WO2016168962A1 - 极化码的译码方法和译码装置 - Google Patents

极化码的译码方法和译码装置 Download PDF

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WO2016168962A1
WO2016168962A1 PCT/CN2015/076958 CN2015076958W WO2016168962A1 WO 2016168962 A1 WO2016168962 A1 WO 2016168962A1 CN 2015076958 W CN2015076958 W CN 2015076958W WO 2016168962 A1 WO2016168962 A1 WO 2016168962A1
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path
decoding
layer
candidate
code
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PCT/CN2015/076958
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English (en)
French (fr)
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陈凯
李斌
沈晖
金杰
李微
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华为技术有限公司
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/13—Linear codes

Definitions

  • the present invention relates to the field of communications, and more particularly to a method and a decoding apparatus for a polarization code.
  • the algorithm of the "Successive Cancellation Hybrid” (“SCH”) algorithm can significantly improve the performance of the Frame Error Rate (“FER").
  • FER Frame Error Rate
  • These algorithms are collectively referred to as the enhanced SC decoding algorithm.
  • the enhanced SC decoding algorithm assisted by Cyclic Redundancy Check (CRC)
  • CRC Cyclic Redundancy Check
  • the polarization code can obtain better FER performance than LDPC and Turbo codes.
  • the search width of the enhanced SC decoding algorithm needs to be set to a larger value, resulting in higher decoding complexity.
  • the enhanced SC decoding algorithm is essentially a path search process on the decoding code tree, the candidate path with a small metric value can be deleted in time by the pruning algorithm in the search process, thereby avoiding unnecessary path expansion process. Reduce the complexity of the purpose.
  • the prior art presents a pruning scheme for the SCL decoding algorithm. The method determines a pruning threshold according to the maximum value of the path metric after each path extension of the SCL decoding: given a tolerable frame error rate (Frame Error Rate, referred to as "FER") performance loss value P tol , In the decoding process (ie, the path search process), after the candidate paths in the list are sorted, if a certain candidate path metric with length i satisfies:
  • the pruning scheme in the prior art can well control the performance loss due to the introduction of the pruning operation within P tol .
  • the signal-to-noise ratio interval is in the CRC-assisted enhanced SC decoding, and the FER is in the working range around 0.1 to 0.0001.
  • the decoding complexity is still very high. high.
  • the invention provides a method and a device for decoding a polarization code, which can control the loss of decoding performance within a preset tolerable performance loss value in the decoding process, and can greatly reduce the decoding of the polarization code. the complexity.
  • a method for decoding a polarization code comprising: determining, according to a pruning threshold and a search width L of each layer of a decoding code tree of a polarization code, from a first decoding path set a second set of decoding paths of the polarization code, wherein a pruning threshold of each layer of the decoding code tree is determined according to a sum of path metric values of all candidate paths of the layer, the first decoding path And a set of all shortest paths formed from the root node to any leaf node on the decoding code tree; determining a bit estimation sequence corresponding to the decoding path having the largest path metric value in the second decoding path set as the The decoding result of the polarization code.
  • each layer of the decoding code tree according to the polarization code is used. Determining the second decoding path set of the polarization code from the first set of decoding paths, including: the pruning threshold and the search width L, including: when the decoding path is extended to each layer of the decoding code tree, A set of candidate path groups whose path metric values in the candidate path set of the layer are greater than the pruning threshold of the layer is determined as the first candidate path set of the layer, where the candidate path set of the first layer of the decoding code tree is a set of all shortest paths formed by the root node to any node of the first layer on the decoding code tree; when the length of the candidate path in the first candidate path set is less than the code length of the polarization code, according to The search width L, determining a candidate path set of the next layer of the layer, and extending the decoding path to the lower layer a
  • each layer of the decoding code tree according to the polarization code a prune threshold and a search width L, determining a second set of decoding paths of the polarization code from the first set of decoding paths, including: when the decoding path is extended to each layer of the decoding code tree, according to The search width L determines a second candidate path set of the layer from the candidate path set of the layer, where the candidate path set of the first layer of the decoding code tree is from the root node to the decoding code tree a set of all shortest paths formed by any node of the first layer; when the length of the candidate path in the second candidate path set is less than the code length of the polarization code, the path metric value in the second candidate path set is greater than And a set of subsequent paths of candidate paths equal to the pruning threshold of the layer is determined as a candidate path set of the next layer of the layer, and the decoding
  • each layer of the decoding code tree according to the polarization code determines a second set of decoding paths of the polarization code from the first set of decoding paths, including:
  • the candidate is determined according to the search width L. a surviving candidate path set in the path stack, adding the subsequent path of the pop-up path to the candidate path stack, and performing the next pop-up operation, or
  • the pop-up path is determined as the decoding path in the second decoding path set of the polarization code, and the next pop-up operation is performed.
