the two through interleaved coding, a new LT coding method is generated, which can effectively improve communication reliability.

[0006] The present invention adopts the following technical solutions:

[0007] An interleaved LT coding method comprises the following steps:

[0008] Step 1), divide the original data intok Input Groups S ={ S 1, S 2,..., S k}, k =1,2,3...;

[0009] Step 2), generating odd-bit coding groups of the coding sequence based on the robust soliton distribution RSD function;

[0010] Step 3), generating even-numbered bit coding groups of the coding sequence based on the improved Poisson distribution IPD function;

[0011] Step 4), repeat steps 2)-3), generate the coding sequence and encoding matrix ,in, For coding grouping, Corresponding to the coding group The "adjacency" relationship to the input group, n =1,2,3...;

[0012] Step 5), when the degree is k / R hour, R In order to obtain the number of coding groups with the expected degree of 1 in the decoding process, the coding group generated by RSD encoding replaces the coding group at the corresponding position, and the “adjacency” relationship replaces the coding matrix column at the corresponding position.

[0013] In the above scheme, step 2) of generating the odd-numbered bit coding group of the coding sequence based on the RSD function specifically includes the following steps:

[0014] Step 2-1), generate RSD function expression :

[0015]

[0016] in

[0017]

[0018]

[0019] In the formula, the number of coding groups with a degree of 1 is expected to remain constant during the decoding process. , is the number of input groups, is a positive constant, is the allowed probability of decoding failure, is the degree of each coding group, is the ideal soliton distribution (ISD).

[0020] Step 2-2), odd-numbered bits of the coding sequence are grouped Produced by the following steps:

[0021] (1) Randomly select a coding group from the RSD degree distribution degree d ;

[0022] (2) Randomly and uniformly select d Input Groups { S n1 , S n2 ,..., S nd} as "adjacency";

[0023] (3) This d "Adjacencies" are XORed to generate a coded group :

[0024] ;

[0025] Steps 2-3) The “adjacency” relationship is stored in the odd columns corresponding to the new encoding matrix, which can be expressed as:

[0026]

[0027] Among them, the column vector Corresponding to the coding group To input group The "adjacency" relationship is: .

[0028] In the above solution, step 3) of generating the even-numbered bit coding group of the coding sequence based on the IPD function specifically includes the following steps:

[0029] Step 3-1), generate IPD function expression :

[0030]

[0031] in

[0032]

[0033] Where, is the degree of each coding group, To enter the number of groups, usually select .

[0034] Step 3-2), the even-numbered bits of the coding sequence are grouped Produced by the following steps:

[0035] (1) Randomly select a coding group from the IPD degree distribution degree d ;

[0036] (2) Randomly and uniformly select d Input Groups As "adjacency";

[0037] (3) This d "Adjacencies" are XORed to generate a coded group :

[0038] .

[0039] Step 3-3), the "adjacency" relationship is stored in the even-numbered columns corresponding to the new encoding matrix, which can be expressed as:

[0040]

[0041] Among them, the column vector Corresponding to the coding group To input group The "adjacency" relationship is: .

[0042] In the above scheme, step 4) repeats steps 2) to 3) to generate a coding sequence and a coding matrix group, which specifically includes the following steps:

[0043] Repeat steps 2) to 3) to generate a new coding sequence, which can be expressed as:

[0044]

[0045] Generate a new encoding matrix, which can be expressed as:

[0046]

[0047] in, .

[0048] In the above scheme, the degree of step 5) is k / R When , the coding group generated by RSD encoding replaces the coding group at the corresponding position, and the "adjacent" relationship replaces the coding matrix column at the corresponding position, specifically including the following steps:

[0049] (1) When k / R ] is an odd number, the coding sequence and coding matrix remain unchanged;

[0050] (2) When k / R ] is an even number, the coding group generated by RSD encoding replaces the coding group at the corresponding position, and the "adjacent" relationship replaces the coding matrix column at the corresponding position.

[0051] Compared with the prior art, the present invention has the following beneficial effects:

[0052] The present invention utilizes the characteristics of IPD (high decoding success rate when decoding overhead is small) and RSD (better decoding performance when decoding overhead is increased), organically combines the advantages of the two through interleaving coding, and generates a new LT coding method. The use of this new method for LT coding can effectively improve the error control performance of LT codes. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 This is a diagram of the interleaved LT coding principle provided by the present invention.

[0054] Figure 2 yes When the decoding performance of the present invention, the RSD-based encoding method and the IPD-based encoding method are compared. DETAILED DESCRIPTION

[0055] The preferred embodiments are described in detail below in conjunction with the accompanying drawings. It should be emphasized that the following description is merely exemplary and is not intended to limit the scope of the present invention and its application.

