CN105068931B - Single-particle soft error reliability calculation method for analyzing DSP software system - Google Patents

Abstract

A single-particle soft error reliability calculation method for analyzing a DSP software system is characterized by utilizing results of module division and module topological relation of the DSP software system, searching all paths between an initial module and a termination module in the module topological relation by using depth-first search, extracting a plurality of paths by using an importance sampling method and solving the single-particle soft error reliability of the DSP software system. The invention adopts a method of dividing and searching paths based on modules for engineering files, solves the problem of probability calculation of correct results output by a DSP system under the single event effect, selects partial path paths by using an importance sampling method, endows the paths with large integral contribution with larger importance weight, extracts more path samples in the part with larger importance weight, inhibits the influence of small weight paths on the system, increases the calculation efficiency, and ensures that the calculation results are more reliable because the extracted sample mean value is unbiased estimation of the overall mean value.

Description

A Reliability Calculation Method for Single Event Soft Errors for Analyzing DSP Software Systems

technical field

The invention relates to a reliability calculation method, in particular to a single particle soft error reliability calculation method for analyzing a DSP software system, and relates to the reliability calculation of a single particle effect DSP system, which can be used to guide and improve system reliability design, belonging to System reliability field.

Background technique

Electronic devices in the aerospace field are often impacted by high-energy particles in space to change the logic state of the circuit. This phenomenon is called the single event effect. The single event effect will pose a great threat to the safety of spacecraft, so people are very concerned about it. In this regard, it is desirable to obtain the reliability of electronic devices under the single event effect.

At present, there are many papers on how to evaluate the reliability due to single event effects. For example, the paper "A systematic methodology to compute the architectural vulnerabilityfactors for a high-performance microprocessor" examines the likelihood of system failure following the occurrence of soft errors. In order to quantify the masking factors of architecture and microarchitecture, the paper introduces architecture Vulnerability factor to express the probability of system failure after a soft error occurs in a certain processor structure. But this method only tracks the instructions and ignores the data, and the analysis granularity is too coarse.

SUMMARY OF THE INVENTION

The technical solution of the present invention is to overcome the deficiencies of the prior art and provide a single particle soft error reliability calculation method for analyzing a DSP software system. This method utilizes the results of the module division of the DSP software system and the module topology relationship, The depth-first search is used to find all paths between the start module and the end module in the module topology relationship, and the importance sampling method is used to extract several paths to obtain the single-particle soft error reliability of the DSP software system; The method based on module division and path search is adopted to solve the problem of probability calculation of the correct output of the DSP system under the single event effect. The importance sampling method is used to select some paths, and the paths that contribute more to the whole are given greater importance weights. , extract more path samples in the larger importance weight part, suppress the influence of the small weight path on the system, increase the calculation efficiency, and the sample mean is an unbiased estimate of the overall mean, making the calculation result more accurate to be reliable.

The technical solution of the present invention is: a single particle soft error reliability calculation method for analyzing a DSP software system, the steps are as follows:

(1) Divide the DSP software system into modules;

(2) establishing the topological relationship graph G(V, E) between the modules divided in step (1);

(3) Use depth-first traversal to search all paths between the start module and the end module in the module topology graph G(V, E);

(4) Set and calculate the relevant parameters of the correct output result of the module, the relevant parameters include the SERF value, the error rate of the current module itself subjected to single event flip, the propagation error rate, the probability of the module transitioning from the failure state to the normal state μ, Mal The continuous-time transition matrix of the Kov model and the probability of each module outputting the correct result;

(5) The importance sampling method is used to select the path and calculate the probability that the DSP system outputs the correct result as a whole.

In the described step (1), the DSP software system is divided into modules; the concrete steps are:

(1-1) Use the TI disassembly tool to analyze the executable .out file of the software system to generate a disassembly file; then read the disassembly file and analyze the assembly code of the DSP software system;

(1-2) Scan the assembly code of the DSP software system for the first time, identify each function under the DSP software system engineering according to the naming rules of the functions in the assembly code, and obtain each function according to the function call instruction inside each function The calling relationship between;

(1-3) Scan the assembly code of the DSP software system for the second time, analyze the assembly instructions in each function obtained by the first scan, determine the entry instructions of each module in each function, and record the corresponding entry instructions the address of;

(1-4) Scan the assembly code of the DSP software system for the third time, divide the modules in each function, and determine the scope of the module according to the entry instruction address information of each module obtained in step (1-3), thereby completing the DSP software system module division.