  • any possible implementation manner of the first to third possible implementation manners of the first aspect in the fourth possible implementation manner of the first aspect, in the fourth possible implementation manner of the first aspect, in the CRC auxiliary decoding, the bit estimation sequence corresponding to the decoding path having the largest path metric value in the second decoding path set is determined as the decoding result of the polarization code, including: the second decoding path set The bit estimation sequence having the largest path metric value and capable of passing the CRC check is determined as the decoding result of the polarization code.
  • the pruning threshold of each layer of the decoding code tree is a path according to all candidate paths of the layer
  • the sum of the metric values is determined, including: the pruning threshold of each layer of the decoding code tree is determined according to the following formula:
  • ⁇ i is the pruning threshold of the i-th layer
  • P tol is a preset tolerable performance loss value
  • K is the length of the information block corresponding to the polarization code
  • L is the search width.
  • the pruning threshold of each layer of the decoding code tree is a path according to all candidate paths of the layer
  • the sum of the metric values is determined, including: the pruning threshold of each layer of the decoding code tree is determined according to the following formula:
  • ⁇ i is the pruning threshold of the i-th layer
  • L is the search width
  • P tol is the preset tolerable performance loss value, a sequence number set of candidate paths that are deleted among all candidate paths of the i'th layer-1, The path metric of the candidate path in which the kth row is deleted among all candidate paths of the i'th layer-1, The sum of the path metrics for all candidate paths of the i''th layer.
  • the pruning threshold of each layer of the decoding code tree is a path according to all candidate paths of the layer
  • the sum of the metric values is determined, including: the pruning threshold of each layer of the decoding code tree is determined according to the following formula:
  • c i is a set of candidate paths that are all or partially deleted in the previous i-1 layer decoding process.
  • the pruning threshold of each layer of the decoding code tree is a path according to all candidate paths of the layer The sum of the metric values is determined, including: the pruning threshold of each layer of the decoding code tree is determined according to the following formula:
  • ⁇ i,t is the pruning threshold of the i-th layer after the t-th stack operation
  • P tol is the preset tolerable performance loss value.
  • a decoding apparatus for a polarization code comprising: a processing module, configured to perform a first decoding from a pruning threshold and a search width L of each layer of a decoding code tree of a polarization code Determining, in the path set, a second set of decoding paths of the polarization code, where a pruning threshold of each layer of the decoding code tree is determined according to a sum of path metric values of all candidate paths of the layer,
  • the first decoding path set is a set of all shortest paths formed by the root node to any leaf node on the decoding code tree; and the determining module is configured to determine, in the second decoding path set determined by the processing module
  • the bit estimation sequence corresponding to the decoding path of the maximum path metric is determined as the decoding result of the polarization code.
  • the processing module is specifically configured to: extend the decoding path to the translation At each layer of the code tree, a set of candidate path paths in the candidate path set of the layer that is larger than the pruning threshold of the layer is determined as the first candidate path set of the layer, where the decoding code
  • the candidate path set of the first layer of the tree is a set of all shortest paths formed by the root node to any node of the first layer on the decoding code tree; the length of the candidate path in the first candidate path set is less than Determining the candidate path set of the next layer of the layer according to the search width L, and extending the decoding path to the next layer of the layer, or the first candidate path
  • the second decoding path set of the polarization code is determined from the first candidate path set according to the search width L.