[0056] See Figure 1 The present invention provides an interleaved LT coding method, comprising the following steps:

[0057] Step 1), divide the original data into k Input Groups S ={ S 1, S 2,..., S k}, k =1,2,3....

[0058] Step 2), generate RSD function expression :

[0059]

[0060] in

[0061]

[0062]

[0063] In the formula, the number of coding groups with a degree of 1 is expected to remain constant during the decoding process. , is the number of input groups, is a positive constant, is the allowed probability of decoding failure, is the degree of each coding group, is the ideal soliton degree distribution ISD.

[0064] Step 3), odd-numbered bits of the coding sequence are grouped Produced by the following steps:

[0065] (1) Randomly select a coding group from the RSD degree distribution degree d ;

[0066] (2) Randomly and uniformly select d Input Groups { S n1 , S n2 ,..., S nd} as "adjacency";

[0067] (3) This d "Adjacencies" are XORed to generate a coded group :

[0068] .

[0069] Step 4), the "adjacency" relationship is stored in the odd columns corresponding to the new encoding matrix, which can be expressed as:

[0070]

[0071] Among them, the column vector Corresponding to the coding group To input group The "adjacency" relationship is: .

[0072] Step 5), generate IPD function expression :

[0073]

[0074] in

[0075]

[0076] Where, is the degree of each coding group, To enter the number of groups, usually select .

[0077] Step 6), the even-numbered bits of the coding sequence are grouped Produced by the following steps:

[0078] (1) Randomly select a coding group from the IPD degree distribution degree d ;

[0079] (2) Randomly and uniformly select d Input Groups As "adjacency";

[0080] (3) This d "Adjacencies" are XORed to generate a coded group :

[0081] .

[0082] Step 7), the "adjacency" relationship is stored in the even columns corresponding to the new encoding matrix, which can be expressed as:

[0083]

[0084] Among them, the column vector Corresponding to the coding group To input group The "adjacency" relationship is: .

[0085] Step 8) Repeat steps 2) to 7) to generate a new coding sequence, which can be expressed as:

[0086]

[0087] Generate a new encoding matrix, which can be expressed as:

[0088]

[0089] in, .

[0090] Step 9), when the degree is k / R When , the coding group generated by RSD encoding replaces the coding group at the corresponding position, and the "adjacent" relationship replaces the coding matrix column at the corresponding position, specifically including the following steps:

[0091] (1) When k / R ] is an odd number, the coding sequence and coding matrix remain unchanged;

[0092] (2) When k / R ] is an even number, the coding group generated by RSD encoding replaces the coding group at the corresponding position, and the "adjacent" relationship replaces the coding matrix column at the corresponding position.

[0093] Specifically, in the present invention, , use IEM encoding method to perform 1000 LT encoding and decoding. Take this as an example to illustrate,

[0094] Step 1) LT encoding is performed using the IEM encoding method, including the following steps:

[0095] Step 1-1), divide the original data into k Input Groups S ={ S 1, S 2,..., S k}, k =1,2,3....

[0096] Step 1-2), generate RSD function expression :

[0097]

[0098] in

[0099]

[0100]

[0101] In the formula, the number of coding groups with a degree of 1 is expected to remain constant during the decoding process. , is the number of input groups, is a positive constant, is the allowed probability of decoding failure, is the degree of each coding group, is the ideal soliton degree distribution ISD.

[0102] Steps 1-3), odd-numbered bits of the coding sequence are grouped Produced by the following steps:

[0103] (1) Randomly select a coding group from the RSD degree distribution degree d ;

[0104] (2) Randomly and uniformly selectd Input Groups { S n1 , S n2 ,..., S nd} as "adjacency";

[0105] (3) This d "Adjacencies" are XORed to generate a coded group :

[0106] .

[0107] Steps 1-4) The "adjacency" relationship is stored in the odd columns corresponding to the new encoding matrix, which can be expressed as:

[0108]

[0109] Among them, the column vector Corresponding to the coding group To input group The "adjacency" relationship is: .

[0110] Steps 1-5), generate IPD function expression :

[0111]

[0112] in

[0113]

[0114] Where, is the degree of each coding group, To enter the number of groups, usually select .

[0115] Steps 1-6), the even-numbered bits of the coding sequence are grouped Produced by the following steps:

[0116] (1) Randomly select a coding group from the IPD degree distribution degree d ;

[0117] (2) Randomly and uniformly select d Input Groups As "adjacency";

[0118] (3) This d "Adjacencies" are XORed to generate a coded group :

[0119] .

[0120] Steps 1-7), the "adjacency" relationship is stored in the even columns corresponding to the new encoding matrix, which can be expressed as:

[0121]

[0122] Among them, the column vector Corresponding to the coding group To input group The "adjacency" relationship is: .

