A convolutional code energy-saving decoding method based on path optimization

Abstract

The invention belongs to the field of convolutional code decoding, and specifically is a convolutional code energy-saving decoding method based on path optimization. The method comprises signal input, signal encoding, weighted graph drawing, graph optimization and bidirectional optimization. The invention adopts a hidden Markov model based on Hamming distance, converts a hidden state graph into a weighted graph, converts the similarity relationship between prediction estimation results in the hidden state graph into the distance between prediction estimations, draws a weighted graph, thereby converting the problem into a path problem, which is easy to calculate. The invention creatively designs a pruning operation based on a smooth maximum operator, optimizes and prunes the weighted graph, removes redundant paths between nodes of the weighted graph, and optimizes the weighted graph. On the basis of optimizing the weighted graph, a bidirectional A* algorithm is introduced, and decoding is optimized in a path optimal search mode, thereby reducing the computational complexity, increasing the adaptability to convolutional codes with long constraint lengths, and reducing the consumption of computational and storage resources.

Description

Technical Field

[0001] The invention belongs to the field of convolutional code decoding, and in particular is a convolutional code energy-saving decoding method based on path optimization. Background Art

[0002] Convolutional code is a coding and decoding technology used for data transmission and communication. This coding technology increases the reliability of data by introducing redundant data to detect and correct errors during channel transmission. Convolutional code decoding is the process of decoding the received codeword to restore the original information. Traditional convolutional code decoding algorithms require a lot of computing and storage resources when processing convolutional codes with long constraint lengths, and have high computational complexity. Summary of the invention

[0003] In view of the above situation, in order to overcome the defects of the prior art and the problem that the prior decoding technology requires a large amount of computing and storage resources, the present invention adopts a hidden Markov model based on the Hamming distance, converts the hidden state graph drawn by the traditional algorithm into a weighted graph, converts the similarity relationship between the prediction estimates in the hidden state graph into the distance between the prediction estimates, and draws a weighted graph, thereby converting the problem into a path problem, which is easy to calculate; the present invention creatively designs the pruning operation based on the smooth maximum operator, optimizes the pruning of the weighted graph, removes redundant paths between the nodes of the weighted graph, and optimizes the weighted graph. On the basis of optimizing the weighted graph, a bidirectional A* algorithm is introduced to optimize the decoding in a way of optimal path search, thereby reducing the computational complexity, increasing the adaptability of the decoding method to convolutional codes with long constraint lengths, and reducing the consumption of computing and storage resources.

[0004] The technical solution adopted by the present invention is as follows: a convolutional code energy-saving decoding method based on path optimization, specifically comprising the following steps:

[0005] Step S1: signal input, the signal to be convolved, i.e. the original signal, is input into the encoder;

[0006] Step S2: signal encoding, using an encoder to encode the original signal to obtain an encoded signal;

[0007] Step S3: weighted graph drawing, using a hidden Markov model based on Hamming distance, drawing a hidden state graph between the encoded signal and the original signal at different times, and converting the hidden state graph into a weighted graph;

[0008] Further, step S3 specifically includes the following steps:

[0009] Step S31: using a hidden Markov model, performing n different prediction estimates on the coded signal to obtain n current moment prediction states;

[0010] Step S32: using the hidden Markov model, perform a prediction and estimation on all states at the current moment, and obtain n predicted states at the next moment;

[0011] Step S33: repeat step S32 until the predicted state is equal to the original signal, and repeat the step m times, that is, after a total of m*n prediction estimates are made, the decoding is successful;

[0012] Step S34: Draw a weighted graph, connect all predicted states at all different moments, and use the Hamming distance function to calculate the Hamming distance of all connections, define all predicted states as nodes of the graph, define all connections between nodes as edges of the graph, and define the Hamming distance as the length of the edge, to obtain a weighted graph G, G=(V, E), where V is a set of nodes and E is a set of edges;

[0013] Step S4: graph optimization, using a pruning operation based on a smooth maximum operator to optimize the weighted graph to obtain an optimized weighted graph;

[0014] Further, step S4 specifically includes the following steps:

