CN116032426A - Stack decoding method, system, equipment, medium and terminal based on soft output - Google Patents
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Abstract
The invention belongs to the technical field of communication, and discloses a stack decoding method, a system, equipment, a medium and a terminal based on soft output, wherein the method comprises the following steps: creating a structure and a stack, and initializing; repeatedly judging the path length in the structure at the top of the stack and the depth of the decoding tree, if the path length in the structure at the top of the stack is smaller than the depth of the decoding tree, recalculating path metrics, sequencing the stacks according to the path metrics until the path length in the structure at the top of the stack is equal to the depth of the decoding tree, and counting the soft output probability of each decoding result; and correcting the decoding result according to a preset threshold value to obtain a final decoding result. The method disclosed by the invention can effectively reduce the computational complexity on the premise of low signal-to-noise ratio. In the case of (128,64), the stack decoding method of polarization-adjusted convolutional codes based on soft output can reduce the calculation amount by 82% compared with the conventional stack decoding.
Description
Technical Field
The invention belongs to the technical field of communication, and particularly relates to a stack decoding method, system, equipment, medium and terminal based on soft output.
Background
The polarization code proposed by Erdal Arikan is a theoretical breakthrough. The polarization code has the advantages of clear construction method, low encoding and decoding complexity, capability of strictly proving the capacity of a near channel, and the like. Meanwhile, in the case of a limited code length, some information bits cannot be correctly decoded due to incomplete channel polarization of the polar code. To solve this problem, serial Cancellation List (SCL) decoding is first proposed to reduce the bit error rate by increasing the number of candidate paths allowed to remain after each layer of path search. In order to further improve the error correction capability of the decoding algorithm, a Cyclic Redundancy Check (CRC) is added to the information sequence, a search path for SCL decoding is selected, and an optimal decoding path is output. CRC-aided serial cancellation list (CA-SCL) decoding greatly improves the performance of polar codes.
Arikan proposes a new scheme to transfer the error correction part to the outer code for encoding. This new scheme is known as polarization-adjusted convolutional (PAC) coding, which uses outer convolutional coding blocks for coding and transmission over polarized channels. PAC coding has better error correction capability than CRC-aided polar codes. Since the convolutional code decoding part of the PAC decoding outer layer is an irregular tree in the decoding process, the sequence decoding suitable for the long constraint length is more suitable for PAC decoding than Viterbi decoding. Moradi et al also propose PAC decoding based on Fano decoding.
The main decoding method of PAC is sequence decoding of convolutional codes, which is mainly divided into two types of stack decoding and Fano decoding. Currently, PAC research is mainly conducted around Fano decoding. There are few reports on the study of stack decoding.
Through the above analysis, the problems and defects existing in the prior art are as follows:
the existing PAC method has less research on stack decoding 。 Fano decoding based on PAC decoding requires relatively slow decoding speed although storage is not required.
Disclosure of Invention
Aiming at the problems existing in the prior art, the invention provides a stack decoding method, a system, equipment, a medium and a terminal based on soft output.
The invention is realized in such a way that a soft-output-based stack decoding method for polarization-adjusted convolutional codes (SOSD-PAC) comprises the following steps:
creating a structure and a stack, and initializing; judging the path length in the structure at the top of the stack and the depth of the decoding tree, if the path length in the structure at the top of the stack is smaller than the depth of the decoding tree, recalculating path metrics, sequencing the stack according to the path metrics until the path length in the structure at the top of the stack is equal to the depth of the decoding tree, and counting the soft output probability of each decoding result; and correcting the decoding result according to a preset threshold value to obtain a final decoding result.
Further, the structure is used for storing the corresponding path, the current node, the path metric and the state bit; and storing the root node structure of the decoding tree into the stack, and starting decoding.
Further, when the path length in the structure at the top of the stack is smaller than the depth of the decoding tree, judging whether the next node of the structure at the top of the stack is in the index set A;
if the next node is in A, removing the structure at the top of the stack from the stack, expanding the structure into two subsequent nodes, calculating path metrics in the two subsequent nodes, and storing the two subsequent nodes into the nodes;
if the next node is not in A, the path in the structure at the top of the stack extends backward and the path metric is recalculated based on the extended path.
Further, after the two subsequent nodes are stored in the node, judging whether overflow exists in the stack, if so, removing the structure at the bottom of the stack from the stack, and storing the structure in an external container.