  • the processing module when the decoding apparatus is applied to the serial cancellation list SCL decoding, the processing module is specifically configured to: extend the decoding path to the translation Each layer of the code tree is determined from the candidate path set of the layer according to the search width L And a second set of candidate paths of the layer, where the candidate path set of the first layer of the decoding code tree is all shortest paths formed by the root node to any node of the first layer in the decoding code tree a set; when the length of the candidate path in the second candidate path set is less than the code length of the polarization code, the path metric value in the second candidate path set is greater than or equal to the successor of the candidate path of the pruning threshold of the layer
  • the set of path components is determined as a candidate path set of the next layer of the layer, and the decoding path is extended to the next layer of the layer, or the length of the candidate path in the second candidate path set is equal to the pole
  • the set of candidate path is determined as a candidate path set of the next layer of the layer, and the decoding path
  • the processing module when the decoding apparatus is applied to the serial cancellation stack SCS decoding, the processing module is specifically configured to:
  • the candidate is determined according to the search width L. a surviving candidate path set in the path stack, adding the subsequent path corresponding to the pop-up path to the candidate path stack, and performing the next pop-up operation, or
  • the pop-up path is determined as the decoding path in the second decoding path set of the polarization code, and the next pop-up operation is performed.
  • the determining module is specifically configured to: determine, in the second decoding path set, a maximum path metric value, and determine a bit estimation sequence corresponding to the decoding path of the CRC check as the translation of the polarization code Code result.
  • the processing module is specifically configured to: determine, according to the following formula, pruning of each layer of the decoding code tree Threshold:
  • ⁇ i is the pruning threshold of the i-th layer
  • P tol is a preset tolerable performance loss value
  • K is the length of the information block corresponding to the polarization code
  • L is the search width.
  • the processing module is specifically configured to: determine, according to the following formula, a cut of each layer of the decoding code tree Branch threshold:
  • ⁇ i is the pruning threshold of the i-th layer
  • L is the search width
  • P tol is the preset tolerable performance loss value, a sequence number set of candidate paths that are deleted among all candidate paths of the i'th layer-1, The path metric of the candidate path in which the kth row is deleted among all candidate paths of the i'th layer-1, The sum of the path metrics for all candidate paths of the i''th layer.
  • the processing module is specifically configured to: determine, according to the following formula, pruning of each layer of the decoding code tree Threshold:
  • c i is a set of candidate paths that are all or partially deleted in the previous i-1 layer decoding process.
  • the processing module is specifically configured to: determine, according to the following formula, pruning of each layer of the decoding code tree Threshold:
  • ⁇ i,t is the pruning threshold of the i-th layer after the t-th stack operation
  • P tol is the preset tolerable performance loss value.
  • the method and the decoding apparatus for the polarization code extend the path of all the candidate paths according to the layer when the path is extended to each layer of the decoding code tree in the decoding process.
  • the sum of the metric values determines a pruning threshold of the layer, and determines a second decoding path set of the polarization code from the first set of decoding paths according to the pruning threshold and the search width of each layer, the second The decoding path having the largest path metric value in the set of coding paths is determined as the decoding result of the polarization code, and the pruning of the layer is determined according to the sum of the path metrics of all candidate paths of each layer of the decoding code tree.
  • the threshold enables the loss of decoding performance to be controlled within a predetermined tolerability performance loss value, and can greatly reduce the complexity of polarization code decoding.
  • FIG. 1 illustrates a wireless communication system in accordance with various embodiments described herein;
  • FIG. 2 is a schematic flowchart of a method for decoding a polarization code according to an embodiment of the present invention
  • 3 is a decoding code tree of a polarization code having a code length of 4 according to an embodiment of the present invention
  • FIG. 4 is another schematic flowchart of a method for decoding a polarization code according to an embodiment of the present invention
  • FIG. 5 is still another schematic flowchart of a method for decoding a polarization code according to an embodiment of the present invention
  • FIG. 6 is still another schematic flowchart of a method for decoding a polarization code according to an embodiment of the present invention.
  • FIG. 7 is a schematic flowchart of a method for decoding a polarization code according to another embodiment of the present invention.
  • FIG. 8 is a schematic flowchart of a method for decoding a polarization code according to still another embodiment of the present invention.