[0015] Step S41: Cost matrix design, designing a cost matrix with dimension V*V ∈R V×V Represents the edge cost in the weighted graph, that is, the length of the edge between nodes;

[0016] Step S42: Design a smoothing maximum operator, the formula used is as follows:

[0017] ;

[0018] ;

[0019] Where v is the input value, For the Input values, is the preset threshold, To preset the cumulative number of times, represents a natural number, and is the designed smooth maximum operator;

[0020] Step S43: Design a loop algorithm, the loop algorithm input is the cost matrix , the output is the probability ∈[0, 1] V×V×V , the loop design is as follows:

[0021] Step S431: Input the initial smoothing probability, the formula used is as follows:

[0022] P[ i ， j ， k ]= 1 ， if i = k and M[ i ， j ]<∞ 0 ， otherwise ;

[0023] In the formula, P[ i ， j ， k ] Represents the smoothing probability, specifically represents Node is a node in the path With Node The probability of the shortest intermediate node between is the cost matrix, M[ i ， j ] Representative Node With Node The length of the side between;

[0024] Step S432: When When the value of is 0 to V-1, execute step S433;

[0025] Step S433: When When the value of is 0 to V-1, execute step S434;

[0026] Step S434: When When the value of is 0 to V-1, execute step S435;

[0027] Step S435: Calculate using the smoothing maximum operator Node is a node in the path With Node The smoothing probability of the shortest intermediate node between is as follows:

[0028] P[ i ， j ， k ]= Φ β (M[ i ， k ]+M[ k ， j ]) ;

[0029] P[ i ， j ， c ]= Φ β (M[ i ， j ]) ， ∀ c < k and c = i ;

[0030] M[ i ， j ]= mi n β (M[ i ， k ]+M[ k ， j ]) ;

[0031] In the formula, and is the designed smooth maximum operator, is the intermediate variable, is the cost matrix, M[ i ， j ] Representative Node With Node The length of the side between P[ i ， j ， k ] represent Node is a node in the path With Node The smoothing probability of the shortest intermediate node between;

[0032] Step S436: When =V-1, =V-1 and =V-1, the loop ends and all smoothed probabilities are output;

[0033] Step S44: Bring all connected nodes in the weighted graph G into the loop and output all final smoothing probabilities. A smoothing probability of 0 represents a node With Node There is no better intermediate node, and the smoothing probability is 1, which means Node is Node With Node The intermediate node with the shortest path between them;

[0034] Step S45: Graph pruning: Prune all smoothing probabilities that are not 0 or 1. Node and contains The edges of the nodes are eliminated to obtain an optimized weighted graph;

[0035] Step S5: Bidirectional optimization, using the bidirectional A* algorithm, with the encoded signal and the original signal as the starting node and the end node respectively, bidirectionally searching for the optimal path on the optimized weighted graph to obtain the final optimal path; the hidden Markov model corresponding to the final optimal path is the optimal decoding path.

[0036] The beneficial effects achieved by the present invention using the above scheme are as follows:

[0037] (1) In order to solve the problem that existing decoding technologies require a large amount of computing and storage resources, the present invention adopts a hidden Markov model based on Hamming distance, converts the hidden state graph drawn by the traditional algorithm into a weighted graph, converts the similarity relationship between the prediction estimates in the hidden state graph into the distance between the prediction estimates, and draws a weighted graph, thereby converting the problem into a path problem, which is easy to calculate;

[0038] (2) The creative design of the present invention is based on the pruning operation of the smooth maximum operator to optimize the pruning of the weighted graph, remove the redundant paths between the nodes of the weighted graph, and optimize the weighted graph. On the basis of the optimized weighted graph, the bidirectional A* algorithm is introduced to optimize the decoding in the form of optimal path search, thereby reducing the computational complexity, increasing the adaptability of the decoding method to convolutional codes with long constraint lengths, and reducing the consumption of computing and storage resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 A flow chart of a convolutional code energy-saving decoding method based on path optimization provided by the present invention;

[0040] Figure 2 is a flow chart of step S4;

[0041] Figure 3 is a schematic diagram of the hidden state diagram;

[0042] Figure 4 A schematic diagram of a weighted graph.

