A method and system for rate optimization of a ra code with combiner structure

Abstract

The application discloses a repetition accumulation code rate optimization method and system containing a Combiner structure, first, based on the extrinsic information transfer analysis method, a mutual information transmission model of the repetition accumulation code containing the Combiner structure in the decoding iteration process is established; based on the mutual information transmission model, an iteration objective function containing the number of parallel paths, the repetition number and the channel parameters is constructed; based on the fixed point theory, the iteration objective function is processed to be steady; under the condition that the number of parallel paths is fixed, the steady objective function is analytically solved; based on the analytical expression, combined with the decoding success constraint condition, the minimum repetition number meeting the constraint is determined as the local optimal repetition number, and the local optimal code rate is calculated. The method improves the transmission efficiency of the point-to-point communication system under the premise of ensuring the decoding reliability.

Description

Technical Field

[0001] This invention relates to the field of communication and channel coding, specifically to a method and system for optimizing the code rate of RA codes with a Combiner structure. Background Technology

[0002] Repeat-Accumulate (RA) codes, as a relatively simple channel coding scheme with good error correction performance, have been widely studied in communication systems. In additive white Gaussian noise (AWGN) channels, existing research on RA code performance analysis and code rate design typically focuses on external information transmission analysis based on a predetermined factor graph structure, and then studies decoding performance and parameter configuration accordingly.

[0003] In traditional RA code structures, the connection relationships in the factor graph typically employ a fixed structure, with a single connection between the check node and the information variable node. Under this structure, the information transmission paths are relatively limited. When the system operates under low signal-to-noise ratio (SNR) conditions, increasing the number of repetitions is often necessary to ensure decoding reliability, leading to a decrease in code rate and impacting system transmission efficiency. Simultaneously, existing structures also have limitations in improving code rate under the same SNR conditions. To improve information transmission efficiency, RA codes with Combiner structures have emerged in recent years, which expand the information transmission channel by introducing multiple parallel paths, showing potential for increasing code rate. However, current research has not yet proposed a systematic code rate optimization method for this type of structure.

[0004] Furthermore, existing RA code parameter optimization methods mostly rely on iterative solutions, typically requiring repeated updates of intermediate variables to approximate the convergent result. These methods are susceptible to factors such as initial value selection, iteration count setting, and convergence conditions, resulting in high computational complexity, lengthy solution processes, and insufficient stability. This makes them unsuitable for quickly obtaining optimal code rate parameters that satisfy decoding reliability constraints.

[0005] Therefore, how to effectively optimize the code rate of RA codes with Combiner structures while ensuring decoding reliability, and reduce the dependence on iterative calculations in the parameter solving process, has become a technical problem that needs to be solved in this field. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method and system for optimizing the code rate of RA codes with a Combiner structure. This solves the problems of limited information transmission efficiency and parameter solving dependence on iteration in the code rate optimization process of RA codes in the prior art, thereby improving the transmission efficiency of point-to-point communication systems while ensuring decoding reliability.

[0007] To achieve the above objectives, the technical solution specifically adopted by the present invention is as follows: A method for optimizing the code rate of a repeating accumulator code with a Combiner structure includes the following steps: Step 1: Based on the external information transfer analysis method, under the conditions of infinite code length and Gaussian approximation, establish the external information transfer functions for variable nodes and check nodes respectively; Step 2: Based on the external information transfer function of the variable node and the check node, construct and iterate an objective function that includes the number of parallel paths, the number of repetitions, and the channel parameters; Step 3: Based on fixed-point theory, the iterative objective function is stabilized to eliminate the dependence of intermediate variables in the iteration process, resulting in a steady-state objective function expressed only by output mutual information, number of parallel paths, number of repetitions, and channel parameters; and an optimization objective function is established with the goal of maximizing the code rate of the repeated accumulator code and the constraint of successful decoding. Step 4: Under the condition of a fixed number of parallel paths, with the objective function as a constraint and the goal of minimizing the number of repetitions, the steady-state objective function is solved analytically to obtain an analytical expression in which the number of repetitions is directly determined by the output mutual information, the number of parallel paths, and the channel parameters.

[0008] Step 5: Based on the analytical expression and the decoding success constraint, determine the minimum number of repetitions that satisfy the constraint as the local optimal number of repetitions, and calculate the local optimal code rate; traverse different numbers of parallel paths, and select the global optimal code rate and its corresponding number of parallel paths and number of repetitions.

[0009] Preferably, in step 1, in the factor graph of the regular RA code, the input information and output information are converted into log-likelihood ratio representation to obtain output mutual information and input mutual information, and then, under the conditions of infinite code length and Gaussian approximation, extrinsic information transfer functions for variable nodes and check nodes are established respectively.

