A method for optimizing the degree distribution of a BATS code based on LDPC precoding

Abstract

The application provides a BATS code degree distribution optimization method based on LDPC precoding, and belongs to the technical field of wireless communication. The method comprises the following steps: in a BATS code transmission system based on LDPC precoding, an outer code degree distribution influences the overall performance of the system, and a target function of outer code degree distribution optimization is constructed; population initialization: a plurality of candidate degree distribution individuals are randomly generated to form an initial population; in each iteration, population mutation, probability constraint repair, population crossover, probability constraint repair and population update operations are performed to obtain an updated population; and an optimal individual is output: when the number of iterations reaches the maximum number of iterations, an individual that minimizes the target function of outer code degree distribution optimization is selected from the finally updated population as the optimal individual of degree distribution optimization. The application constructs the BATS code degree distribution optimization based on LDPC precoding, obtains the optimal degree distribution through the degree distribution optimization, provides effective parameters for the engineering implementation complexity, and thus improves the deployability of the BATS code in the actual network.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, and in particular relates to a BATS code degree distribution optimization method based on LDPC precoding. Background Technology

[0002] With the rapid development of emerging applications such as the Internet of Things (IoT), drone networks, vehicle-to-everything (V2X) communication, emergency communications, and ubiquitous 5G wireless connectivity, modern wireless communication networks are characterized by node density, dynamic environments, and highly randomized topologies. In these scenarios, nodes are often far apart or obstructed by obstacles, making single-hop communication insufficient to meet coverage and reliability requirements. Multi-hop transmission has gradually become an important means of building large-scale wireless communication networks. Multi-hop networks expand coverage through tiered cooperation among forwarding nodes, improving communication flexibility and scalability, but also bringing more complex problems such as channel degradation and packet loss accumulation.

[0003] In multi-hop wireless transmission, due to factors such as link quality differences, node buffer limitations, channel interference, and forwarding instability, data packets experience cumulative packet loss during multi-hop processes, leading to a significant decrease in end-to-end reliability. Traditional end-to-end erasure coding (such as Lysos codes, RS codes, or LDPC codes) requires maintaining a global redundancy structure, and its decoding relies on complete redundancy relationships, resulting in low efficiency and insufficient robustness under multi-hop conditions. Furthermore, although random linear network coding can improve packet loss to some extent, its encoding and decoding complexity is high, making it difficult to apply directly, especially when intermediate node resources are limited. Batched Sparse Code (BATS Code), through its two-layer structure of outer and inner codes, has good scalability and capacity approximation potential in multi-hop scenarios, but the receiver is prone to the problem of a small number of packets failing to be recovered for a long time when relying solely on BATS decoding. Summary of the Invention

[0004] The purpose of this invention is to provide a BATS code degree distribution optimization method based on LDPC precoding. For wireless multi-hop transmission scenarios, this invention combines LDPC precoding and BATS codes to construct a joint transmission model suitable for multi-hop networks. The degree distribution of the outer BATS code layer determines the number of input packets participating in encoding in each batch and the coverage balance, thus affecting the formation of the effective batch rank, the evolution of the decodeable structure, and the generation rate of recoverable packets during joint decoding. This invention aims to optimize the outer code degree distribution by minimizing the number of received batches. It employs a differential evolution algorithm to search for the optimal degree distribution that satisfies the constraints in the continuous probability space. Simulation analysis is used to analyze the impact of key parameters (such as batch size and the number of original packets) on decoding efficiency, determining the engineering implementation parameters to address the limitations of existing multi-hop transmission systems in terms of performance improvement and hardware complexity implementation.

[0005] To solve the above-mentioned technical problems, the specific technical solution of the present invention is as follows:

[0006] A method for optimizing the code-degree distribution of BATS based on LDPC precoding, the method comprising the following steps:

[0007] Step S1: In the BATS code transmission system based on LDPC precoding, the external code degree distribution affects the overall system performance. Construct an objective function for optimizing the external code degree distribution.

[0008] Step S2: Solve the objective function for optimizing the external code degree distribution to obtain the optimal degree distribution;

[0009] Step S2 includes the following steps:

[0010] Step S21: Population initialization: Randomly generated Individuals with candidate degree distributions are used to form the initial population;

[0011] Step S22: In each iteration, perform population mutation, probability constraint repair, population crossover, probability constraint repair, and population update operations to obtain the updated population;

[0012] Step S23: Output the optimal individual: When the number of iterations reaches the maximum number of iterations, select the individual that minimizes the objective function of the outer key degree distribution optimization from the final updated population as the optimal individual for degree distribution optimization.

[0013] Furthermore, in step S1, the objective function for optimizing the external code degree distribution is:

[0014]

[0015] in, The objective function for optimizing the external code degree distribution is denoted by the average number of received batches. This represents a random variable indicating the number of batches received. Represents the expectation operator; Indicates the number of experiments; Indicates the distribution of external code degree; Indicates system parameters.