[0043] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention. DETAILED DESCRIPTION

[0044] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments; based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0045] Example 1, see Figures 1 to 4 , a convolutional code energy-saving decoding method based on path optimization, characterized in that: it specifically comprises the following steps:

[0046] Step S1: Signal input, input the character string 110011, i.e. the original signal, into the encoder;

[0047] Step S2: signal encoding, using an encoder to encode the original signal to obtain an encoded signal 001100;

[0048] Step S3: weighted graph drawing, using a hidden Markov model based on Hamming distance, drawing a hidden state graph between the encoded signal and the original signal at different times, and converting the hidden state graph into a weighted graph, specifically including the following steps:

[0049] Step S31: using the hidden Markov model, perform four different prediction estimates on the coded signal to obtain four current prediction states;

[0050] Step S32: using the hidden Markov model, a prediction is made for each of the states at the current moment to obtain four predicted states at the next moment;

[0051] Step S33: repeat step S32 until the predicted state is equal to the original signal, and repeat the step 3 times, that is, decoding is successful after a total of 12 prediction estimates;

[0052] Step S34: Draw a weighted graph, connect all predicted states at all different moments, and use the Hamming distance function to calculate the Hamming distance of all connections, define all predicted states as nodes of the graph, define all connections between nodes as edges of the graph, and define the Hamming distance as the length of the edge, to obtain a weighted graph G, G=(V, E), where V is a set of nodes and E is a set of edges;

[0053] Step S4: graph optimization, using a pruning operation based on a smooth maximum operator to optimize the weighted graph to obtain an optimized weighted graph;

[0054] Step S5: Bidirectional optimization, using the bidirectional A* algorithm, with the encoded signal and the original signal as the starting node and the end node respectively, bidirectionally searching for the optimal path on the optimized weighted graph to obtain the final optimal path; the hidden Markov model corresponding to the final optimal path is the optimal decoding path.

[0055] By performing the above operations, in order to address the problem that existing decoding technologies require a large amount of computing and storage resources, the present invention adopts a hidden Markov model based on Hamming distance, converts the hidden state graph drawn by the traditional algorithm into a weighted graph, converts the similarity relationship between the prediction estimates in the hidden state graph into the distance between the prediction estimates, and draws a weighted graph, thereby converting the problem into a path problem, which is easy to calculate.

[0056] Embodiment 2: This embodiment is based on the above embodiment, and the Hamming distance function specifically includes the following steps:

[0057] Step S341: determining two character strings, determining two character strings to be compared, that is, predicted states at two different moments;

[0058] Step S342: Compare the two strings character by character, starting from the first character, and compare the characters at the same position of the two strings one by one;

[0059] Step S343: Calculate the number of different characters. During the comparison process, if it is found that the characters at the corresponding positions of the two character strings are different, the number of different characters is increased by one.

[0060] Step S344: Compare character by character, repeating steps S342 and S343 until all characters are compared;

[0061] Step S345: Calculate the Hamming distance, the final Hamming distance is the number of different characters found in the comparison process;

[0062] Step S346: Taking two predicted states as an example, the Hamming distance is calculated. 101100 and 010010 are predicted states at different times, and their Hamming distance is 5.

[0063] By performing the above operations, the gaps between the predicted states at different times are compared in the form of Hamming distance, and the character-level gaps are converted into Hamming distances. The larger the distance, the greater the difference in the strings, which means that the cost required for the prediction estimation is greater. By converting the cost in the form of Hamming distance, the original problem can be converted into a path optimization problem, which is easy to calculate and optimize.