[0010] Preferably, the extrinsic information transfer function of the variable node is expressed as: the output mutual information is equal to the result of the variance of the input mutual information after being mapped by the J function; the extrinsic information transfer function of the verification node is expressed as: the output mutual information is equal to 1 minus the J function value corresponding to the input mutual information; the J function is the integral form of the Gaussian error function of the variance of the input mutual information.

[0011] Preferably, the J function is specifically expressed as: a function in which the output mutual information is equal to the variance of the input mutual information. This function is calculated by integrating the Gaussian error function and is used to describe the transmission relationship of mutual information under additive white Gaussian noise channel conditions.

[0012] Preferably, in step 2, the specific method for constructing the objective function is as follows: for a repeating accumulator encoder with a Combiner structure, the information transmission path is expanded to... k Parallel paths, of which k For integers greater than or equal to 1, the code rate is expressed as the ratio of the reciprocal of the number of repetitions to the number of parallel paths; based on the external information transfer functions established in step 1, the output mutual information from the channel node to the first variable node, the output mutual information from the first variable node to the check node, the output mutual information from the check node to the second variable node, the output mutual information fed back from the second variable node to the check node, the output mutual information from the check node to the first variable node, and the final output mutual information fed back from the first variable node to the channel node are constructed sequentially, thus obtaining the first... i The objective function after the next iteration includes, in addition to the mutual information output from the previous iteration, the number of parallel paths k, the number of repetitions q, and the channel parameters, intermediate variables that depend on the previous iteration process.

[0013] Preferably, the first step in step 2 is described in step 3. i The objective function after the nth iteration is specifically expressed as: i The output mutual information of the next iteration is equal to a combination function of the initial output mutual information of the channel nodes and the feedback mutual information of the check nodes. This function includes the number of parallel paths. k Number of repetitions q Channel equivalent variance and the first i -1 iterations output the expression for mutual information.

[0014] Preferably, in step 3, the fixed point satisfies the following: when the number of iterations approaches infinity, the output mutual information at each node converges to the minimum element in the solution set of the equation. The bit error probability corresponding to this minimum fixed point is an exponential function of negative two times the fixed point value with the natural constant e as the base. When the fixed point approaches 1, the bit error probability approaches 0, which represents the decoding success condition.

[0015] Preferably, in step 4, the specific method is as follows: [Information on the number of parallel paths is missing]. k Under fixed conditions, the steady-state objective function obtained in step 3 is transformed by rearranging terms, inverting the function, and squaring to derive the number of repetitions. q The parsing expression, which is composed of output mutual information. I Number of parallel paths k Furthermore, the channel parameters are directly determined, eliminating the need for iterative updates of intermediate variables.

[0016] Preferably, the number of repetitions in step 4 qThe derivation of the analytical expression includes: taking the inverse of both sides of the mutual information equation in the steady-state objective function, then squaring the equation, rearranging the terms, and finally obtaining the expression containing only output mutual information and the number of parallel paths. k The expression for the number of repetitions of the channel parameters.

[0017] Preferably, step 5 is implemented by substituting the decoding failure condition into the number of repetitions obtained in step 4. q The analytical expression is used to construct the set of repetition counts corresponding to decoding failures, i.e., the unreliable region; the absolute complement of this unreliable region is taken to obtain the set of repetition counts corresponding to successful decoding, i.e., the reliable region; the smallest positive integer in the reliable region is taken as the local optimal repetition count, and substituted into the code rate formula to obtain the local optimal code rate; the number of feasible parallel paths is then traversed. k Calculate each k The value corresponds to the local optimal number of repetitions and the local optimal bitrate. All local optimal bitrates are combined into a set, and the maximum value in this set is selected as the global optimal bitrate. The corresponding number of parallel paths and the number of repetitions are the global optimal number of parallel paths and the global optimal number of repetitions, respectively.

[0018] Preferably, the decoding success constraint in step 5 is: the output mutual information approaches 1, at which point the system error probability approaches 0; the decoding failure constraint is: the output mutual information approaches 0, at which point the system cannot decode correctly.

[0019] Preferably, in step 5, when traversing all feasible parallel paths k, the value of k ranges from 1 to a preset maximum number of parallel paths, which is determined by system hardware resources and coding complexity constraints.