In the step (2), establish the topological relationship graph G(V, E) between the modules divided in the step (1); specifically: first obtain the relationship between the modules in each function, and then according to the step The calling relationship between the functions obtained in (1-2) obtains the topological relationship between the modules in the entire DSP software system engineering; the directed graph G(V, E) in the data structure is used to represent the topological relationship of the modules, where the point The set V={v _i |i=1,2,,...,M} represents a module, and E represents a connection relationship between two modules.

In the described step (3), depth-first traversal is used to search all paths between the start module and the end module in the module topology relation graph G(V, E); the steps are:

(3-1) Determine the start module and the end module of the module topology relation graph G(V, E); the start module of the topological relation graph G(V, E) is the first module of the main function; the described The termination module of the topological relationship graph G(V, E) is a module without a successor module;

(3-2) Use the C language standard library function malloc function to apply for a memory space of the size of a module structure in the computer memory to store the data and pointer information of the module;

(3-3) Push the start module into the stack and set it as accessed;

(3-4) judge whether the current stack top module is a termination module, if it is a termination module, then execute step (3-5), otherwise execute step (3-6);

(3-5) Create a new array to save each element in the stack, all elements in the array form a path, and execute step (3-7);

(3-6) Check whether the module at the top of the stack has a subsequent and unvisited module, if so, randomly select one of the succeeding and unvisited modules and push it into the stack, and set the pushed module as visited, and return Step (3-4), otherwise, execute step (3-7);

(3-7) Check whether the element in the stack is empty, if so, end the execution, otherwise, pop the top module of the stack from the stack and set it as not accessed, and execute step (3-6).

The SERF value is a soft error robustness factor, which represents the probability of visible errors caused by each bit flip under the single event effect, specifically by the formula:

Given, where ACE represents the bit whose execution result will affect the output result of the application; B _H represents the number of bits of the hardware structure H; N represents the number of cycles of the CPU; the numerator represents the hardware structure H in N instruction cycles The total number of ACE bits; the denominator represents the total number of bits in the hardware structure H in N instruction cycles;

The error rate of the current module itself subject to single event flipping is specifically defined by the formula:

λ _seu = SERF × R _p × B

is given, where R _p is the single-particle turnover rate, that is, the probability that the data of the DSP software system will be turned over after being hit by high-energy particles; B is the sum of the code size and data size of the current module program storage area.

The propagation error rate is specified by the formula:

is given, where _λj represents the error rate of the _jth module in all modules entering the current module, and nj is its corresponding out-degree; the out-degree is the total number of other modules directly reached by a module.

The probability μ of the module transitioning from the failed state to the normal state is specified by the formula:

is given, where T _rc represents the module cycle repair interval; τ represents the time required to perform a DSP software system reconstruction.

The continuous-time transition matrix of the Markov model is specified by the formula:

is given, where T represents the continuous-time transition matrix, Δt represents the time interval, where λ is the error rate of the current module and λ=λ _seu +λ _prop .

The probability of each module outputting the correct result is given by the formula:

given.

In the step (5), the importance sampling method is adopted to select the path and calculate the probability of the DSP system outputting the correct result as a whole, specifically:

(5-1) The number of all paths between the start module and the end module obtained in step (3) is S;

(5-2) Number each path between the start module and the end module, 1, 2, ..., S in sequence;

(5-3) Calculate the importance weight of each path, specifically by the formula:

is given, where w _i is the importance weight of the i-th path; l _i represents the number of modules contained in the i-th path, and n _j represents the out-degree of the j-th module in the i-th path;

(5-4) Sort all the paths according to the importance weights of the paths in step (5-3);

(5-5) Divide the sorted paths into k segments evenly, then the number of paths in each segment is:

(5-6) Calculate the sampling rate of each path, specifically by the formula:

is given, where η _i is the sampling rate of the i-th path, and w _j is the importance weight of the j-th path in the i-th path;

(5-7) Randomly sample each path, and the number of samples to be sampled is determined by the formula:

n _i =S×η _i i =1,2,..,k;

given, where n _i is the number of sampling samples of the i-th path;

(5-8) Read the probability that each module in each path in the sample works normally;

(5-9) Calculate the probability that all paths between the start module and the end module output the correct result, specifically by the formula:

为m段中第i条路径的第j个模块输出正确结果的概率；given, where n _m is the number of samples sampled in the mth segment, that is, the number of paths; P _i ^m is the probability that the i-th path between the start module and the termination module in the mth segment outputs the correct result;

The probability of outputting the correct result for the jth module of the ith path in the m segment;

即为DSP软件系统整体输出正确结果的概率，具体由公式：(5-10) Calculate the weighted mean of the correct results of the n paths extracted between the start module and the end module

It is the probability that the DSP software system outputs the correct result as a whole, which is specified by the formula:

其中

in

given.