[0123] Step 1-8) repeats step 1-2) - step 1-7) to generate a new coding sequence, which can be expressed as:

[0124]

[0125] Generate a new encoding matrix, which can be expressed as:

[0126]

[0127] in, .

[0128] Steps 1-9), when the degree is k / R When , the coding group generated by RSD encoding replaces the coding group at the corresponding position, and the "adjacent" relationship replaces the coding matrix column at the corresponding position, specifically including the following steps:

[0129] (1) When k / R ] is an odd number, the coding sequence and coding matrix remain unchanged;

[0130] (2) When k / R ] is an even number, the coding group generated by RSD encoding replaces the coding group at the corresponding position, and the "adjacent" relationship replaces the coding matrix column at the corresponding position.

[0131] Step 2) uses the belief propagation BP decoding algorithm to perform LT decoding, including the following steps:

[0132] The receiving end receives slightly larger k The coding matrix is ​​reconstructed and then the BP algorithm is used for decoding, which includes the following steps:

[0133] Step 2-1), the degree is 1 ( d = 1) is directly copied to the input packet connected to it.

[0134] In step 2-2, the translated input group is XORed with its "adjacent" group and then replaces the original encoded group. At the same time, its connection relationship is deleted and the degree of the encoded group is reduced by 1.

[0135] Repeat steps 2-1) and 2-2) until the decoding is completed.

[0136] Figure 2 Given when When , the performance comparison of IEM method, RSD-based coding method and IPD-based coding method is shown. Figure 2 It can be seen from the figure that when the parameters are the same, the decoding performance of LT coding using the IEM method is better than that of the other two classic methods.

[0137] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. An interleaved LT encoding method (IEM), characterized in that: The following steps are involved: Step 1), divide the original data into k Input Groups S ={ S 1, S 2,..., S k }, k =1,2,3...; Step 2), generating odd-bit coding groups of the coding sequence based on the robust soliton distribution RSD function; Step 3), generating even-numbered bit coding groups of the coding sequence based on the improved Poisson distribution IPD function; Step 4), repeat steps 2)-3), generate the coding sequence and encoding matrix ,in, For coding grouping, Corresponding to the coding group The "adjacency" relationship to the input group, n =1,2,3...; Step 5), when the degree is k / R hour, R In order to obtain the number of coding groups with the expected degree of 1 during the decoding process, the coding group generated by RSD encoding replaces the coding group at the corresponding position, and the "adjacency" relationship replaces the coding matrix column at the corresponding position.

2. The interleaved LT coding method according to claim 1, wherein: The step 2) specifically includes the following steps: Step 2-1), generate RSD function expression ,in The degree of each coding group; In step 2-2), the odd-numbered bit coding group of the coding sequence is generated by the following steps: (1) Randomly select a coding group from the RSD degree distribution degree d ; (2) Randomly and uniformly select d Input Groups { S n1 , S n2 ,..., S nd } as "adjacency"; (3) This d "Adjacencies" are XORed to generate a coded group : ； Steps 2-3) The "adjacency" relationship is stored in the odd columns corresponding to the new encoding matrix, which can be expressed as: Among them, the column vector Corresponding to the coding group To input group The "adjacency" relationship is: .

3. The interleaved LT coding method according to claim 1, wherein: The step 3) specifically includes the following steps: Step 3-1), generate IPD function expression ,in The degree of each coding group; In step 3-2), the even-numbered bit coding group of the coding sequence is generated by the following steps: (1) Randomly select a coding group from the IPD degree distribution degree d ; (2) Randomly and uniformly select d Input Groups As "adjacency"; (3) This d "Adjacencies" are XORed to generate a coded group : ； Step 3-3), the "adjacency" relationship is stored in the even-numbered columns corresponding to the new encoding matrix, which can be expressed as: Among them, the column vector Corresponding to the coding group To input group The "adjacency" relationship is: .

4. The interleaved LT coding method according to claim 1, wherein: The step 4) specifically includes the following steps: Repeat steps 2) to 3) to generate a new coding sequence, which can be expressed as: Generate a new encoding matrix, which can be expressed as: in, .

5. The interleaved LT coding method according to claim 1, wherein: The step 5) specifically includes the following steps: When the degree is k / R When , the coding group generated by RSD encoding replaces the coding group at the corresponding position, and the "adjacency" relationship replaces the coding matrix column at the corresponding position: (1) When k / R ] is an odd number, the coding sequence and coding matrix remain unchanged; (2) When k / R ] is an even number, the coding group generated by RSD encoding replaces the coding group at the corresponding position, and the "adjacent" relationship replaces the coding matrix column at the corresponding position.

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