[0020] This invention also provides a rate optimization system for repeated accumulator codes with a Combiner structure, comprising: The mutual information modeling module is used to establish extrinsic information transfer functions for variable nodes and check nodes under the conditions of infinite code length and Gaussian approximation, based on the extrinsic information transfer analysis method. The extrinsic information transfer function for variable nodes is expressed as: the output mutual information equals the variance of the input mutual information mapped by the J function. The extrinsic information transfer function for check nodes is expressed as: the output mutual information equals 1 minus the J function value corresponding to the input mutual information; the J function is the integral form of the Gaussian error function of the variance of the input mutual information. The iterative objective function building module is used to expand the information transmission path for repeating accumulator encoders with Combiner structures. k Parallel paths, of which kFor integers greater than or equal to 1, the code rate is expressed as the ratio of the reciprocal of the number of repetitions to the number of parallel paths; based on the external information transfer functions established by the mutual information modeling module, the output mutual information relationships from the channel node to the first variable node, from the first variable node to the check node, from the check node to the second variable node, from the second variable node back to the check node, from the check node to the first variable node, and from the first variable node back to the channel node are constructed sequentially to obtain the first... i The objective function after the next iteration; The steady-state optimization module, based on fixed-point theory, aims to stabilize the system when the number of iterations approaches infinity, ensuring that the mutual information expression of each node is stable. This process utilizes fixed-point relationships to eliminate the dependence of intermediate variables on the iteration process, resulting in a value containing only the output mutual information. I Number of parallel paths k Number of repetitions q The steady-state objective function of the channel parameters is used, and an optimization objective function is established with the code rate maximization as the objective and successful decoding as the constraint. The analytical solution module is used to solve problems involving parallel paths. k Under fixed conditions, the steady-state objective function is transformed by rearranging terms, inverting the function, and performing squaring operations to derive the number of repetitions. q The parsing expression, which is composed of output mutual information. I Number of parallel paths k And the channel parameters are directly determined; combined with the code rate formula, the smallest positive integer that satisfies the decoding success constraint is taken as the local optimal number of repetitions, and the corresponding local optimal code rate is calculated; The global optimization module is used to substitute the decoding failure condition into the number of repetitions. q The parsing expression constructs an unreliable region, and the absolute complement is taken to obtain the reliable region. The smallest positive integer within the reliable region is selected as the locally optimal repetition count, and the locally optimal code rate is calculated. All feasible parallel paths are traversed. k Calculate each k The value corresponds to the local optimal number of repetitions and the local optimal bitrate. All local optimal bitrates are combined into a set, and the maximum value is selected as the global optimal bitrate. The corresponding number of parallel paths and the number of repetitions are the global optimal number of parallel paths and the global optimal number of repetitions, respectively.

[0021] This invention has the following characteristics and beneficial effects: Improving information transmission efficiency and increasing system code rate: This invention introduces RA codes with a Combiner structure, extending traditional single-path information transmission into multiple parallel paths. Combined with the joint adjustment of repetition counts, this significantly improves information transmission efficiency. Under the same signal-to-noise ratio, a higher code rate can be achieved, thereby effectively improving the transmission efficiency of point-to-point communication systems.

[0022] Eliminating iterative dependencies and reducing computational complexity: This invention optimizes the iterative objective function based on fixed-point theory, eliminating the dependence of intermediate variables on the iterative process. It transforms the parameter optimization problem, which originally required repeated updates, into a directly solvable analytical problem. Compared to existing iterative methods, this method eliminates the need to set initial values, iteration counts, and convergence conditions, significantly reducing computational complexity and solution time, and improving the stability and operability of parameter solving.

[0023] Achieving local and global two-level code rate optimization: Under the condition of a fixed number of parallel paths, this invention derives an analytical expression for the number of repetitions, which can quickly determine the local optimal number of repetitions and the local optimal code rate. Furthermore, by traversing all feasible parallel paths, the optimal number of parallel paths, the optimal number of repetitions, and the globally optimal code rate can be selected globally, realizing systematic, two-level code rate optimization for RA codes with Combiner structures.

[0024] Supports adaptive signal-to-noise ratio coding: The method of this invention can dynamically adjust the encoder structure (including the number of parallel paths and the number of repetitions) according to different signal-to-noise ratio conditions, and automatically match the optimal code rate while ensuring decoding reliability. It has strong environmental adaptability and engineering practical value.

[0025] Rigorous Theory and Reliable Results: This invention is based on external information transfer analysis and fixed-point theory, combined with set theory to divide the decoding reliable and unreliable regions, ensuring the theoretical rigor and reliability of the parameter solution process. Simulation results (as shown in Table 1) demonstrate that, under different signal-to-noise ratio conditions, this invention can stably obtain relatively optimal or optimal code rate parameters that satisfy the decoding success conditions. Attached Figure Description

[0026] Figure 1 This is a graph of RA code factors containing the Combiner structure in this embodiment.

[0027] Figure 2 This is a fixed-point curve under the conditions of SNR = 0 dB and k = 2 in this embodiment.