[0016] Further, step S22 includes the following steps:

[0017] Step S221: Population variation: Perturb each degree-distributed individual by applying the difference information between degree-distributed individuals, thereby generating mutated individuals of the degree-distributed individuals;

[0018] Step S222: Probability constraint repair: Perform probability constraint repair on each mutated individual to obtain normalized mutated individuals;

[0019] Step S223: Population crossover: After generating normalized mutated individuals, execute the crossover operator to generate crossover individuals;

[0020] Step S224: Probabilistic constraint repair: Perform probabilistic constraint repair on each crossover individual to obtain normalized crossover individuals;

[0021] Step S225: Population Update: After generating normalized crossover individuals, execute the selection operator to update the population;

[0022] Step S226: Determine whether the number of iterations has reached the maximum number of iterations. If the maximum number of iterations has not been reached, proceed to step S221; if the maximum number of iterations has been reached, proceed to step S23.

[0023] Furthermore, in step S221, starting from the previous iteration... In the next iteration, three distinct indices are randomly selected from the population. , , Corresponding degree distribution individuals , , Constructing mutated individuals, the first The iteration of the ... The individual variants are represented as follows:

[0024]

[0025] in, Indicates the first The iteration of the ... Individuals with varying degrees of distribution; t is the scaling factor; t is the number of iterations;

[0026] No. The iteration of the ... Each individual variant is represented by a dimension:

[0027]

[0028] in, Indicates the first The iteration of the ... The j-th dimension component of a mutant individual;

[0029] Generate the first The next iteration The mutated individuals constitute the _____th ... The set of mutated individuals in the next iteration .

[0030] Furthermore, in step S222, for the first... The iteration of the ... The probability constraint repair of the j-th dimension component of the mutated individuals is achieved in the following way:

[0031]

[0032] in, Indicates the first The iteration of the ... The j-th normalized component of each variant individual;

[0033] For the The iteration of the ... After performing probabilistic constraint repair on all dimensions of the mutated individual, we obtain the _th ... The iteration of the ... A normalized variant individual, represented as , for the After performing probability constraint repair on all mutated individuals in the next iteration, we obtain the first... The normalized set of mutated individuals in the next iteration is represented as: .

[0034] Furthermore, in step S223, the first The iteration of the ... The j-th dimension component of each crossover individual is obtained by executing the crossover operator, which is implemented as follows:

[0035]

[0036] in, Indicates the first The iteration of the ... The j-th dimension component of each intersecting individual; Indicates the first The iteration of the ... The j-th dimension component of an individual with degree distribution; Indicates the crossover probability; In the set A uniformly distributed random number;

[0037] The first step is obtained by executing the crossover operator. The iteration of the ... The components of all dimensions of the intersecting individuals are obtained to obtain the first... The iteration of the ... A number of overlapping individuals, represented as ; and thus obtain the first The iteration of the ... A set of overlapping individuals, denoted as .

[0038] Furthermore, in step S224, for the first... The iteration of the ... The probabilistic constraint repair of the j-th dimension component of the intersecting individuals is achieved in the following way:

[0039]

[0040] in, Indicates the first The iteration of the ... The j-th normalized component of each crossover individual;

[0041] For the The iteration of the ... After performing probabilistic constraint repair on all dimensions of the intersecting individuals, we obtain the first... The iteration of the ... A normalized crossover individual, denoted as , for the After performing probability constraint repair on all cross individuals in the nth iteration, we obtain the nth... The normalized set of crossover individuals in the next iteration is denoted as: .

[0042] Further, in step S225, the calculation of the first... The average number of normalized crossover individuals in the first iteration and the number of batches received in the second iteration. The average number of batches received by individuals with degree distribution in the next iteration is used to update the population based on the selection operator, according to the normalized crossover individuals and the average number of batches received by individuals with degree distribution. The selection operator is expressed as follows:

[0043]

[0044] in, Indicates the first The second iteration Normalized crossover individuals The average number of batches received; Indicates the first The second iteration The average number of batches received by individuals with a degree distribution; Indicates the first The second iteration Individuals with degree distribution;

[0045] Thus, the first Population in the next iteration .

[0046] Compared with the prior art, the present invention has the following beneficial technical effects:

[0047] 1) This invention introduces Low-Density Parity-Check (LDPC) constraints into BATS codes, constructs a joint encoding and decoding system for BATS codes based on LDPC precoding, and uniformly models the LDPC check constraints and BATS code batching structure in a binary domain to achieve end-to-end transmission. This effectively improves the resistance to initial packet loss and is of great significance for enhancing the deployability of BATS codes in practical networks.

[0048] 2) Compared with traditional end-to-end wireless multi-hop transmission networks, LDPC constraints are introduced into BATS codes to construct a BATS code degree distribution optimization problem based on LDPC precoding. The degree distribution is optimized to obtain an approximate optimal degree distribution, providing effective parameters for engineering implementation complexity, thereby improving the deployability of BATS codes in actual networks. Attached Figure Description

[0049] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0050] Figure 1 This is a flowchart of the BATS code-degree distribution optimization method based on LDPC precoding of the present invention.