[0064] Example 3, see Figure 4 This embodiment is based on the above embodiment, and step S4 specifically includes the following steps:

[0065] Step S41: Cost matrix design, designing a cost matrix with a dimension of 12*12 ∈R V×V Represents the edge cost in the weighted graph, that is, the length of the edge between nodes;

[0066] Step S42: Design a smoothing maximum operator, the formula used is as follows:

[0067] ;

[0068] ;

[0069] Where v is the input value, For the Input values, is the preset threshold, To preset the cumulative number of times, represents a natural number, and is the designed smooth maximum operator;

[0070] Step S43: Design a loop algorithm, the loop algorithm input is the cost matrix And the weighted graph G, the output is the smoothed probability ;

[0071] Step S44: Bring all connected nodes in the weighted graph G into the loop and output all final smoothing probabilities. A smoothing probability of 0 represents a node With Node There is no better intermediate node, and the smoothing probability is 1, which means Node is Node With Node The intermediate node with the shortest path between them;

[0072] Step S45: Graph pruning: Prune all smoothing probabilities that are not 0 or 1. Node and contains The edges of the nodes are eliminated, the original 3*4 graph is pruned, and 5 nodes in the graph are removed, that is, five redundant prediction states are removed to obtain an optimized weighted graph.

[0073] By performing the above operations, the present invention creatively designs a pruning operation based on a smooth maximum operator to optimize the pruning of the weighted graph, remove redundant paths between the nodes of the weighted graph, and optimize the weighted graph. On the basis of optimizing the weighted graph, a bidirectional A* algorithm is introduced to optimize the decoding in a path-optimal search manner, thereby reducing the computational complexity, increasing the adaptability of the decoding method to convolutional codes with long constraint lengths, and reducing the consumption of computing and storage resources.

[0074] Embodiment 4: This embodiment is based on the above embodiment. In step S43, the loop algorithm specifically includes the following steps:

[0075] Step S431: Input the initial smoothing probability, the formula used is as follows:

[0076] P[ i ， j ， k ]= 1 ， if i = k and M[ i ， j ]<∞ 0 ， otherwise ;

[0077] In the formula, P[ i ， j ， k ] Represents the smoothing probability, specifically represents Node is a node in the path With Node The probability of the shortest intermediate node between is the cost matrix, M[ i ， j ] Representative Node With Node The length of the side between;

[0078] Step S432: When When the value of is 0 to 11, execute step S433;

[0079] Step S433: When When the value of is 0 to 11, execute step S434;

[0080] Step S434: When When the value of is 0 to 11, execute step S435;

[0081] Step S435: Calculate using the smoothing maximum operator Node is a node in the path With Node The smoothing probability of the shortest intermediate node between is as follows:

[0082] P[ i ， j ， k ]= Φ β (M[ i ， k ]+M[ k ， j ]) ;

[0083] P[ i ， j ， c ]= Φ β (M[ i ， j ]) ， ∀ c < k and c = i ;

[0084] M[ i ， j ]= mi n β (M[ i ， k ]+M[ k ， j ]) ;

[0085] In the formula, and is the designed smooth maximum operator, is the intermediate variable, is the cost matrix, M[ i ， j ] Representative Node With Node The length of the side between P[ i ， j ， k ] represent Node is a node in the path With Node The smoothing probability of the shortest intermediate node between;

[0086] Step S436: When =11, =11 and =11 are all satisfied, the loop ends and all smoothed probabilities are output.

[0087] Embodiment 5: This embodiment is based on the above embodiment, and the bidirectional A* algorithm specifically includes the following steps:

[0088] Step Q1: Mark the starting node, i.e., the coded signal 001100, as the "current node" and calculate the cost value and estimated cost value of the starting node

[0089] Step Q2 marks the target node, i.e. the original signal 110011, as the "target current node" and calculates its cost value and estimated cost value;

[0090] Step Q3: Add the start node and the target node to two sets of nodes to be visited, and initialize two empty sets of visited nodes;

[0091] Step Q4: Loop until the shortest path is found, and select the node with the smallest "f value" from the starting node set as the current node;

[0092] Step Q5: If the current node is also in the target node set, the paths meet, the shortest path is found, and the search stops. Otherwise, the current node is removed from the starting node set and added to the visited node set;

[0093] Step Q6: For each unvisited node among the neighboring nodes of the current node, calculate their cost values, estimated cost values ​​and “f values”;

[0094] Step Q7: If the adjacent node is not in the starting node set, add it to the starting node set; if it is in the starting node set and the newly calculated cost value is smaller, update the cost value of the node;

[0095] Step Q8: Reverse search, select the node with the smallest "f value" from the target node set as the target current node, and repeat steps Q4 to Q7;

[0096] Step Q9: Path merging, the two search directions meet, and the shortest path is constructed based on the search results of the two directions.