Further, when the path length in the structure at the top of the stack is equal to the depth of the decoding tree, the path information in the stack is counted, and the calculation formula of the soft output probability is as follows:
in the method, in the process of the invention,
representing the decoding result of node j, +.>
Representing the probability that the j-node decoding result is 0,
the probability that the j node decoding result is 1 is represented.
Further, the specific process of correcting the decoding result by the preset threshold value is as follows:
and if the soft output probability is larger than a preset threshold t, judging a decoding result according to the soft output probability result, otherwise, judging by using the result of the stacked top path, wherein the expression is as follows:
another object of the present invention is to provide a soft output-based polarization-adjusted convolutional code stack decoding system for implementing the soft output-based polarization-adjusted convolutional code stack decoding method, the soft output-based polarization-adjusted convolutional code stack decoding system comprising:
the initialization module is used for creating a structure and a stack and initializing the structure and the stack;
a decoding module, configured to decode according to the path length in the structure at the top of the stack and the depth of the decoding tree;
and the correction module is used for correcting the decoding result according to a preset threshold value to obtain a final decoding result.
It is a further object of the present invention to provide a computer device comprising a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to perform the steps of the stack coding method of soft output based polarization-adjusted convolutional codes.
It is another object of the present invention to provide a computer readable storage medium storing a computer program which, when executed by a processor, causes the processor to perform the steps of the soft output based stack decoding method of polarization-adjusted convolutional codes.
Another object of the present invention is to provide an information data processing terminal for implementing the soft output-based stacked decoding system of polarization-adjusted convolutional codes.
In combination with the technical scheme and the technical problems to be solved, the technical scheme to be protected has the following advantages and positive effects:
first, aiming at the technical problems in the prior art and the difficulty in solving the problems, the technical problems solved by the technical proposal of the invention are analyzed in detail and deeply by tightly combining the technical proposal to be protected, the results and data in the research and development process, and the like, and some technical effects brought after the problems are solved have creative technical effects. The specific description is as follows:
the invention relates to SOSD-PAC decoding. On the basis of SD algorithm, a new decoding result judgment is defined. By limiting the stack size, the discarded path information is reserved, so that the decoding result is modified, and the decoding complexity is reduced under the condition of losing a certain bit error rate. Simulation results show that SOSD-PAC decoding has higher efficiency than PAC SD decoding. By carefully selecting the stack size S and the threshold t, the proposed soft output stack decoder has similar FER performance as a stack decoder. The results show that the proposed method can achieve a good tradeoff between decoding performance and complexity compared to stack coding of PAC. In the case of PAC codes having a code length of 128 and a code rate of 1/2, the SOSD algorithm can reduce the calculation amount by 82% compared with the conventional SD algorithm.
Secondly, the technical scheme is regarded as a whole or from the perspective of products, and the technical scheme to be protected has the following technical effects and advantages:
the invention reduces the decoding complexity under the condition of losing a certain error rate, has higher efficiency compared with the SD decoding of PAC, and realizes good balance between decoding performance and complexity.
Thirdly, as inventive supplementary evidence of the claims of the present invention, the following important aspects are also presented:
the technical scheme of the invention verifies the feasibility of stack decoding by using a stack decoding mode which is basically unmanned on an externally connected decoding scheme, provides technical support for optimizing stack decoding and improving PAC decoding, and overcomes the prejudice of low stack decoding reference scene under common general knowledge.
Drawings
FIG. 1 is a flow chart of stack decoding according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of path elimination and statistical soft output probability in a stack according to an embodiment of the present invention, (a) a path diagram of two new paths entering the stack, (b) a stack path diagram after elimination of bad paths, and (c) a statistical diagram of path decoding conditions when bad paths are not eliminated;
fig. 3 is a diagram of PAC coding and decoding processes provided by an embodiment of the present invention;
FIG. 4 is a graph of performance over a BIAWGN channel provided by an embodiment of the invention;
FIG. 5 is a pseudo code schematic diagram of a stack decoding method of a soft output based polarization-adjusted convolutional code according to an embodiment of the present invention;
FIG. 6 is a graph showing bit error rate curves for different stack sizes S and soft outputs t according to an embodiment of the present invention;
fig. 7 is a graph comparing the number of paths S and soft output probability t generated in the decoding process of different stacks in the case of a hundred thousand frames according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the following examples in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
In order to fully understand how the invention may be embodied by those skilled in the art, this section is an illustrative embodiment in which the claims are presented for purposes of illustration.