[0051] Figure 2 This is a schematic diagram of the evolution surface of the population penalty function of the present invention with the number of iterations (1 to 200 iterations).

[0052] Figure 3 This is a magnified view of the penalty function and a schematic diagram of the optimal individual position (50-200 iterations) of the present invention.

[0053] Figure 4 This is a schematic diagram comparing the decoding efficiency of the present invention with M=8 and different K values.

[0054] Figure 5 This is a schematic diagram comparing the decoding performance of the present invention with K=100 and different M values. Detailed Implementation

[0055] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] This invention proposes a BATS code-degree distribution optimization method based on LDPC precoding, the method comprising the following steps:

[0057] Step S1: In the BATS code transmission system based on LDPC precoding, the external code degree distribution affects the overall system performance. Construct an objective function for optimizing the external code degree distribution.

[0058] In the BATS code transmission system based on LDPC precoding, the encoding and decoding process is "LDPC precoding, BATS external code batch fountain encoding, multi-hop batch intra-RLNC recoding, and one-step joint decoding recovery".

[0059] The source maps the original set of data packets to a set of lengths of... The original block sequence, each original block sequence is of length . Furthermore, sparse check constraints are introduced between blocks using LDPC precoding to obtain an expanded precoded block set. The total number of precoded blocks is [number missing]. Subsequently, the pre-encoded blocks are used as input to the BATS foreign key, which is based on the degree distribution of the BATS foreign key. Using batches as the basic unit, random selection and linear combination are performed to generate multiple batch codes, each batch being of size [size missing]. During wireless multi-hop transmission, each relay node performs random linear network coding recoding on the received coded packets only within a batch, thereby forming the hop-by-hop linear transformation corresponding to the internal code and resisting link erasure.

[0060] At the receiving end, decoding employs a one-step joint decoding mechanism synchronized with the transmission process. Upon receiving each new batch, the destination node first performs elimination processing within the batch based on the coefficient matrix of the current batch, extracting directly determinable precoded packets. For unsolvable received combinations, these are accumulated and stored as sparse linear equations, and iteratively updated globally using recovered packets to eliminate edges, gradually reducing some equations to single-variable constraints and triggering new packet recovery. Furthermore, the receiving end introduces LDPC precoding check constraints to eliminate the contribution of recovered packets to the check node, and continuously searches the check matrix for check relationships with a remaining unknown of 1 to fill in residual erased packets. This "intra-batch elimination—global edge elimination—LDPC edge elimination" process is repeated cyclically after each batch arrives until all original information packets are recovered; if the recovery conditions are still not met, new batches are received and the process is repeated, thereby minimizing additional receiving overhead while ensuring a high probability of successful recovery.

[0061] In BATS code transmission systems based on LDPC precoding, the overall system performance depends not only on the batch size. Precoding bitrate It also relates to the degree distribution of the BATS foreign code. Closely related.

[0062] External code degree distribution The number of input packets participating in linear combination in each batch is determined, directly affecting two key processes: first, the balance of cross-packet coverage, the frequency distribution of different precoded packets being selected; and second, the formation and evolution of the effective rank of the batch, the number of effective linear constraints obtained by the receiver after multi-hop deletion and recoding. These two key processes jointly determine whether one-step joint decoding can continuously generate recoverable packets, ultimately reflected in the receiver overhead required for end-to-end recovery. Therefore, under fixed network and channel conditions, optimizing the degree distribution of the outer code is crucial. Reducing the number of batches required for decoding at the receiving end is one of the core ways to improve the end-to-end efficiency of the system.

[0063] The range of external code value is: ; Represents the set of all foreign key degree values. Indicates the first Each degree value, This indicates the total number of degree values, and has The distribution of external code degree is represented by a probability vector:

[0064]

[0065] in, Represents the degree distribution of the outer code, which is a probability vector of the degree distribution. Let j represent the j-th dimension of the external code degree distribution, where j is the degree value. The probability of; This indicates a probability calculation.

[0066] Due to the distribution of external code degree This describes a discrete probability distribution, whose feasible region is determined by the following constraints:

[0067]

[0068] Maximum degree This is the upper limit of the degree distribution cutoff, which affects performance. Too small a value reduces coding coverage and the number of effective constraints, also impacting implementation complexity; too large a value increases the overhead of random packet selection, coefficient updates, and decoding. Furthermore, the maximum degree value... The selection of the degree distribution can also be combined with the two-stage decoding threshold relationship of the pre-coding BATS code to give a guiding upper bound. Under the premise of ensuring performance, the degree distribution is truncated and its maximum degree satisfies a certain upper bound constraint.