  • FIG. 9 is a schematic diagram showing a comparison between the decoding method of the embodiment of the present invention and the decoding method of the prior art in terms of FER performance;
  • Figure 11 is a graph showing the relationship between the FER performance and performance loss value and the preset tolerable performance loss value at a signal-to-noise ratio of 1.5 dB;
  • FIG. 12 is a schematic block diagram of a decoding apparatus according to an embodiment of the present invention.
  • Figure 13 is a schematic block diagram of an apparatus in accordance with an embodiment of the present invention.
  • GSM Global System of Mobile communication
  • CDMA Code Division Multiple Access
  • WCDMA Wideband Code Division Multiple Access
  • GPRS General Packet Radio Service
  • LTE Long Term Evolution
  • FDD Frequency Division Duplex
  • TDD Time Division Duplex
  • UMTS Universal Mobile Telecommunication System
  • FIG. 1 illustrates a wireless communication system 100 in accordance with various embodiments described herein.
  • System 100 includes a base station 102 that can include multiple antenna groups.
  • one antenna group may include antennas 104 and 106
  • another antenna group may include antennas 108 and 110
  • additional groups may include antennas 112 and 114.
  • Two antennas are shown for each antenna group, however more or fewer antennas may be used for each group.
  • Base station 102 can additionally include a transmitter chain and a receiver chain, as will be understood by those of ordinary skill in the art, which can include multiple components associated with signal transmission and reception (e.g., processor, modulator, multiplexer, demodulation) , demultiplexer or antenna, etc.).
  • Base station 102 can communicate with one or more access terminals, such as access terminal 116 and access terminal 122. However, it will be appreciated that base station 102 can communicate with substantially any number of access terminals similar to access terminals 116 and 122. Access terminals 116 and 122 can be, for example, cellular telephones, smart phones, portable computers, handheld communication devices, handheld computing devices, satellite radios, global positioning systems, PDAs, and/or any other for communicating over wireless communication system 100. Suitable for equipment. As shown, access terminal 116 is in communication with antennas 112 and 114, with antennas 112 and 114 transmitting information to access terminal 116 over forward link 118 and receiving information from access terminal 116 over reverse link 120.
  • access terminal 116 is in communication with antennas 112 and 114, with antennas 112 and 114 transmitting information to access terminal 116 over forward link 118 and receiving information from access terminal 116 over reverse link 120.
  • access terminal 122 is in communication with antennas 104 and 106, wherein antennas 104 and 106 transmit information to access terminal 122 over forward link 124 and receive information from access terminal 122 over reverse link 126.
  • FDD Frequency Division Duplex
  • the forward link 118 can utilize different frequency bands than those used by the reverse link 120, and the forward link 124 can be utilized and reversed. Different frequency bands used by link 126.
  • TDD Time Division Duplex
  • the forward link 118 and the reverse link 120 can use a common frequency band, and the forward link 124 and the reverse link 126 can be used in common. frequency band.
  • Each set of antennas and/or regions designed for communication is referred to as a sector of base station 102.
  • the antenna group can be designed to communicate with access terminals in sectors of the coverage area of base station 102.
  • the transmit antennas of base station 102 may utilize beamforming to improve the signal to noise ratio for forward links 118 and 124 of access terminals 116 and 122.
  • the base station 102 transmits to the randomly dispersed access terminals 116 and 122 in the relevant coverage area by the base station as compared to all of the access terminals transmitted by the base station, the mobile devices in the adjacent cells are subject to Less interference.
  • base station 102, access terminal 116, and/or access terminal 122 may be transmitting wireless communication devices and/or receiving wireless communication devices.
  • the transmitting wireless communication device can encode the data for transmission.
  • the transmitting wireless communication device can have (eg, generate, obtain, store in memory, etc.) a certain number of information bits to be transmitted over the channel to the receiving wireless communication device.
  • Such information bits may be included in a transport block (or multiple transport blocks) of data that may be segmented to produce a plurality of code blocks.
  • the transmitting wireless communication device can encode each code block using a polarization code encoder (not shown) to improve the reliability of data transmission, thereby ensuring communication quality.
  • SCS decoding uses an ordered stack instead of a list to store candidate paths.