Stack coding is one type of sequential coding. Stack decoding stores paths in a stack in order of path metrics from high to low. During each decoding process, the top path of the stack is taken out of the stack and split into two new paths. These two new paths are then inserted into the stack and their metrics are calculated. Next, the stacks are reordered according to the metric values of the paths. Finally, repeating the above operation, and completing decoding when the top-level path in the stack is at the end of the decoding tree. The decoding process is shown in fig. 1.
As can be seen from the above stack decoding process, the best path at the top of the stack will be extended during each decoding process. When the stack capacity is limited, the worst path at the bottom of the stack will be discarded. The soft output is a record of discarded paths from which the present invention wishes to explore some valuable information.
Fig. 2 is a calculation program of soft output probability according to an embodiment of the present invention. In fig. 2 (a), two new paths enter the stack, the metrics of the new paths are calculated, and the paths in the stack are reordered. The dotted path represents a bad path to be deleted from the stack. As shown in fig. 2 (b), this figure represents the case of stacking after eliminating bad paths. Fig. 2 (c) is the statistics of path branches held in the stack, i.e., the statistics of (a).
When introducing the soft output probability calculation procedure, it is necessary to determine the amount of valid information present for the current node i, e.g., in fig. 2 (c), i=2 has 4 valid information. And then converting the effective information into probability through formulas (1) and (2), and judging the decoding result of the current node according to the probability.
The embodiment of the invention briefly outlines PAC codes, and no matter whether the PAC codes put the error correction part into the external codes or not, the PAC codes still need to carry out polarization effect before polarization codes are coded. The block length n of PAC code is similar to that of the polarization code and is also a power of 2, and as shown in fig. 3, the PAC coding process is divided into three parts.
The first part is rate profiling. In this section, the embodiment of the present invention needs to determine the index set a, which is critical to good performance of PAC decoding. Arikan proposes to use RM rate analysis, i.e. by judging the binary extension of the channel using hamming weights and extracting the largest top k to form the index set a. Next, a source word d of length k is inserted into a data carrier vector v of length n by using equation (3).
The second step is to perform convolutional code precoding. Similar to conventional convolutional coding, the convolution is performed using an impulse response, c= (c 0 ,c 1 ,...,c n ),c 0 ≠0，c n Not equal to 0. And (3) obtaining an output vector u through a formula (4) by using the vector v obtained in the previous step.
Unlike convolutional codes, PAC codes are not irregular trees generated during encoding. The splitting operation is only performed when the current tree node is in the information bit.
Finally, in the PAC code polarization part coding stage, the coding method is consistent with the polarization code coding. Let the
And
becomes an N matrix. The output vector x is obtained from equation (5) where the polarization generating matrix +.>
And B N Is a bit permutated matrix.
The stack decoding of PAC is similar to the stack algorithm, the main difference is the pattern of decoding tree, PAC decoding generates an irregular tree, so the following correction needs to be made in decoding splitting stage: firstly, extracting the top of a stack path and removing the top of the stack path from the stack, then judging whether the next node is in an index set A, and if so, splitting the next node into two new paths; if at A c If the path is not split, the path is unfolded backwards along the node.
Note that PAC decoding path metrics are calculated differently than convolutional code path metrics. First, the current path needs to be brought into the polarization code, and then a Log Likelihood Ratio (LLR) z is calculated according to equation (6) j 。
Then z j The metric value of the current path is calculated according to equation (7) by being transferred to the stack decoder of PAC.
The stack decoding of PAC can save the path of each segment and select the best path as possible, thereby approaching shannon capacity. However, at low signal-to-noise ratios, memory limits the size of the stack, resulting in stack overflows that increase the bit error rate.
Fig. 4 shows the Frame Error Rate (FER) of Polar SC decoding, fano decoding of PAC and stack decoding of PAC, wherein the signal is BPSK modulated and transmitted over a gaussian white noise channel (AWGN). It can be found that when the stack is large enough, the error rate of stack decoding of PAC is comparable to that of Fano decoding of PAC.
As shown in fig. 5, in the soft output-based stack decoding method for polarization adjustment convolutional codes, SOSD-PAC decoding is obtained by improving PAC stack decoding, and the specific process is as follows:
firstly, defining a structure to store a corresponding path, a current node, path measurement and state bits, then creating a stack and limiting the size of the stack, creating a structure according to the root node of a decoding tree, storing the structure in the stack and starting decoding;
if the path length in the structure at the top of the stack is less than the depth of the decoding tree, the invention needs to determine if the next node of this structure is in index set a, if the next node is in a, then remove the structure at the top of the stack from the stack and expand it into two subsequent nodes, calculate the path metrics in these two nodes, and then store these two modules in the nodes. After storage, it is necessary to determine if there is an overflow in the stack, and if so, the structure at the bottom of the stack is removed from the stack and stored in an external container. If the next node of the structure is not in A, then the path in the structure at the top of the stack extends directly backward and the path metric is recalculated based on the extended path. After sorting the stacks according to the size of the path metric, repeating the steps;
when the path length in the top structure of the stack is equal to the depth of the decoding tree, the path information in the stack is counted, the counted information and the information in the external container are brought into the formula (1) (2) and converted into corresponding probabilities, and then judgment is carried out according to the formula (8), so that a final decoding result is obtained.