[0069] LDPC precoding code rate An equivalent recoverable erase threshold can be used under the condition of channel deletion. This describes the precoding's ability to compensate for residual erasure. The recoverable erasure threshold is expressed as follows:

[0070]

[0071] in, Indicates the recoverable erase threshold; Indicates the scaling factor. The scaling factor can match the loss caused by finite length and suboptimal decoding. Under the recoverable erasure threshold, the maximum degree value can be... The upper bound is represented as:

[0072]

[0073] The upper bound of the maximum degree value reflects the batch size. With precoding redundancy strength Coupling effect on maximum degree value: When precoding is stronger (precoding code rate) When smaller, a smaller maximum degree value is allowed. This can achieve better end-to-end recovery results; while when the precoding bitrate... When the value approaches 1, to compensate for insufficient precoding redundancy, the outer key degree distribution often requires larger tail support, resulting in a maximum degree value. The corresponding increase.

[0074] System parameters are ,in The original number of groups, This represents the number of blocks after LDPC precoding. For group length, For batch size, For the number of jumps, For link packet loss rate, The precoding bitrate for LDPC. (In system parameters) Degree distribution under fixed conditions The external code generation process is determined, thereby inducing a random variable in the number of receiving batches required for the receiver to complete decoding. .

[0075] This invention employs a Monte Carlo method to evaluate minimizing receiver overhead under given successful recovery requirements, for a given candidate degree distribution. Repeat independent experiments Next, the objective function for optimizing the external code degree distribution is defined as the average number of received batches:

[0076]

[0077] in, The objective function for optimizing the external code degree distribution is denoted by the average number of received batches. This represents a random variable indicating the number of batches received. Represents the expectation operator; Indicates the number of experiments.

[0078] Using the average number of receive batches directly reflects the end-to-end receive overhead and facilitates fair comparisons with different degree distributions. Based on the above definitions, external code degree distribution optimization can be formulated as a continuous optimization problem with probabilistic constraints, as follows:

[0079]

[0080] in, This represents the optimal external code degree distribution that minimizes the objective function value of the external code degree distribution optimization.

[0081] Step S2: Solve the objective function for optimizing the external code degree distribution to obtain the optimal degree distribution.

[0082] The difficulty in optimizing the external code degree distribution lies in the average number of received batches. The degree distribution problem is determined by the overall link of batched sparse code transmission based on LDPC precoding, making it difficult to obtain a directly differentiable closed-form expression, thus unsuitable for traditional gradient-based methods. Therefore, this paper transforms the outer code degree distribution optimization problem into a continuous vector optimization problem. An adaptive search for the degree distribution is achieved by minimizing the average number of received batches required for successful decoding. A global search is performed in a continuous space, and the fitness is evaluated through simulation in each iteration, thereby obtaining an approximately optimal degree distribution.

[0083] like Figure 1 As shown, step S2 includes the following steps:

[0084] Step S21: Population initialization: Randomly generated Individuals with candidate degree distributions form the initial population.

[0085] Specifically, the randomly generated first Individuals with a degree distribution are represented as follows:

[0086]

[0087] in, Indicates the first Individuals with degree distribution; , Indicates the first The j-th dimension component of an individual with degree distribution is the j-th dimension component. Individual lower degree value in degree distribution The probability, , Indicates the total number of degree values.

[0088] To ensure sufficient diversity in the population, the first The j-th dimension component of an individual with degree distribution is as follows:

[0089]

[0090] in, and Representing the first The maximum and minimum values ​​of the j-th dimension component of an individual with degree distribution. It is evenly distributed in Random numbers on the array.

[0091] Since each dimension of the degree distribution is a probability component , After generating individuals, normalization is performed to satisfy probability constraints.

[0092] Randomly generated Individuals with candidate degree distributions form the initial population. That is, the population in the 0th iteration.

[0093] Step S22: In each iteration, perform population mutation, probability constraint repair, population crossover, probability constraint repair, and population update operations to obtain the updated population.

[0094] Step S221: Population variation: Perturb each degree-distributed individual by applying the difference information between degree-distributed individuals, thereby generating mutated individuals of degree-distributed individuals.

[0095] Specifically, from the previous iteration's... In the next iteration, three distinct indices are randomly selected from the population. , , Corresponding degree distribution individuals , , Constructing mutated individuals, the first The iteration of the ... The individual variants are represented as follows:

[0096]

[0097] in, Indicates the first The iteration of the ... Individuals with varying degrees of distribution; is the scaling factor used to adjust the perturbation amplitude. t is the iteration number, with a maximum iteration number of . .

[0098] No. The iteration of the ... Each individual variant is represented by a dimension:

[0099]

[0100] in, Indicates the first The iteration of the ... The j-th dimension component of a variant individual.

[0101] The first one is generated in the manner described above. The next iteration The mutated individuals constitute the _____th ... The set of mutated individuals in the next iteration .

[0102] Step S222: Probabilistic constraint repair: Perform probabilistic constraint repair on each mutated individual to obtain normalized mutated individuals.

[0103] To satisfy the probability constraint of the degree distribution, this invention employs a "non-negative truncation + normalization" method to ensure that the mutated individuals always follow the valid degree distribution. For the first... The iteration of the ... The probability constraint repair of the j-th dimension component of the mutated individuals is achieved in the following way:

[0104]

[0105] in, Indicates the first The iteration of the ... The j-th normalized component of each variant individual.