  • each time only based on the candidate path with the highest reliability metric (on the top of the stack) is extended.
  • the top line path reaches a certain leaf node of the code tree, the decoding process is stopped, and the bit estimation sequence corresponding to the path is output as a decoding result.
  • SCL decoding can be seen as a breadth-first search on the code tree, while SCS decoding is the best priority search on the code tree.
  • SCL decoding allows for lower spatial complexity, while SCS decoding has lower computational complexity.
  • the two modes are mixed, that is, SCH decoding.
  • SCH decoding implementation class Like SCS decoding, an ordered stack is also used to store candidate paths. The difference is that the stack depth of the SCH is much smaller than the SCS decoding, and by flexibly switching between the two modes, the number of candidate paths will never overflow the stack.
  • the computational complexity of SCH decoding is slightly higher than SCS decoding, much smaller than SCL decoding; the spatial complexity is slightly higher than SCL decoding is much smaller than SCS decoding.
  • the essence of enhanced SC decoding is to search for a set of candidate path sets with larger path metrics, and select the one with the largest path metric as the decoding output.
  • the CRC-assisted enhanced SC decoding algorithm can be used for decoding, that is, selecting from the finally obtained candidate path set.
  • a candidate path having the largest path metric and capable of passing the CRC check is used as the decoded output.
  • FIG. 2 is a flow chart of a method of decoding a polarization code according to an embodiment of the present invention.
  • the method of Figure 1 is performed by a decoding end. As shown in FIG. 1, the method 100 includes:
  • S110 Determine, according to a pruning threshold and a search width L of each layer of the decoding code tree of the polarization code, a second decoding path set of the polarization code from the first decoding path set, where the translation
  • the pruning threshold of each layer of the code tree is determined according to the sum of path metric values of all candidate paths of the layer, the first decoding path set being from the root node to any leaf node in the decoding code tree a collection of all the shortest paths that make up;
  • the decoding process of the polarization code when the decoding path is extended to each layer of the decoding code tree corresponding to the polarization code, the sum is determined according to the sum of the path metric values of all candidate paths of the layer.
  • the pruning threshold of the layer and determining the surviving path and the deleting path of the layer according to the pruning threshold and the search width L, splitting the surviving path and deleting the deleted path, wherein the path metric of the surviving path is greater than or equal to the The pruning threshold, the path metric of the deleted path is smaller than the pruning threshold.
  • the set of surviving paths of the number of layers of the decoding code tree in which the leaf node is located is determined as the second decoding path set, and the second decoding is performed.
  • a bit estimation sequence corresponding to the decoding path having the largest path metric in the path set is determined as the polarization code The result of the decoding.
  • the decoding path when the decoding path is extended to each layer of the decoding code tree in the decoding process, the sum is determined according to the sum of the path metric values of all candidate paths of the layer.
  • a pruning threshold of the layer and determining, according to the pruning threshold and the search width of each layer, a second decoding path set of the polarization code from the first decoding path set, where the second decoding path set has
  • the bit estimation sequence corresponding to the decoding path of the maximum path metric is determined as the decoding result of the polarization code, since the pruning of the layer can be determined according to the sum of the path metrics of all candidate paths of each layer of the decoding code tree.
  • the threshold enables the loss of decoding performance to be controlled within a predetermined tolerable performance loss value, and can greatly reduce the complexity of polarization code decoding.
  • the operation of deleting the candidate path may be referred to as a pruning operation, but the present invention is not limited thereto.
  • a polarization code having a code length of N may correspond to a binary decoding code tree composed of N layer edges, and the first decoding path set refers to a decoding code of the polarization code.
  • the set of all shortest paths formed by the root node to any leaf node in the tree if it is CRC-assisted enhanced SC decoding, requires that the information bit sequence corresponding to the decoding path in the first decoding path set can pass the CRC calibration. Test.
  • each node in the decoding code tree has two successor nodes, and the two edges associated with the node and the two successor nodes of the node are labeled 0 and 1, respectively.
  • the translation of the second decoding path set having the largest path metric value and capable of passing the CRC check is performed.
  • the bit estimation sequence corresponding to the code path is determined as the decoding result of the polarization code.