The embodiment of the invention also provides a stack decoding system of the polarization adjustment convolutional code based on soft output, which comprises:
the initialization module is used for creating a structure and a stack and initializing the structure and the stack;
a decoding module, configured to decode according to the path length in the structure at the top of the stack and the depth of the decoding tree;
and the correction module is used for correcting the decoding result according to a preset threshold value to obtain a final decoding result.
In order to prove the inventive and technical value of the technical solution of the present invention, this section is an application example on specific products or related technologies of the claim technical solution.
The stack decoding method of the soft output-based polarization adjustment convolutional code provided by the application embodiment of the invention is applied to signal transmission, and the signal transmission is used for realizing intermediate processes such as optical communication, encryption communication and the like.
The stack decoding method of the soft-output-based polarization adjustment convolutional code provided by the application embodiment of the invention is applied to computer equipment, wherein the computer equipment comprises a memory and a processor, the memory stores a computer program, and the computer program, when being executed by the processor, causes the processor to execute the steps of the stack decoding method of the soft-output-based polarization adjustment convolutional code.
The stack decoding method of the soft-output-based polarization adjustment convolutional code provided by the application embodiment of the invention is applied to an information data processing terminal, and the information data processing terminal is used for realizing a stack decoding system of the soft-output-based polarization adjustment convolutional code.
It should be noted that the embodiments of the present invention can be realized in hardware, software, or a combination of software and hardware. The hardware portion may be implemented using dedicated logic; the software portions may be stored in a memory and executed by a suitable instruction execution system, such as a microprocessor or special purpose design hardware. Those of ordinary skill in the art will appreciate that the apparatus and methods described above may be implemented using computer executable instructions and/or embodied in processor control code, such as provided on a carrier medium such as a magnetic disk, CD or DVD-ROM, a programmable memory such as read only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The device of the present invention and its modules may be implemented by hardware circuitry, such as very large scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., as well as software executed by various types of processors, or by a combination of the above hardware circuitry and software, such as firmware.
The embodiment of the invention has some positive effects in the research and development or use process, as shown in fig. 4, compared with the existing PAC based on Fano decoding, the error rate level is similar, and the decoding efficiency is higher. The following is described in connection with data, charts, etc. of the experimental procedure.
Next, embodiments of the present invention perform a simple analysis of the complexity of the SOSD-PAC decoding. Branches of the PAC coding tree are generated by information bit nodes, and the embodiment of the present invention assumes that L is the height of the coding tree. The decoding process from the root node to the leaf node doubles the path each time it passes the information bit node, until the end of L, creating many paths altogether.
In one aspect, limiting the size of the stack amounts to eliminating all sub-coding trees rooted at the current path, thus reducing the number of decisions and improving speed. Second, soft output statistics are only recorded during access, with negligible overhead. The actual path number of SOSD-PAC decoding is affected by factors such as signal to noise ratio, code rate and the like, and mathematical description is difficult to give. Through simulation, the invention obtains the number of paths actually accessed.
The embodiment of the invention compares the performance and complexity of PAC codes under standard stack decoding and a stack decoding algorithm based on soft output. Consider a binary input additive white gaussian noise (biagn) channel, frame size n=128, code rate r=0.5, impulse response c= (1,0,1,1,0,1,1).
First, the size of the stack S needs to be considered. If the value of S is too small, a large number of paths will be deleted when the signal-to-noise ratio is low, affecting the bit error rate. If too large, a large number of bad paths remain, which not only wastes memory, but also increases decoding complexity. Secondly, the influence of the soft output threshold t on the bit error rate needs to be considered. If the threshold t is too large or too small, no judgment can be made effectively.
Fig. 5 and 6 show a comparison of bit error rate and complexity with a conventional stack at different stack S and soft output thresholds t. By limiting the stack size and preserving information of a bit stack algorithm, a 90% gain can be achieved at low signal to noise ratios. However, as the signal-to-noise ratio increases, the gain gradually decreases with little bit error rate.