[0106] For the The iteration of the ... After performing probabilistic constraint repair on all dimensions of the mutated individual, we obtain the _th ... The iteration of the ... A normalized variant individual, represented as , for the After performing probability constraint repair on all mutated individuals in the next iteration, we obtain the first... The normalized set of mutated individuals in the next iteration is represented as: .

[0107] By fixing the probabilistic constraints, the normalized mutant individuals satisfy the probabilistic constraints, which can maintain the search mechanism of the algorithm and ensure the effectiveness of the subsequent degree value sampling process based on degree distribution.

[0108] Step S223: Population crossover: After generating normalized mutant individuals, execute the crossover operator to generate crossover individuals to further increase the diversity of the population.

[0109] Specifically, randomly starting from the 1st iteration of the previous round... Sub-iteration population Select an individual with a degree distribution, and replace some elements of that degree distribution with some elements of a normalized mutated individual to obtain the first individual. The crossover individuals in the next iteration.

[0110] No. The iteration of the ... The j-th dimension component of each crossover individual is obtained by executing the crossover operator, which is implemented as follows:

[0111]

[0112] in, Indicates the first The iteration of the ... The j-th dimension component of each intersecting individual; Indicates the first The iteration of the ... The j-th normalized component of each variant individual; Indicates the first The iteration of the ... The j-th dimension component of an individual with degree distribution; This represents the crossover probability. A higher crossover probability is beneficial for improving convergence speed and local convergence speed; while a lower crossover probability... It helps maintain population diversity and enhances global exploration capabilities; In the set The uniformly distributed random numbers ensure that at least one dimension of the crossover individuals is provided by the mutated individuals.

[0113] The first step is obtained by executing the crossover operator. The iteration of the ... The components of all dimensions of the intersecting individuals are obtained to obtain the first... The iteration of the ... A number of overlapping individuals, represented as ; and thus obtain the first The iteration of the ... A set of overlapping individuals, denoted as .

[0114] Step S224: Probabilistic constraint repair: Perform probabilistic constraint repair on each crossover individual to obtain normalized crossover individuals.

[0115] For the The iteration of the ... The probabilistic constraint repair of the j-th dimension component of the intersecting individuals is achieved in the following way:

[0116]

[0117] in, Indicates the first The iteration of the ... The j-th dimension normalized component of each crossover individual.

[0118] For the The iteration of the ... After performing probabilistic constraint repair on all dimensions of the intersecting individuals, we obtain the first... The iteration of the ... A normalized crossover individual, denoted as , for the After performing probability constraint repair on all cross individuals in the nth iteration, we obtain the nth... The normalized set of crossover individuals in the next iteration is denoted as: .

[0119] Step S225: Population Update: After generating normalized crossover individuals, execute the selection operator to update the population.

[0120] Specifically, calculate the first The average number of received batches for the normalized crossover individuals in the second iteration (the objective function for optimizing the outer code degree distribution) and the... The average number of received batches for individuals with degree distribution in the next iteration (the objective function for optimizing the outer code degree distribution) is used to update the population based on the selection operator, according to the average number of received batches for normalized crossover individuals and individuals with degree distribution. The selection operator is represented as follows:

[0121]

[0122] in, Indicates the first The second iteration Normalized crossover individuals The average number of batches received; Indicates the first The second iteration The average number of batches received by individuals with a degree distribution; Indicates the first The second iteration Individuals with degree distribution.

[0123] Thus, the first Population in the next iteration .

[0124] The population with the better average number of batches received advances to the next iteration, thus achieving the greedy evolution of the population.

[0125] Step S226: Determine the number of iterations Has the maximum number of iterations been reached? If the maximum number of iterations has not been reached, proceed to step S221; if the maximum number of iterations has been reached, proceed to step S23.

[0126] Step S23: Output the optimal individual: when the number of iterations reaches the maximum number of iterations. At that time, from the final updated population The individual that minimizes the objective function of the external code degree distribution optimization is selected as the optimal individual for degree distribution optimization.

[0127] Since the optimization objective is to reduce the additional receiving overhead required by the receiver to complete the recovery, the smaller the objective function (average number of receiving batches) for optimizing the external code degree distribution in the selection operation, the better the individual is, thus achieving an adaptive search for the degree distribution with the minimum average number of receiving batches.

[0128] Output the individual with the smallest average number of batches received from the final updated population. The optimized external code degree distribution is the result of this optimization. And output the optimal external code degree distribution. The corresponding minimum average number of received batches .