  • S110 when applied to the serial cancellation list SCL decoding, specifically includes the following steps:
  • a candidate path set wherein the candidate path set of the first layer of the decoding code tree is a set of all shortest paths formed by the root node to any node of the first layer in the decoding code tree;
  • the length of the candidate path refers to the length of the bit estimation sequence corresponding to the candidate path.
  • S111 when the length of the candidate path in the first candidate path set is less than the code length of the polarization code, after the decoding path is extended to the next layer of the layer, S111 is performed. S112 and S111 are cyclically executed until the length of the candidate path in the first candidate path set is equal to the code length of the polarization code in S112, and the polarization code is determined from the first candidate path set according to the search width L. A second set of decoding paths.
  • the specific step is: when the number of candidate paths in the first candidate path set is greater than the search width L, the maximum path metric is included in the first candidate path set
  • the set of subsequent paths of the L candidate paths of the value is determined as the candidate path set of the next layer of the layer, and the decoding path is extended to the next layer of the layer; the candidate path in the first candidate path set
  • the set of subsequent paths of all candidate paths in the first candidate path set is determined as the candidate path set of the next layer of the layer, and the decoding path is extended to the The next layer of the layer.
  • the Each candidate path in a candidate path set is sorted according to the size of the path metric value, and the L candidate paths with the largest path metric value are reserved, and the set of the subsequent paths of the L candidate paths is determined as the next layer of the layer.
  • Each candidate path in the first candidate path set is sorted according to the size of the path metric value, or may not be sorted, and the subsequent path of all candidate paths in the first candidate path set is directly determined as the next step of the layer.
  • the candidate path set of the layer is not limited by the present invention.
  • the first candidate path set is determined according to the search width L.
  • a second decoding path set of the polarization code the specific step is: when the number of candidate paths in the first candidate path set is greater than the search width L, the first candidate path set has the largest path metric value
  • a set of L candidate path groups is determined as a second decoding path set of the polarization code; when the number of candidate paths in the first candidate path set is less than or equal to the search width L, the first candidate path is used
  • the set is determined to be a second set of decoding paths of the polarization code.
  • the Each candidate path in the first candidate path set is sorted according to the size of the path metric value, and the set of L candidate path paths with the largest path metric value is determined as the second decoding path set of the polarization code, and the first a candidate path deletion other than the L candidate paths in a candidate path set; when the number of candidate paths in the first candidate path set is less than or equal to the search width L, the candidate may be in the first candidate path set Each candidate path is sorted according to the size of the path metric, or may not be sorted, and the first candidate path set is directly determined as the second decoding path set of the polarization code, which is not limited by the present invention.
  • the pruning threshold of each layer of the decoding code tree may be determined according to formula (1):
  • ⁇ i is the pruning threshold of the i-th layer
  • P tol is a preset tolerable performance loss value
  • K is the length of the information block corresponding to the polarization code
  • L is the search width.
  • the performance loss value P tol (for example, the frame error rate) that can be tolerated in the entire decoding process can be set in advance according to actual needs, and It can be calculated according to formula (2):
  • the path metric value of each candidate path can be calculated according to the calculation method in the prior art, which is not limited in the present invention.
  • the pruning threshold of each layer of the decoding code tree may be determined according to formulas (3) and (4):
  • ⁇ i is the pruning threshold of the i-th layer
  • L is the search width
  • P tol is the preset tolerable performance loss value, a sequence number set of candidate paths that are deleted among all candidate paths of the i'th layer-1, The path metric of the candidate path in which the kth row is deleted among all candidate paths of the i'th layer-1, The sum of the path metrics for all candidate paths of the i''th layer.
  • the sum is determined according to the sum of the path metric values of all candidate paths of the layer.
  • a pruning threshold of the layer and after determining the first candidate path set of the layer according to the pruning threshold, determining a candidate path set of the layer of the layer or a second decoding path set of the polarization code according to the search width,
  • S110 when applied to the serial cancellation list SCL decoding, specifically includes the following steps:
  • the first set of candidate path sets is a set of all shortest paths formed by the root node to any node of the first layer on the decoding code tree;
  • the path metric value in the second candidate path set is greater than or equal to the successor of the candidate path of the pruning threshold of the layer.