[0028] Figure 3 This is the EXIT plot under the condition of SNR = 0 dB in this embodiment. Detailed Implementation

[0029] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0030] Example 1 This embodiment provides a method for optimizing the code rate of a repeating accumulator code with a Combiner structure, applicable to point-to-point communication scenarios under AWGN channels, and particularly suitable for communication systems using RA codes with a Combiner structure for encoding and transmission. The method includes the following steps: Step 1. Establish mutual information models for each node based on the external information transfer analysis method: Based on the external information transfer analysis method, under the conditions of infinite code length and Gaussian approximation, establish external information transfer functions for variable nodes and check nodes respectively.

[0031] Specifically, in the factor graph of the regular RA code, the decoding process of input and output information is represented by the log-likelihood ratio, and extrinsic information transfer functions for variable nodes and check nodes are established under the conditions of infinite code length and Gaussian approximation. In this embodiment, the factor graph is as follows: Figure 1 As shown, letters U and V represent variable nodes, letter C represents a check node, and letter S represents a channel node.

[0032] For degrees d The variable node, its external information transfer function T v Represented as: (1) Where, 0≤ I A,i ≤1 indicates that the check node i To variable node j Input mutual information, The function represents the output of mutual information. The variance of the input information can be understood in degrees. d In a factor graph, the degree of a variable node is equal to the total number of edges connected to that node.

[0033] Furthermore, the J function can be expressed as: (2) For degrees d The verification node, its external information transfer function The output mutual information used to describe the verification node is represented as: (3) In this embodiment, if there exists w The input mutual information corresponding to each edge is the same, that is... ,in w This indicates that the node is connected to the current node and its input mutual information is... I A If the number of edges is given, then equations (1) and (3) can be simplified accordingly to: and .node S To variable node V During the information transmission process, for the first l In the next iteration, let the root mean square of the channel noise be... σ Then the channel node S The output mutual information at the point can be represented as: (4) in, This represents the channel equivalent variance. From equation (4), it can be seen that as channel noise decreases, the mutual information output by the channel nodes increases. As the capacity increases, the reliability of information transmission improves accordingly.

[0034] Step 2. Derive the output mutual information of the RA code with Combiner structure and construct the iterative objective function.

[0035] Specifically, in point-to-point AWGN channels, for encoders containing Combiner-structured RA codes, the original single-path information transmission method is extended to... k The code rate for a parallel path can be expressed as: (5) It should be noted that the number of parallel paths is adjusted jointly. k With the number of repetitions q It can adjust the system bitrate.

[0036] Based on the external information transfer function of the variable node and the check node, firstly, according to the channel node... S The output mutual information at the location, combined with the information from the check node. C Feedback mutual information can be used to obtain variable nodes. V To the verification node C Output mutual information: (6) Secondly, for the verification node C To variable node U Information transmission, verification node C The input includes variable nodes V Output mutual information and the variable nodes in the previous iteration U Feedback mutual information Based on the external information function of the verification node, the verification node can be obtained. C Output mutual information: (7) Then, based on the repetitive accumulation property of RA codes, variable nodes U Receive from the verification node CAfter the mutual information is output, it is repeatedly accumulated and fed back to the verification node. C Output mutual information: (8) Next, combine the variable nodes V Input information and variable nodes U The feedback information can be used to obtain the verification node. C To variable node V Output mutual information: (9) Finally, variable nodes V To the channel node S The mutual information of each node is used as the final output mutual information. Combining the mutual information transmission relationships of all nodes mentioned above, the final output mutual information can be obtained as follows: (10) At this point, the channel node needs to be reconsidered. S The final output mutual information at the point, because (11) The first can be obtained The objective function after the next iteration: (12) Among them, parameters A and parameters B The expressions are as follows: , Therefore, the first l The output mutual information of the next iteration is related not only to the output of the previous iteration and the system parameters, but also to the intermediate variables. Related. Because intermediate variables need to be updated based on previous iterations, subsequent solutions still depend on the iteration process, which is not conducive to obtaining concise parameter analysis relationships. Therefore, it is necessary to optimize the iterative objective function based on fixed-point theory to eliminate the dependency on intermediate variables and reduce the number of repetitions. This lays the foundation for analytical solutions and bitrate optimization.

[0037] Step 3. Optimize the iterative objective function based on fixed-point theory to eliminate intermediate variable dependencies.

[0038] Specifically, as the number of iterations approaches infinity, the system gradually reaches a steady-state convergence, and the output mutual information at each node no longer changes with the number of iterations, that is: (13) in, Indicates the firstl During the iteration process, the mutual information of the output at each node of the factor graph is a process quantity that changes with the number of iterations; The smallest element in the solution set of the equation is called the minimum fixed point. According to channel coding theory, for any edge of the factor graph, the output mutual information after steady-state convergence is... The corresponding bit error probability can be expressed as: (14) From equation (14), it can be seen that when hour, This result is consistent with the conditions for successful decoding, indicating that the fixed point... It can characterize the reliability of decoding.