[0129] To ensure that the external code degree distribution can adapt to different system configurations under multi-hop deletion channels, this invention does not perform degree distribution search only at a single parameter point, but rather around the number of original information groups. Batch size Channel deletion probability , number of jumps Group optimization was carried out on key parameters. For different... , , , The corresponding optimal external code degree distribution is obtained by solving the problem. The reason for this is that the optimal form of the degree distribution is closely coupled with the end-to-end decoding process: when As the size increases, the outer code needs to balance coverage balance with the generation of a sparse, strippable structure; when or When changes occur, the effective rank within a batch and the cross-batch constraint strength change; while the number of jumps... Increasing the degree distribution amplifies the deletion effect and alters the statistical properties of the transition matrix. These changes lead to significant differences in the optimal degree distribution under different configurations. Therefore, this invention views degree distribution optimization as an adaptive design process oriented towards system parameters, and uses the optimized decoding efficiency as an important basis for selecting engineering parameters.

[0130] Example

[0131] The following is a simulation result analysis of the BATS code-degree distribution optimization method based on LDPC precoding of the present invention, using a specific embodiment.

[0132] The optimization result analysis of this embodiment is divided into two parts: firstly, based on... Figure 2 and Figure 3 Using two typical simulation surfaces as examples, the search and convergence process of degree distribution optimization under a single configuration is demonstrated, illustrating that degree distribution optimization design can stably output individuals with the optimal degree distribution. Next, the optimal external code degree distributions obtained under different system parameter conditions are summarized. By comparing the corresponding decoding overhead and the pattern of decoding efficiency changes with parameters after optimization, the parameter combination under the constraint of successful decoding probability is determined, providing a basis for engineering implementation design.

[0133] (1) Degree distribution optimization simulation analysis

[0134] Table 1 presents the simulation configuration used for this example, and explains the evolutionary phenomena of individuals in the population during the iteration process. It should be noted that the simulation here will... The recoverable erase threshold can be obtained from the formula for calculating the recoverable erase threshold. The maximum degree value can be calculated from the upper bound of the maximum degree value. .

[0135] Table 1 Simulation parameters for degree distribution optimization based on differential evolution

[0136]

[0137] Under this parameter configuration, the present invention uses the "number of batches required for successful decoding" as a fitness index to perform visual analysis of the iteration process. Figure 2 The surface curves showing the change in the number of batches required for successful decoding for different populations (a total of 50 candidate degree distributions) within the complete iteration interval (1 to 200 iterations) are presented. Figure 3 Further local magnification of the later stages of the iteration (50-200 times) is used to highlight the slight improvements after convergence and the location of the optimal individual (marked with red circles).

[0138] Depend on Figure 3It can be observed that in the initial stage, the performance differences of different candidate degree distributions are large, and the number of batches required for successful decoding fluctuates within a wide range, reflecting the diversity of the randomly initialized population. As the iteration progresses, the fitness surface rapidly shifts downward and tends to flatten within the first 50 iterations, and the average performance of the population quickly converges to a level of about 15 batches. This phenomenon indicates that under the current system parameters and channel conditions, the differential evolution algorithm can effectively filter the search space in a relatively small number of iterations, eliminating obviously unsuitable degree distribution patterns through the competitive mechanism of "mutation-crossover-selection," and causing most individuals to move towards a more reasonable degree value probability quality allocation. In terms of the optimization mechanism, the reason for the large decrease in the early stage is mainly that it can quickly correct the extreme cases of excessively large degree values ​​leading to redundancy waste or excessively small degree values ​​leading to insufficient coverage in the global exploration stage, thereby achieving an initial balance between the coverage balance and the ability to generate strippable structures in the outer code batches, and the decoding overhead is significantly reduced accordingly.

[0139] After 50 iterations Figure 2 The downward trend of the mid-curvature surface has slowed significantly, and the overall change is more gradual than before, but from... Figure 3 The local magnification results show that the fitness of each individual is still slowly decreasing, with better individuals continuously emerging. This stage reflects the characteristic of differential evolution shifting from "coarse-grained global exploration" to "local fine-grained development." At this point, the population as a whole is already in a relatively optimal region. Further reducing the number of decoding batches requires more subtle probability adjustments to the degree distribution (e.g., redistributing the probability quality near the medium degree value). The benefits of this adjustment are diminishing marginally, so the changes are not significant from a macroscopic perspective, but gradual improvement can still be observed at the local scale. In other words, the role of later iterations is not to find a new feasible solution, but to continuously compress the receiving overhead near the feasible solution, improving the stability and optimality of the optimization results.

[0140] Under the constraint of the maximum number of iterations, the algorithm selects the individual with the smallest average number of received batches from the final population as the optimized outer key degree distribution. . Figure 3 The area circled in red corresponds to the optimal individual that emerged during this simulation iteration, whose required number of batches for successful decoding is the minimum under the current parameter configuration. This result demonstrates that the degree distribution optimization method proposed in this invention not only possesses a clear convergence trend but also continuously mines better solutions in later iterations, ultimately outputting an external code degree distribution with lower receive overhead in a statistical sense.