  • the set of path components is determined as a candidate path set of the next layer of the layer, and the decoding path is extended to the next layer of the layer, or the length of the candidate path in the second candidate path set is equal to the pole
  • the set of candidate path paths whose path metric values in the second candidate path set are greater than or equal to the pruning threshold of the layer is determined as the second decoding path set of the polarization code.
  • S113 when the length of the candidate path in the second candidate path set is less than the code length of the polarization code, after the decoding path is extended to the next layer of the layer, S113 is performed.
  • the loop performs S113 and S114 until the length of the candidate path in the second candidate path set is equal to the code length of the polarization code in S114, and the path metric value in the second candidate path set is greater than or equal to the pruning of the layer
  • the set of candidate path components of the threshold is determined to be the second set of decoding paths of the polarization code.
  • the specific step when the number of candidate paths in the candidate path set of the layer is greater than the search width L, the set of L candidate paths having the largest path metric value in the candidate path set of the layer is determined as the first layer of the layer.
  • the second candidate path set when the number of candidate paths in the candidate path set of the layer is less than or equal to the search width L, the candidate path set of the layer is determined as the second candidate path set of the layer.
  • each of the candidate path sets may be extended when the coding path is extended to each layer of the coding code tree and the number of candidate paths in the candidate path set of the layer is greater than the search width L.
  • the candidate path is sorted according to the size of the path metric, and the set of L candidate paths with the largest path metric is determined as the second candidate path set of the layer, and the candidate path except the L candidate path is deleted;
  • each candidate path in the candidate path set of the layer may be sorted according to the size of the path metric value, or may not be sorted.
  • the candidate path set of the layer is directly determined as the second candidate path set of the layer, which is not limited by the present invention.
  • the pruning threshold of each layer of the decoding code tree may be determined according to formula (5):
  • c i is a set of candidate paths that are all or partially deleted in the previous i-1 layer decoding process.
  • the path of the part pruned is: the path metric estimated value in the i-th layer is larger than the first In the pruned path of the minimum path metric in the i-layer survivor path, the set of the paths with the largest performance loss estimate is calculated as follows:
  • the candidate path that was deleted in the pruning step when decoding to the i-th layer of the decoding code tree is in the list
  • the serial number is j
  • the path metric is The sequence number of the candidate path that is deleted in the pruning step when decoding reaches the i-th layer of the code tree.
  • the candidate path of the jth layer is pruned and deleted (serial number is k), and the upper bound of the metric of the subsequent path of the path is The impact of the deletion of this path on performance is
  • Definition set The set indicates all candidate paths deleted by the pruning operation in the previous (i-1) layer decoding; Satisfaction: Any Have And to any Have Represented by all belonging to the collection But not belonging to the collection Made up of elements a subset of.
  • the polarized channel corresponding to the bit of sequence i can be obtained.
  • the received signal log likelihood ratio LLR i ln(W (i) (y
  • the upper bound of the path metric is:
  • the method for decoding a polarization code after the decoding path is extended to each layer of the decoding code tree in the decoding process, after determining the second candidate path set of the layer according to the search width L, Determining a pruning threshold of the layer according to a sum of path metric values of all candidate paths of the layer, and determining, according to the pruning threshold, a candidate path set of the next layer of the layer or a second decoding path set of the polarization code,
  • the calculation operation of the path metric value of the candidate path, the copy operation of the candidate path, and the sorting operation of the path metric value of the candidate path can be reduced, whereby the decoding performance loss can be controlled within a preset tolerable performance loss value And can greatly reduce the complexity of polarization code decoding.
  • S110 when applied to the serial cancellation stack SCS decoding, S110 specifically includes the following steps:
  • the path metric value of the pop-up path is greater than or equal to the pruning threshold corresponding to the number of layers of the decoding code tree corresponding to the pop-up path, and the length of the pop-up path is less than the code length of the polarization code, determining the a surviving candidate path set in the candidate path stack, adding the subsequent path of the pop-up path to the candidate path stack, and performing the next pop-up operation, or
  • the pop-up path is determined as the decoding path in the second decoding path set of the polarization code, and the next pop-up operation is performed.