The beneficial effects of the present invention compared with the prior art are:

(1) Compared with the traditional calculation method, the present invention adopts the depth-first traversal algorithm to search the path on the basis of the DSP topology relationship diagram, which can make full use of the information of the topology relationship diagram, making the path search more accurate, and solving the problem of single Evaluation of system function due to particle soft errors.

(2) The present invention introduces the importance sampling method to select partial paths, assigns greater importance weights to the paths with greater overall contribution, and extracts more path samples from the larger importance weights, suppressing small weights The influence of the value path on the system increases the computational efficiency, and the sample mean is an unbiased estimate of the population mean, making the calculation result more reliable.

Description of drawings

Fig. 1 is the flow chart of the method for calculating the reliability probability of single particle soft error reliability of the DSP system that adopts importance sampling in the present invention;

Fig. 2 is a schematic diagram of a module structure;

Figure 3 module singly linked list storage form;

Figure 4 is a schematic diagram of the module relationship of the project;

Figure 5 is a flow chart of the module relationship of the search project.

Detailed ways

The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

The core idea of the present invention is to find the path based on depth-first search on the divided topological relationship graph of modules, then use importance sampling to sample all paths, and use the sample value to evaluate the single-particle soft error reliability of the DSP system. Therefore, firstly, the module division and module topology relationship are established according to the existing module division method; then, all paths of the module topology relationship are searched using depth-first traversal; finally, the importance sampling method is used to extract samples from all paths to solve the sample path. The weighted average of , obtains the single-event soft error reliability of the DSP system.

Fig. 1 is the method flow chart of the present invention, as can be seen from Fig. 1, a kind of single particle soft error reliability calculation method of analyzing DSP software system proposed by the present invention, its realization steps are as follows:

(1) Divide the DSP software system into modules; specifically:

(1-1) Use the TI disassembly tool to analyze the executable .out file of the software system to generate a disassembly file; then read the disassembly file and analyze the assembly code of the DSP software system;

(1-2) Scan the assembly code of the DSP software system for the first time, identify each function under the DSP software system engineering according to the naming rules of the functions in the assembly code, and obtain each function according to the function call instruction inside each function The calling relationship between the functions and the calling relationship between the functions are shown in Figure 4, and each letter in the figure represents different functions;

(1-3) Scan the assembly code of the DSP software system for the second time, analyze the assembly instructions in each function obtained by the first scan, determine the entry instructions of each module in each function, and record the corresponding entry instructions the address of;

(1-4) Scan the assembly code of the DSP software system for the third time, divide the modules in each function, and determine the scope of the module according to the entry instruction address information of each module obtained in step (1-3), thereby completing the The DSP software system is divided into modules, and a structure is established to store the information of the module. The schematic diagram of the structure is shown in Figure 2. The data area represents the information of the corresponding module, and the pointer area stores the address of the adjacent module.

(2) Establish the topological relationship graph G(V, E) between the modules divided in step (1); specifically:

Establish a topological relationship graph G(V, E) between the modules divided in step (1); specifically: first obtain the relationship between modules in each function, and then obtain according to step (1-2) The calling relationship between the various functions of the DSP can obtain the topology relationship between modules in the entire DSP software system engineering; the schematic diagram of the algorithm is shown in Figure 5. First, the module topology relationship of each function is obtained, and then each module is analyzed from the main function. If there are modules To call other functions, the function call relationship obtained in Figure 4, insert the module topology relationship of the called function into this module, continue to analyze the information of the called function module, until the function module of the entire software is analyzed, and the DSP software is obtained. Topological relationship between modules in systems engineering; the topological relationship of modules is represented by a directed graph G(V, E) in the data structure. The point set V={v _i |i=1,2,,...,M} represents the module, and E represents the connection between the two modules. The schematic diagram of the storage structure of the topology map is shown in Figure 3. The data information of each module and all adjacent modules of the module are stored in the form of a linked list.