[0141] (2) Comparative analysis of decoding efficiency and performance under different system parameters

[0142] After optimizing the external code degree distribution under different system parameter combinations, we further focus on the variation of the optimized decoding efficiency with system parameters. The purpose of this analysis is not only to demonstrate the performance improvement brought about by optimization, but also to identify the key parameters that should be fixed or adjusted in priority during engineering implementation through parameter sensitivity comparison, thereby achieving a more reasonable trade-off between feasibility and decoding overhead.

[0143] Table 2. Comparison of decoding efficiency and performance under different system parameters (simulation parameter table)

[0144]

[0145] It needs to be emphasized that, Figure 4-5 These all correspond to the optimal degree distribution obtained through the differential evolution algorithm under given hop count, link deletion probability, and corresponding system parameters. The results show that the comparison reflects the impact of the system parameters themselves on decoding efficiency under their respective optimal degree distributions. Table 2 gives the parameters corresponding to this part of the simulation.

[0146] Figure 4 The batch size is given as a fixed value. At that time, the number of different original information groups Decoding efficiency curves are shown under two link packet loss rates (10% and 20%). Decoding efficiency is defined as the ratio of the total number of data packets required for successful decoding to the original number of data packets, used to characterize the receiving overhead required to recover a unit of information. The results show that under the same link packet loss rate, and The two sets of curves almost overlap, and their trends with increasing hop count are highly consistent. This phenomenon indicates that in batch digital transmission based on LDPC precoding, when the degree distribution is optimized for the corresponding conditions, the end-to-end decoding overhead is relatively more determined by channel deletion accumulation and batch structure, and is not sensitive to the dependence on K. In other words, changes in K mainly reflect scaling (the absolute number of received packets increases with K), but do not bring significant differences in the normalized decoding efficiency index.

[0147] This conclusion has direct implications for engineering implementation. In hardware design, the choice of K is more about the constraints of application-layer business requirements (the size of a data block transmitted in one transmission) and on-chip memory depth, rather than considering it as the main parameter tuning method affecting decoding efficiency. In comparison, the coupling effect between batch size M and link deletion probability and hop count is more noteworthy, as they determine the statistical characteristics of the effective rank within a batch, thus directly affecting the solvability and iteration speed on the decoding side.

[0148] Figure 5 With a fixed original number of groups Under the premise of comparing the sizes of different batches The trend of decoding overhead (vertical axis represents the total number of packets required for successful decoding) with hop count under two link packet loss rates (10% and 20%). It can be seen that, at the same packet loss rate, the total number of received packets required for successful decoding generally decreases as the batch size M increases. Meanwhile, as the hop count continues to increase, a larger M corresponds to a flatter curve, demonstrating better stability and resistance to multi-hop cumulative deletion.

[0149] Figure 5 With a fixed original number of groups Under the premise of comparing the sizes of different batches The trend of decoding overhead (vertical axis represents the total number of packets required for successful decoding) with hop count under two link packet loss rates (10% and 20%). It can be seen that, at the same packet loss rate, the total number of received packets required for successful decoding generally decreases as the batch size M increases. Meanwhile, as the hop count continues to increase, a larger M corresponds to a flatter curve, demonstrating better stability and resistance to multi-hop cumulative deletion.

[0150] The fundamental reason for this pattern lies in the fact that as the batch size increases, the linear combination space that a single batch can carry is larger. After multi-hop RLNC and deletion, the receiver is still more likely to obtain enough linear independent combinations to maintain the effective rank within the batch, thereby improving the efficiency of local elimination and cross-batch updates. Taking a link packet loss rate of 10% as an example... The curve shows a clear upward trend with the number of hops, and the increase gradually widens, indicating that multi-hop cumulative deletion requires receiving more batches to compensate for the rank loss. The curve slope is significantly smaller and the rate of change is more stable with increasing hop count, indicating that it is less sensitive to rank decay in multi-hop environments. This difference becomes even more pronounced at a 20% packet loss rate. Smaller batches are more prone to insufficient effective information within the batch under high deletion conditions, leading to a rapid increase in additional receiving overhead, while larger batches can still maintain relatively stable recovery capabilities.

[0151] comprehensive Figure 4 and Figure 5 The comparison results show that when using the optimized external code degree distribution for the corresponding conditions, the decoding efficiency is less sensitive to the number of original information blocks K, but more sensitive to the batch size M. Meanwhile, the batch size is selected as... Compared to It exhibits more stable decoding overhead and a more moderate performance degradation trend under multi-hop conditions, while avoiding This results in a significant increase in batch caching and intra-batch matrix operation size, thus achieving a trade-off between decoding performance gains and hardware complexity.

[0152] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A BATS code-degree distribution optimization method based on LDPC precoding, characterized in that, The method includes the following steps: Step S1: In the BATS code transmission system based on LDPC precoding, the external code degree distribution affects the overall system performance. Construct an objective function for optimizing the external code degree distribution. Step S2: Solve the objective function for optimizing the external code degree distribution to obtain the optimal degree distribution; Step S2 includes the following steps: Step S21: Population initialization: Randomly generated Individuals with candidate degree distributions are used to form the initial population; Step S22: In each iteration, perform population mutation, probability constraint repair, population crossover, probability constraint repair, and population update operations to obtain the updated population; Step S23: Output the optimal individual: When the number of iterations reaches the maximum number of iterations, select the individual that minimizes the objective function of the outer key degree distribution optimization from the final updated population as the optimal individual for degree distribution optimization.