[0039] When the number of iterations As the system approaches infinity, it satisfies the fixed-point relation. Based on this relation, the mutual information expression of each node is stabilized. Reconsidering equation (6), we can obtain: (15) Furthermore, by processing equation (9) and replacing the intermediate variables with fixed-point variables, we obtain: (16) Simplifying equation (16) and rearranging terms, we get: (17) Take both sides at the same time By squaring, we get: (18) After further processing, we can obtain only those containing of expression: (19) Building upon this, further eliminating intermediate variable dependencies yields a result containing only... The final expression for mutual information: (20) Among them, parameters C and parameters D The expressions are as follows: , The optimized steady-state objective function retains only the fixed points. I With parameters k , q and The direct mapping relationship is established. Compared with the original iterative objective function, the optimized expression no longer depends on intermediate variables and information from previous iterations, thus reducing the dependence of subsequent solutions on the iterative process; at the same time, the function form is simplified, facilitating the subsequent derivation of the number of repetitions. q This provides the foundation for the parsing and implementation of bitrate optimization.

[0040] Based on this, with the goal of maximizing the RA code rate and the constraint of successful decoding, an optimization objective function is established, clarifying the objective and constraints of the optimization problem: (twenty one) Step 4. Fix the number of parallel paths k Derive the number of repetitions q The analytical expression.

[0041] Number of parallel paths k Under fixed conditions, it can be seen from the bitrate expression that when k The number of repetitions is fixed and satisfies the successful decoding constraint. q The smaller the value, the higher the corresponding bitrate. To solve the optimization objective function for maximizing the bitrate established in step 3, it is necessary to further determine the number of repetitions. q The analytical expression is given. Therefore, achieving the optimization objective function can be transformed into solving for the minimum number of repetitions that satisfy the constraints. q This process requires no iteration; the parameters can be directly solved simply by transforming the formula.

[0042] Under the condition that the number of iterations approaches infinity, reconsidering equation (8), after transformation, it can be written as: (twenty two) Take both sides at the same time And by squaring further, we get: (twenty three) After being organized, it can be written as: (twenty four) To further simplify expression (24), The derivations are performed separately.

[0043] Reconsider equation (19), for Pick After squaring, it can be written as: (25) Reconsidering equations (7) and (19), they can be written as: (26) After further processing, we can obtain: (27) Substituting equations (25) and (27) into equation (24), we can obtain the number of repetitions. q The final parsed expression: (28) Therefore, the number of repetitions It can be derived from output mutual information I Number of parallel paths k and channel parameters This directly determines the relationships between system parameters, establishing a direct mapping without relying on iterative updates of intermediate variables. Combined with the optimization objective function, it can be seen that when... k When the value is fixed, take the smallest positive integer that satisfies the decoding success constraint. This allows us to obtain the local optimal bitrate under that condition.

[0044] Step 5. Determine the local optimal number of repetitions, the local optimal bitrate, and the global optimal parameters based on set theory.

[0045] To further determine the feasible range of repetitions that satisfy the decoding success condition, it is necessary to analyze the range of values ​​for the objective function. Since equation (28) contains an inverse function term, and when decoding is successful... I = 1, at this time Therefore, it is not possible to directly... I Equation (28) is solved under the condition that = 1. To this end, set theory is used to divide the feasible range of the number of repetitions.

[0046] First, define the decoding failure condition. Substituting into equation (28), we can construct the set of repeated times corresponding to decoding failures, i.e., the unreliable region. Secondly, by taking the absolute complement of the set UR, we can obtain the set of repetition counts corresponding to successful decoding, i.e., the reliable region. This indicates that when the number of repetitions... q When the value is RR, the RA code containing the Combiner structure can satisfy the decoding success constraint in the optimization objective function. Then, within the reliable region RR, the smallest positive integer is selected, denoted as... ,like Figure 2 As shown, and substituting into the bitrate formula, we can obtain the local optimal bitrate: (29) Thus, given the signal-to-noise ratio (SNR) and a fixed number of parallel paths, k Under the given conditions, by selecting reliable regions and determining the minimum number of repetitions, the local optimum solution of the objective function was found, and the local optimum number of repetitions was determined. and the corresponding local optimal bitrate It can be accessed through Figure 3 The EXIT plot verifies that the decoding can converge stably at this number of repetitions, and that it is the minimum value that satisfies the convergence condition.

[0047] In practical systems, the number of parallel paths k These are adjustable parameters, and different k This corresponds to different local optimal repetition counts and local optimal bit rates. Therefore, for all feasible... k The values ​​are solved separately, where , This represents the maximum number of parallel paths. For each... k The corresponding local optimal repetition count and local optimal bitrate are calculated as follows: (30) All k The corresponding local optimal bitrate constitutes a set The maximum value in the set is selected as the globally optimal bitrate. The number of parallel paths corresponding to it k and number of repetitions Let be the number of globally optimal parallel paths. and the global optimal number of repetitions By employing the above method, the encoder structure can be dynamically adjusted according to different signal-to-noise ratio (SNR) conditions while ensuring decoding reliability, thereby achieving adaptive SNR coding and maximizing system transmission efficiency.