The embodiment of the invention provides SOSD-PAC decoding. On this basis, a new decoding result judgment is defined. By limiting the stack size, the discarded path information is reserved, so that the decoding result is modified, and the decoding complexity is reduced under the condition of losing a certain bit error rate. Simulation results show that SOSD-PAC decoding has higher efficiency than PAC stack decoding. By carefully selecting the stack size S and the threshold t, the proposed soft output stack decoder has similar FER performance as the stack decoder; the proposed method can achieve a good trade-off between decoding performance and complexity compared to stack coding of PAC.
The foregoing is merely illustrative of specific embodiments of the present invention, and the scope of the invention is not limited thereto, but any modifications, equivalents, improvements and alternatives falling within the spirit and principles of the present invention will be apparent to those skilled in the art within the scope of the present invention.
Claims (10)
1. A soft-output-based stack decoding method for polarization-adjusted convolutional codes, comprising:
creating a stack and a container, initializing, and storing the root node of the decoding tree into the stack; judging whether the path length of the top of the stack is greater than or equal to the depth of the decoding tree, if so, ending decoding and outputting a decoding result; if the node is smaller than the depth of the decoding tree, the log-likelihood ratio of the node is calculated, and the extension path is judged according to whether the node is in the index set A or not: if in A, expanding into two paths, wherein one path is expanded by 0 and one path is expanded by 1; if not in A, then the extension is 0 along the decoding result. Metrics of the extended path are computed and stored in the stack, and then the original node is moved from the stack to the container. And after sequencing the stacks, repeating the steps until the path length to the top of the stacks is more than or equal to the depth of the decoding tree.
2. The soft-output based stack decoding method of polarization-adjusted convolutional codes as recited in claim 1, wherein said structure holds corresponding paths, current nodes, path metrics and status bits; and storing the root node structure of the decoding tree into the stack, and starting decoding.
3. The method for decoding a stack of soft output based polarization-adjusted convolutional codes as recited in claim 1, wherein when a path length in a structure at a top of the stack is smaller than a depth of a decoding tree, determining whether a next node of the structure at the top of the stack is in an index set a;
if the next node is in A, removing the structure at the top of the stack from the stack, expanding the structure into two subsequent nodes, calculating path metrics in the two subsequent nodes, and storing the two subsequent nodes into the nodes;
if the next node is not in A, the path in the structure at the top of the stack extends backward and the path metric is recalculated based on the extended path.
4. A method of decoding a stack of soft output based polarization-adjusted convolutional codes as recited in claim 3, wherein after said two subsequent nodes are stored in a node, determining if there is overflow in said stack, and if so, removing the structure at the bottom of the stack from said stack and storing it in an external container. If there is no overflow, the stack is sorted according to the path metric and the loop is restarted.
5. The method for decoding a stack of soft output-based polarization-adjusted convolutional codes as recited in claim 1, wherein when the path length in the structure at the top of the stack is equal to the depth of the decoding tree, the path information in the stack is counted, and the soft output probability is calculated by the following formula:
in the method, in the process of the invention,
representing the decoding result of node j, +.>
Representing the probability of the decoding result of j node being 0, < >>
The probability that the j node decoding result is 1 is represented.
6. The stack decoding method of soft output-based polarization adjustment convolutional code according to claim 1, wherein the specific process of correcting the decoding result by the preset threshold is:
and if the soft output probability is larger than a preset threshold t, judging a decoding result according to the soft output probability result, otherwise, judging by using the result of the stacked top path, wherein the expression is as follows:
7. a soft-output polarization-adjusted convolutional code-based stack decoding system that implements the soft-output polarization-adjusted convolutional code-based stack decoding method of any one of claims 1-6, comprising:
the initialization module is used for creating a structure and a stack and initializing the structure and the stack;
a decoding module, configured to decode according to the path length in the structure at the top of the stack and the depth of the decoding tree;
and the correction module is used for correcting the decoding result according to a preset threshold value to obtain a final decoding result.
8. A computer device comprising a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to perform the steps of the soft-output based stack decoding method of polarization-adjusted convolutional codes according to any one of claims 1-6.
9. A computer readable storage medium storing a computer program which, when executed by a processor, causes the processor to perform the steps of the soft-output based polarization-adjusted convolutional code stack decoding method of any one of claims 1-6.
10. An information data processing terminal for implementing a soft-output based polarization-adjusted convolutional code stack decoding system as recited in claim 7.
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