2. The BATS code-degree distribution optimization method based on LDPC precoding according to claim 1, characterized in that, In step S1, the objective function for optimizing the external code degree distribution is: in, The objective function for optimizing the external code degree distribution is denoted by the average number of received batches. This represents a random variable indicating the number of batches received. Represents the expectation operator; Indicates the number of experiments; Indicates the distribution of external code degree; Indicates system parameters.

3. The BATS code-degree distribution optimization method based on LDPC precoding according to claim 2, characterized in that, Step S22 includes the following steps: Step S221: Population variation: Perturb each degree-distributed individual by applying the difference information between degree-distributed individuals, thereby generating mutated individuals of the degree-distributed individuals; Step S222: Probability constraint repair: Perform probability constraint repair on each mutated individual to obtain normalized mutated individuals; Step S223: Population crossover: After generating normalized mutated individuals, execute the crossover operator to generate crossover individuals; Step S224: Probabilistic constraint repair: Perform probabilistic constraint repair on each crossover individual to obtain normalized crossover individuals; Step S225: Population Update: After generating normalized crossover individuals, execute the selection operator to update the population; Step S226: Determine whether the number of iterations has reached the maximum number of iterations. If the maximum number of iterations has not been reached, proceed to step S221; if the maximum number of iterations has been reached, proceed to step S23.

4. The BATS code-degree distribution optimization method based on LDPC precoding according to claim 3, characterized in that, In step S221, starting from the th iteration of the previous iteration... In the next iteration, three distinct indices are randomly selected from the population. , , Corresponding degree distribution individuals , , Constructing mutated individuals, the first The iteration of the ... The individual variants are represented as follows: in, Indicates the first The iteration of the ... Individuals with varying degrees of distribution; t is the scaling factor; t is the number of iterations; No. The iteration of the ... Each individual variant is represented by a dimension: in, Indicates the first The iteration of the ... The j-th dimension component of a mutant individual; Generate the first The next iteration The mutated individuals constitute the _____th ... The set of mutated individuals in the next iteration .

5. The BATS code-degree distribution optimization method based on LDPC precoding according to claim 4, characterized in that, In step S222, for the first The iteration of the ... The probability constraint repair of the j-th dimension component of the mutated individuals is achieved in the following way: in, Indicates the first The iteration of the ... The j-th normalized component of each variant individual; For the The iteration of the ... After performing probabilistic constraint repair on all dimensions of the mutated individual, we obtain the _th ... The iteration of the ... A normalized variant individual, represented as , for the After performing probability constraint repair on all mutated individuals in the next iteration, we obtain the first... The normalized set of mutated individuals in the next iteration is represented as: .

6. The BATS code-degree distribution optimization method based on LDPC precoding according to claim 5, characterized in that, In step S223, the first The iteration of the ... The j-th dimension component of each crossover individual is obtained by executing the crossover operator, which is implemented as follows: in, Indicates the first The iteration of the ... The j-th dimension component of each intersecting individual; Indicates the first The iteration of the ... The j-th dimension component of an individual with degree distribution; Indicates the crossover probability; In the set A uniformly distributed random number; The first step is obtained by executing the crossover operator. The iteration of the ... The components of all dimensions of the intersecting individuals are obtained to obtain the first... The iteration of the ... A number of overlapping individuals, represented as ; and thus obtain the first The iteration of the ... A set of overlapping individuals, denoted as .

7. The BATS code-degree distribution optimization method based on LDPC precoding according to claim 6, characterized in that, In step S224, for the first The iteration of the ... The probabilistic constraint repair of the j-th dimension component of the intersecting individuals is achieved in the following way: in, Indicates the first The iteration of the ... The j-th normalized component of each crossover individual; For the The iteration of the ... After performing probabilistic constraint repair on all dimensions of the intersecting individuals, we obtain the first... The iteration of the ... A normalized crossover individual, denoted as , for the After performing probability constraint repair on all cross individuals in the nth iteration, we obtain the nth... The normalized set of crossover individuals in the next iteration is denoted as: .

8. The BATS code-degree distribution optimization method based on LDPC precoding according to claim 7, characterized in that, In step S225, the calculation of the first... The average number of normalized crossover individuals in the first iteration and the number of batches received in the second iteration. The average number of batches received by individuals with degree distribution in the next iteration is used to update the population based on the selection operator, using the normalized crossover individuals and the average number of batches received by individuals with degree distribution. The selection operator is expressed as follows: in, Indicates the first The second iteration Normalized crossover individuals The average number of batches received; Indicates the first The second iteration The average number of batches received by individuals with a degree distribution; Indicates the first The second iteration Individuals with degree distribution; Thus, the first Population in the next iteration .

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