[0048] This embodiment proposes a rate optimization method based on fixed-point theory for RA codes with Combiner structures. This method optimizes the iterative objective function, eliminates dependencies on intermediate variables, and transforms the rate optimization problem dependent on iterative updates into an analytical problem of solving parameters; it also addresses the issue of parallel paths... k Under fixed conditions, derive the number of repetitions. q The analytical expression provides an analytical foundation for determining the local optimal repetition count and local optimal code rate. Simultaneously, by combining set theory methods to divide the decoding into reliable and unreliable regions, the local optimal repetition count and local optimal code rate can be determined under a given signal-to-noise ratio. Furthermore, after traversing the number of feasible parallel paths, the global optimal repetition count, global optimal code rate, and global optimal number of parallel paths can be determined. Through this approach, the dependence of the code rate optimization process on iterative solutions is reduced, enabling global code rate optimization of RA codes with Combiner structures while ensuring decoding reliability.

[0049] Table 1. Local optimal repetition count, local optimal bit rate, and global optimal results under different signal-to-noise ratios.

[0050] Table 1 lists the number of parallel paths under different signal-to-noise ratios. k Corresponding local optimal number of repetitions and local optimal bit rate And the globally optimal number of repetitions obtained by further filtering among all feasible parallel paths. and global optimal bitrate As shown in Table 1, the local optimal results corresponding to a fixed number of parallel paths differ under different signal-to-noise ratios. By further comparing the local optimal bit rates, the global optimal number of repetitions and the global optimal bit rate under the corresponding signal-to-noise ratio can be determined.

[0051] Example 2 This embodiment provides a code rate optimization system for repeated accumulating codes with a Combiner structure for implementing the method of Embodiment 1, including: The mutual information modeling module is used to establish extrinsic information transfer functions for variable nodes and check nodes under the conditions of infinite code length and Gaussian approximation, based on the extrinsic information transfer analysis method. The extrinsic information transfer function for variable nodes is expressed as: the output mutual information equals the variance of the input mutual information mapped by the J function. The extrinsic information transfer function for check nodes is expressed as: the output mutual information equals 1 minus the J function value corresponding to the input mutual information; the J function is the integral form of the Gaussian error function of the variance of the input mutual information. The iterative objective function building module is used to expand the information transmission path for repeating accumulator encoders with Combiner structures. k Parallel paths, of which k For integers greater than or equal to 1, the code rate is expressed as the ratio of the reciprocal of the number of repetitions to the number of parallel paths; based on the external information transfer functions established by the mutual information modeling module, the output mutual information relationships from the channel node to the first variable node, from the first variable node to the check node, from the check node to the second variable node, from the second variable node back to the check node, from the check node to the first variable node, and from the first variable node back to the channel node are constructed sequentially to obtain the first... l The objective function after the next iteration; The steady-state optimization module, based on fixed-point theory, aims to stabilize the system when the number of iterations approaches infinity, ensuring that the mutual information expression of each node is stable. This process utilizes fixed-point relationships to eliminate the dependence of intermediate variables on the iteration process, resulting in a value containing only the output mutual information. I Number of parallel paths k Number of repetitions q The steady-state objective function of the channel parameters is used, and an optimization objective function is established with the code rate maximization as the objective and successful decoding as the constraint. The analytical solution module is used to solve problems involving parallel paths. k Under fixed conditions, the steady-state objective function is transformed by rearranging terms, inverting the function, and performing squaring operations to derive the number of repetitions. q The parsing expression, which is composed of output mutual information. I Number of parallel paths k And the channel parameters are directly determined; combined with the code rate formula, the smallest positive integer that satisfies the decoding success constraint is taken as the local optimal number of repetitions, and the corresponding local optimal code rate is calculated; The global optimization module is used to substitute the decoding failure condition into the number of repetitions. q The parsing expression constructs an unreliable region, and the absolute complement is taken to obtain the reliable region. The smallest positive integer within the reliable region is selected as the locally optimal repetition count, and the locally optimal code rate is calculated. All feasible parallel paths are traversed. k Calculate each k The value corresponds to the local optimal number of repetitions and the local optimal bitrate. All local optimal bitrates are combined into a set, and the maximum value is selected as the global optimal bitrate. The corresponding number of parallel paths and the number of repetitions are the global optimal number of parallel paths and the global optimal number of repetitions, respectively.