[0097] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device.

[0098] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

[0099] The present invention and its embodiments are described above, and such description is not restrictive. The drawings show only one embodiment of the present invention, and the actual structure is not limited thereto. In short, if ordinary technicians in the field are inspired by it, without departing from the purpose of the invention, they can design a structure and embodiment similar to the technical solution without creativity, which should belong to the protection scope of the present invention.

Claims

1. A convolutional code energy-saving decoding method based on path optimization, characterized in that: The specific steps include: Step S1: signal input, the signal to be convolved, i.e. the original signal, is input into the encoder; Step S2: signal encoding, using an encoder to encode the original signal to obtain an encoded signal; Step S3: weighted graph drawing, using a hidden Markov model based on Hamming distance, drawing a hidden state graph between the encoded signal and the original signal at different times, and converting the hidden state graph into a weighted graph, specifically including the following steps: Step S31: using a hidden Markov model, performing n different prediction estimates on the coded signal to obtain n current moment prediction states; Step S32: using the hidden Markov model, perform a prediction and estimation on all states at the current moment, and obtain n predicted states at the next moment; Step S33: repeat step S32 until the predicted state is equal to the original signal, and repeat the step m times, that is, after a total of m*n prediction estimates are made, the decoding is successful; Step S34: Draw a weighted graph, connect all predicted states at all different moments, and use the Hamming distance function to calculate the Hamming distance of all connections, define all predicted states as nodes of the graph, define all connections between nodes as edges of the graph, and define the Hamming distance as the length of the edge, to obtain a weighted graph G, G=(V, E), where V is a set of nodes and E is a set of edges; Step S4: Graph optimization, using a pruning operation based on a smooth maximum operator to optimize the weighted graph to obtain an optimized weighted graph, specifically including the following steps: Step S41: Cost matrix design, designing a cost matrix with dimension V*V ∈R V×V Represents the edge cost in the weighted graph, that is, the length of the edge between nodes; Step S42: Design a smoothing maximum operator, the formula used is as follows: ； ； Where v is the input value, For the Input values, is the preset threshold, To preset the cumulative number of times, represents a natural number, and is the designed smooth maximum operator; Step S43: Design a loop algorithm, the loop algorithm input is the cost matrix And the weighted graph G, the output is the smoothed probability ; Step S44: Bring all connected nodes in the weighted graph G into the loop and output all final smoothing probabilities. A smoothing probability of 0 represents a node With Node There is no better intermediate node, and the smoothing probability is 1, which means Node is Node With Node The intermediate node with the shortest path between them; Step S45: Graph pruning: Prune all smoothing probabilities that are not 0 or 1. Node and contains The edges of the nodes are eliminated to obtain an optimized weighted graph; Step S5: Bidirectional optimization, using the bidirectional A* algorithm, with the encoded signal and the original signal as the starting node and the end node respectively, bidirectionally searching for the optimal path on the optimized weighted graph to obtain the final optimal path; the hidden Markov model corresponding to the final optimal path is the optimal decoding path.

2. The energy-saving convolutional code decoding method based on path optimization according to claim 1, characterized in that: In step S43, the loop algorithm specifically includes the following steps: Step S431: Input the initial smoothing probability, the formula used is as follows: ； In the formula, Represents the smoothing probability, specifically represents Node is a node in the path With Node The probability of the shortest intermediate node between is the cost matrix, Representative Node With Node The length of the side between; Step S432: When When the value of is 0 to V-1, execute step S433; Step S433: When When the value of is 0 to V-1, execute step S434; Step S434: When When the value of is 0 to V-1, execute step S435; Step S435: Calculate using the smoothing maximum operator Node is a node in the path With Node The smoothing probability of the shortest intermediate node between is as follows: ； ； ； In the formula, and is the designed smooth maximum operator, is the intermediate variable, is the cost matrix, Representative Node With Node The length of the side between represent Node is a node in the path With Node The smoothing probability of the shortest intermediate node between; Step S436: When =V-1, =V-1 and =V-1, the loop ends and all smoothed probabilities are output.

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