(3) Use depth-first traversal to search for all paths between the start module and the end module in the module topology graph G(V, E); specifically:

(3-1) Determine the start module and the end module of the module topology relation graph G(V, E); the start module of the topological relation graph G(V, E) is the first module of the main function; the described The termination module of the topological relationship graph G(V, E) is a module without a successor module;

(3-2) Use the C language standard library function malloc function to apply for a module structure in the computer memory (the module structure is used to store various information of the module, including the start address, end address and The memory space of the size of the successor module of the module in the topology diagram is used to store the data and pointer information of the module;

(3-3) Push the start module into the stack and set it as accessed;

(3-4) judge whether the current stack top module is a termination module, if so, execute step (3-5), otherwise execute step (3-6);

(3-5) Create a new array to save each element (module) in the stack, all elements in the array form a path, and execute step (3-7);

(3-6) Check whether the module at the top of the stack has a subsequent and unvisited module, if so, randomly select one of the succeeding and unvisited modules and push it into the stack, and set the pushed module as visited, and return Step (3-4), otherwise, execute step (3-7);

(3-7) Check whether the element in the stack is empty, if so, end the execution, otherwise, pop the top module of the stack from the stack and set it as not accessed, and execute step (3-6).

(4) Set and calculate the relevant parameters of the correct output result of the module, the relevant parameters include the SERF value, the error rate of the current module itself subjected to single event flip, the propagation error rate, the probability of the module transitioning from the failure state to the normal state μ, Mal The continuous-time transition matrix of the Kov model and the probability of each module outputting the correct result;

The SERF (Soft Error Robust Factor) value is a soft error robustness factor, which represents the probability that each bit flip causes a visible error (referring to an output error that can be detected) under the single event effect, specifically by the formula:

Given, where ACE represents the bit whose execution result will affect the output result of the application; B _H represents the number of bits of the hardware structure H; N represents the number of cycles of the CPU; the numerator represents the hardware structure H in N instruction cycles The total number of ACE bits; the denominator represents the total number of bits in the hardware structure H in N instruction cycles;

The error rate of the current module itself subject to single event flipping is specifically defined by the formula:

λ _seu = SERF × R _p × B

is given, where R _p is the single-particle turnover rate, that is, the probability that the data of the DSP software system will be turned over after being hit by high-energy particles; B is the sum of the code size and data size of the current module program storage area.

The propagation error rate is specified by the formula:

is given, where _λj represents the error rate of the _jth module in all modules entering the current module, and nj is its corresponding out-degree; the out-degree is the total number of other modules directly reached by a module.

The probability μ of the module transitioning from the failed state to the normal state is specified by the formula:

is given, where T _rc represents the module cycle repair interval; τ represents the time required to perform a DSP software system reconstruction, and for the DSP of the model C6701, its value is 6.378ms.

The continuous-time transition matrix of the Markov model is specified by the formula:

is given, where T represents the continuous-time transition matrix, Δt represents the time interval, where λ is the error rate of the current module and λ=λ _seu +λ _prop .

Based on the transition matrix, the probability that the module is in the normal working state and the failure state at time t+Δt is obtained. The mathematical expression is:

[p _0i (t+Δt),p _1i (t+Δt)]=[p _0i (t),p _1i (t)]T

Among them, p _0i (t) represents the probability that the module is still working normally under the single event effect at time t, and p _1i (t) represents the probability that the module is in a failure state under the single event effect at time t.

The probability calculation formula is obtained by deforming the above equation as follows:

p _0i (t) As time t increases, the probability of this module output error due to single event flipping increases and the probability of normal operation decreases. According to the above formula, the probability of each module outputting the correct result can be calculated, which is recorded as p _0i (t), where i represents each divided module.

So the probability of each module outputting the correct result is obtained:

given.