[0052] Furthermore, in the steady-state optimization module, the fixed point satisfies the following: when the number of iterations approaches infinity, the output mutual information converges to the smallest element in the solution set of the equation, and the error probability corresponding to this smallest fixed point is an exponential function of the value of the fixed point with the natural constant e as the base.

[0053] In the global optimization module, all feasible parallel paths are traversed. k hour, k The value ranges from 1 to the preset maximum number of parallel paths, which is determined by system hardware resources and coding complexity constraints.

[0054] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely preferred examples and are not intended to limit the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for optimizing the code rate of a repeating accumulator code containing a Combiner structure, characterized in that, Includes the following steps: Step 1: Based on the external information transfer analysis method, under the conditions of infinite code length and Gaussian approximation, establish the external information transfer functions for variable nodes and check nodes respectively; Step 2: Based on the external information transfer function of the variable node and the check node, construct and iterate an objective function that includes the number of parallel paths, the number of repetitions, and the channel parameters; Step 3: Based on fixed-point theory, the iterative objective function is stabilized to eliminate the dependence of intermediate variables in the iteration process, resulting in a steady-state objective function expressed only by output mutual information, number of parallel paths, number of repetitions, and channel parameters; and an optimization objective function is established with the goal of maximizing the code rate of the repeated accumulator code and the constraint of successful decoding. Step 4: Under the condition of a fixed number of parallel paths, with the optimization objective function as a constraint and the goal of obtaining the minimum number of repetitions, the steady-state objective function is solved analytically to obtain an analytical expression in which the number of repetitions is directly determined by the output mutual information, the number of parallel paths, and the channel parameters. Step 5: Based on the analytical expression and the decoding success constraint, determine the minimum number of repetitions that satisfy the constraint as the local optimal number of repetitions, and calculate the local optimal code rate; traverse different numbers of parallel paths, and select the global optimal code rate and its corresponding number of parallel paths and number of repetitions.

2. The method according to claim 1, characterized in that, In step 1, in the factor graph of the regular RA code, the input information and output information are converted into log-likelihood ratio representation to obtain output mutual information and input mutual information. Then, under the conditions of infinite code length and Gaussian approximation, the extrinsic information transfer functions of the variable node and the check node are established respectively.

3. The method according to claim 1, characterized in that, The extrinsic information transfer function of the variable node is expressed as: the output mutual information is equal to the result of the variance of the input mutual information after being mapped by the J function; the extrinsic information transfer function of the verification node is expressed as: the output mutual information is equal to 1 minus the J function value corresponding to the input mutual information; the J function is the integral form of the Gaussian error function of the variance of the input mutual information.

4. The method according to claim 3, characterized in that, The J function is specifically expressed as a function in which the output mutual information equals the variance of the input mutual information. This function is calculated using the integral form of the Gaussian error function and is used to describe the transmission relationship of mutual information under additive white Gaussian noise channel conditions.

5. The method according to claim 1, characterized in that, In step 2, the specific method for constructing the objective function is as follows: For a repeating accumulator encoder with a Combiner structure, the information transmission path is expanded to... k Parallel paths, of which k For integers greater than or equal to 1, the bitrate is expressed as the ratio of the reciprocal of the number of repetitions to the number of parallel paths; Based on the external information transfer functions established in step 1, the output mutual information from the channel node to the first variable node, the output mutual information from the first variable node to the check node, the output mutual information from the check node to the second variable node, the output mutual information fed back from the second variable node to the check node, the output mutual information from the check node to the first variable node, and the final output mutual information fed back from the first variable node to the channel node are constructed sequentially, thus obtaining the first... l The objective function after the next iteration contains the mutual information from the previous iteration. I Number of parallel paths k Number of repetitions q In addition to channel parameters, it also includes intermediate variables that depend on the previous iteration process.

6. The method according to claim 5, characterized in that, The first step described in step 2 l The objective function after the nth iteration is specifically expressed as: l The output mutual information of the next iteration is equal to a combination function of the initial output mutual information of the channel nodes and the feedback mutual information of the check nodes. This function includes the number of parallel paths. k Number of repetitions q Channel equivalent variance and the first l -1 iterations output the expression for mutual information.

7. The method according to claim 1, characterized in that, In step 3, the fixed point satisfies the following: when the number of iterations approaches infinity, the output mutual information converges to the smallest element in the solution set of the equation. The error probability corresponding to this smallest fixed point is an exponential function of negative two times the value of the fixed point with the natural constant e as the base. When the fixed point approaches 1, the error probability approaches 0, which represents the decoding success condition.

8. The method according to claim 1, characterized in that, In step 4, the specific method is as follows: [The text abruptly ends here, likely due to an incomplete sentence or a formatting error.] k Under fixed conditions, the steady-state objective function obtained in step 3 is transformed by rearranging terms, inverting the function, and squaring to derive the number of repetitions. q The parsing expression, which is composed of output mutual information. I Number of parallel paths k And the channel parameters are directly determined, without the need for iterative updates of intermediate variables; Combining the code rate formula, the smallest positive integer that satisfies the decoding success constraint is taken as the local optimal number of repetitions, and the corresponding local optimal code rate is calculated.

9. The method according to claim 8, characterized in that, The number of repetitions mentioned in step 4 q The derivation of the analytical expression includes: taking the inverse of both sides of the mutual information equation in the steady-state objective function, then squaring the equation, rearranging the terms, and finally obtaining the expression containing only output mutual information and the number of parallel paths. k The expression for the number of repetitions of the channel parameters.

10. The method according to claim 1, characterized in that, In step 5, the specific implementation method is as follows: substitute the decoding failure condition into the number of repetitions obtained in step 4. q The analytical expression is used to construct the set of repetition counts corresponding to decoding failures, i.e., the unreliable region; the absolute complement of this unreliable region is taken to obtain the set of repetition counts corresponding to successful decoding, i.e., the reliable region; the smallest positive integer in the reliable region is taken as the local optimal repetition count, and substituted into the code rate formula to obtain the local optimal code rate; the number of feasible parallel paths is then traversed. k Calculate each k The value corresponds to the local optimal number of repetitions and the local optimal bitrate. All local optimal bitrates are combined into a set, and the maximum value in this set is selected as the global optimal bitrate. The corresponding number of parallel paths and the number of repetitions are the global optimal number of parallel paths and the global optimal number of repetitions, respectively.

11. The method according to claim 10, characterized in that, The successful decoding constraint in step 5 is: the output mutual information approaches 1, at which point the system error probability approaches 0; the decoding failure constraint is: the output mutual information approaches 0, at which point the system cannot decode correctly.

12. The method according to claim 10, characterized in that, In step 5, all feasible parallel paths are traversed. k hour, k The value ranges from 1 to the preset maximum number of parallel paths, which is determined by system hardware resources and coding complexity constraints.

13. A rate optimization system for a repeating accumulator code containing a Combiner structure, characterized in that, include: The mutual information modeling module is used to establish extrinsic information transfer functions for variable nodes and check nodes under the conditions of infinite code length and Gaussian approximation, based on the extrinsic information transfer analysis method. The extrinsic information transfer function for variable nodes is expressed as: the output mutual information equals the variance of the input mutual information mapped by the J function. The extrinsic information transfer function for check nodes is expressed as: the output mutual information equals 1 minus the J function value corresponding to the input mutual information; the J function is the integral form of the Gaussian error function of the variance of the input mutual information. The iterative objective function building module is used to expand the information transmission path for repeating accumulator encoders with Combiner structures. k Parallel paths, of which k For integers greater than or equal to 1, the code rate is expressed as the ratio of the reciprocal of the number of repetitions to the number of parallel paths; based on the external information transfer functions established by the mutual information modeling module, the output mutual information relationships from the channel node to the first variable node, from the first variable node to the check node, from the check node to the second variable node, from the second variable node back to the check node, from the check node to the first variable node, and from the first variable node back to the channel node are constructed sequentially to obtain the first... l The objective function after the next iteration; The steady-state optimization module, based on fixed-point theory, aims to stabilize the system when the number of iterations approaches infinity, ensuring that the mutual information expression of each node is stable. This process utilizes fixed-point relationships to eliminate the dependence of intermediate variables on the iteration process, resulting in a value containing only the output mutual information. I Number of parallel paths k Number of repetitions q The steady-state objective function of the channel parameters is used, and an optimization objective function is established with the code rate maximization as the objective and successful decoding as the constraint. The analytical solution module is used to solve problems involving parallel paths. k Under fixed conditions, the steady-state objective function is transformed by rearranging terms, inverting the function, and performing squaring operations to derive the number of repetitions. q The parsing expression, which is composed of output mutual information. I Number of parallel paths k And the channel parameters are directly determined; combined with the code rate formula, the smallest positive integer that satisfies the decoding success constraint is taken as the local optimal number of repetitions, and the corresponding local optimal code rate is calculated; The global optimization module is used to substitute the decoding failure condition into the number of repetitions. q The parsing expression constructs unreliable regions, and the absolute complement is taken to obtain reliable regions. The smallest positive integer within a reliable region is selected as the locally optimal repetition count, and the locally optimal bitrate is calculated. All feasible parallel paths are then traversed. k Calculate each k The value corresponds to the local optimal number of repetitions and the local optimal bitrate. All local optimal bitrates are combined into a set, and the maximum value is selected as the global optimal bitrate. The corresponding number of parallel paths and the number of repetitions are the global optimal number of parallel paths and the global optimal number of repetitions, respectively.

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