(5) The importance sampling method is used to select the path and calculate the probability that the DSP system outputs the correct result as a whole. Specifically:

(5-1) The number of all paths between the start module and the end module obtained in step (3) is S;

(5-2) Number each path between the start module and the end module, 1, 2, ..., S in sequence;

(5-3) Calculate the importance weight of each path, specifically by the formula:

is given, where w _i is the importance weight of the i-th path; l _i represents the number of modules contained in the i-th path, and n _j represents the out-degree of the j-th module in the i-th path;

(5-4) Sort all the paths according to the importance weights of the paths in step (5-3);

(5-5) Divide the sorted paths into k segments evenly, then the number of paths in each segment is:

(5-6) Calculate the sampling rate of each path, specifically by the formula:

is given, where η _i is the sampling rate of the i-th path, and w _j is the importance weight of the j-th path in the i-th path;

(5-7) Randomly sample each path, and the number of samples to be sampled is determined by the formula:

n _i =S×η _i i =1,2,..,k;

given, where n _i is the number of sampling samples of the i-th path;

(5-8) Read the probability that each module in each path in the sample works normally;

(5-9) Calculate the probability that all paths between the start module and the end module output the correct result, specifically by the formula:

为m段中第i条路径的第j个模块输出正确结果的概率；is given, where n _m is the number of samples sampled in the mth segment, that is, the number of paths; P _i ^m is the probability that the i-th path between the start module and the termination module in the mth segment outputs the correct result;

The probability of outputting the correct result for the jth module of the ith path in the m segment;

即为DSP软件系统整体输出正确结果的概率，具体由公式：(5-10) Calculate the weighted mean of the correct results of the n paths extracted between the start module and the end module

It is the probability that the DSP software system outputs the correct result as a whole, which is specified by the formula:

其中

in

given.

Contents that are not described in detail in the specification of the present invention belong to the well-known technology of those skilled in the art.

Claims (10)

1. a single particle soft error reliability calculation method of analyzing DSP software system, is characterized in that step is as follows: (1) Divide the DSP software system into modules; (2) establishing the topological relationship graph G(V, E) between the modules divided in step (1); (3) Use depth-first traversal to search all paths between the start module and the end module in the module topology graph G(V, E); (4) Set and calculate the relevant parameters of the correct output result of the module, the relevant parameters include the SERF value, the error rate of the current module itself subjected to single event flip, the propagation error rate, the probability of the module transitioning from the failure state to the normal state μ, Mal The continuous-time transition matrix of the Kov model and the probability of each module outputting the correct result; (5) The importance sampling method is used to select the path and calculate the probability that the DSP system outputs the correct result as a whole. 2. a kind of single particle soft error reliability calculation method of analyzing DSP software system according to claim 1, is characterized in that: in described step (1), DSP software system is carried out module division; Concrete steps are: (1-1) Use the TI disassembly tool to analyze the executable .out file of the software system to generate a disassembly file; then read the disassembly file and analyze the assembly code of the DSP software system; (1-2) Scan the assembly code of the DSP software system for the first time, identify each function under the DSP software system engineering according to the naming rules of the functions in the assembly code, and obtain each function according to the function call instruction inside each function The calling relationship between; (1-3) Scan the assembly code of the DSP software system for the second time, analyze the assembly instructions in each function obtained by the first scan, determine the entry instructions of each module in each function, and record the corresponding entry instructions the address of; (1-4) Scan the assembly code of the DSP software system for the third time, divide the modules in each function, and determine the scope of the module according to the entry instruction address information of each module obtained in step (1-3), thereby completing the DSP software system module division. 3. the single particle soft error reliability calculation method of a kind of analysis DSP software system according to claim 2, is characterized in that: in described step (2), establishes between each module divided in step (1) Topological relationship graph G(V, E); specifically: first obtain the relationship between the modules in each function, and then obtain the entire DSP software system engineering according to the calling relationship between the functions obtained in step (1-2). Topological relationship between modules; the topological relationship of modules is represented by a directed graph G(V, E) in the data structure, where the point set V={v _i |i=1,2,,...,M} represents module, E represents the connection relationship between two modules. 4. the single particle soft error reliability calculation method of a kind of analysis DSP software system according to claim 1 or 2 or 3, is characterized in that: in described step (3), utilize depth-first traversal to search for module topology relation graph G All paths between the start module and the end module in (V,E); the steps are: (3-1) Determine the start module and the end module of the module topology relation graph G(V, E); the start module of the topological relation graph G(V, E) is the first module of the main function; the described The termination module of the topological relationship graph G(V, E) is a module without a successor module; (3-2) Use the C language standard library function malloc function to apply for a memory space of the size of a module structure in the computer memory to store the data and pointer information of the module; (3-3) Push the start module into the stack and set it as accessed; (3-4) judge whether the current stack top module is a termination module, if it is a termination module, then execute step (3-5), otherwise execute step (3-6); (3-5) Create a new array to save each element in the stack, all elements in the array form a path, and execute step (3-7); (3-6) Check whether the module at the top of the stack has a subsequent and unvisited module, if so, randomly select one of the succeeding and unvisited modules and push it into the stack, and set the pushed module as visited, and return Step (3-4), otherwise, execute step (3-7); (3-7) Check whether the element in the stack is empty, if so, end the execution, otherwise, pop the top module of the stack from the stack and set it as not accessed, and execute step (3-6). 5. the single particle soft error reliability calculation method of a kind of analysis DSP software system according to claim 1, is characterized in that: described SERF value is soft error robustness factor, what represents is each under single particle effect. The probability of a bit flip causing a visible error is given by the formula:

Given, where ACE represents the bit whose execution result will affect the output result of the application; B _H represents the number of bits of the hardware structure H; N represents the number of cycles of the CPU; the numerator represents the hardware structure H in N instruction cycles The total number of ACE bits; the denominator represents the total number of bits in the hardware structure H in N instruction cycles; The error rate of the current module itself subject to single event flipping is specifically defined by the formula: λ _seu = SERF × R _p × B is given, where R _p is the single-particle turnover rate, that is, the probability that the data of the DSP software system will be turned over after being hit by high-energy particles; B is the sum of the code size and data size of the current module program storage area. 6. the single particle soft error reliability calculation method of a kind of analysis DSP software system according to claim 5, is characterized in that: described propagation error rate, specifically by formula:

is given, where _λj represents the error rate of the _jth module in all modules entering the current module, and nj is its corresponding out-degree; the out-degree is the total number of other modules directly reached by a module. 7. a kind of single particle soft error reliability calculation method of analyzing DSP software system according to claim 6, is characterized in that: the probability μ that described module transfers from failure state to normal state is specifically by formula:

is given, where T _rc represents the module cycle repair interval; τ represents the time required to perform a DSP software system reconstruction. 8. the single particle soft error reliability calculation method of a kind of analysis DSP software system according to claim 7, is characterized in that: the continuous time transition matrix of described Markov model is specifically by formula:

is given, where T represents the continuous-time transition matrix, Δt represents the time interval, where λ is the error rate of the current module and λ=λ _seu +λ _prop . 9. the single particle soft error reliability calculation method of a kind of analysis DSP software system according to claim 8, is characterized in that: the probability that described each module outputs correct result by formula:

given. 10. a kind of single particle soft error reliability calculation method for analyzing DSP software system according to claim 1, is characterized in that: in described step (5), adopt importance sampling method to select path and calculate DSP system overall output is correct The probability of the outcome, specifically: (5-1) The number of all paths between the start module and the end module obtained in step (3) is S; (5-2) Number each path between the start module and the end module, 1, 2, ..., S in sequence; (5-3) Calculate the importance weight of each path, specifically by the formula:

is given, where w _i is the importance weight of the i-th path; l _i represents the number of modules contained in the i-th path, and n _j represents the out-degree of the j-th module in the i-th path; (5-4) Sort all the paths according to the importance weights of the paths in step (5-3); (5-5) Divide the sorted paths into k segments evenly, then the number of paths in each segment is:

(5-6) Calculate the sampling rate of each path, specifically by the formula:

is given, where η _i is the sampling rate of the i-th path, and w _j is the importance weight of the j-th path in the i-th path; (5-7) Randomly sample each path, and the number of samples to be sampled is determined by the formula: n _i =S×η _i i =1,2,..,k; given, where n _i is the number of sampling samples of the i-th path; (5-8) Read the probability that each module in each path in the sample works normally; (5-9) Calculate the probability that all paths between the start module and the end module output the correct result, specifically by the formula:

is given, where n _m is the number of samples sampled in the mth segment, that is, the number of paths; P _i ^m is the probability that the i-th path between the start module and the termination module in the mth segment outputs the correct result;

The probability of outputting the correct result for the jth module of the ith path in the m segment; (5-10) Calculate the weighted mean of the correct results of the n paths extracted between the start module and the end module

It is the probability that the DSP software system outputs the correct result as a whole, which is specified by the formula:

in

given.

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