  • the pruning threshold corresponding to the number of layers of the decoding code tree corresponding to the pop-up path is determined according to the sum of path metric values of all candidate paths of the layer number, and all candidate paths of the layer number are determined. Refers to all pop-up paths that are popped up during the stack operation prior to the stack operation and that are the same length as the pop-up path that pops up during the stack operation.
  • the pruning threshold of each layer of the decoding code tree may be determined according to formula (7):
  • ⁇ i,t is the pruning threshold of the i-th layer after the t-th stack operation
  • P tol is the preset tolerable performance loss value.
  • the pruning threshold of each layer of the decoding code tree may be determined according to formula (8):
  • the performance loss introduced by the pruning operation when decoding the i-th layer is defined as a set of candidate paths of length i popped up in t-threshold operations, the set sequence Will be updated as t increases, so when SCS is decoded, different t not exactly.
  • the embodiment of the present invention when the decoding method of the embodiment of the present invention is applied to the SCH decoding, if the SCH decoder works in the breadth-first search mode, the embodiment of the present invention is applied.
  • the method for decoding the polarization code of the embodiment of the present invention when applied to the SCS decoding, is popped up according to the length of the previous pop-up operation and the pop-up operation after each pop-up operation in the decoding process.
  • the sum of the metric values of the pop-up paths having the same length of the candidate path determines the pruning threshold of the layer corresponding to the pop-up path popped up by the pop-up operation, and performs subsequent decoding operations according to the pruning threshold and the search width L,
  • the calculation operation of reducing the path metric value of the candidate path and the sorting operation of the path metric value of the candidate path thereby being able to control the decoding performance loss within a preset tolerable performance loss value, and can greatly reduce the pole
  • the complexity of decoding when applied to the SCS decoding.
  • FIG. 7 is a schematic flowchart of a polarization code decoding method according to another embodiment of the present invention. As shown in FIG. 7, the method 200 includes:
  • the path metric values of the two subsequent paths of the candidate paths in the list may be calculated according to the method for calculating the path metric value in the prior art, but the present invention is not limited thereto.
  • the pruning threshold of each layer of the decoding code tree is calculated by using the formula (1) or the formula (3) for calculating the pruning threshold of the embodiment of the present invention, and the path metric value in the candidate path is deleted. A candidate path that is smaller than the pruning threshold.
  • all candidate paths in the list that are not deleted are sorted according to the size of the path metric value.
  • the L candidate paths having the largest path metric value are reserved, and the path is expanded, and the L candidate paths are deleted.
  • S208 is directly executed.
  • S211 is executed to increase the value of i by 1, and then the steps S202 and S202 are performed again until the value of i and the code of the polarization code are re-executed.
  • the length N is equal.
  • S204 after deleting the candidate path whose path metric value is smaller than the pruning threshold, when the number of candidate paths that are not deleted is less than L, S205 may not be performed, and correspondingly, in S206, all are not The deleted candidate path is used for path expansion.
  • S204 may also be performed after S206.
  • the pruning threshold of each layer of the decoding code tree may be calculated according to the formula (5) and formula (6) for calculating the pruning threshold according to the embodiment of the present invention.
  • FIG. 8 is a schematic flowchart of a polarization code decoding method according to still another embodiment of the present invention. As shown in FIG. 8, the method 300 includes:
  • the formula (7) or (8) for calculating the pruning threshold may be used to calculate each layer of the decoding code tree according to the embodiment of the present invention.
  • the pruning threshold is determined, and it is determined whether the path metric of the pop-up path of the pop-up operation is smaller than the pruning threshold of the i-th layer.
  • the path metric value of the pop-up path is greater than or equal to the pruning threshold of the i-th layer, it is determined whether the value of the counter reaches L.
  • the path is expanded with bits 0 and 1, respectively, and the path metric value of each path in the stack is updated.
  • the extended path is pushed onto the stack, and the paths in the stack are arranged according to the path metric value from large to small (top of the stack to the bottom of the stack);
  • the path metric value of the pop-up path determined in S305 is smaller than the pruning threshold of the i-th (i is the length of the pop-up path) layer, all candidate paths in the stack whose length is less than or equal to i are deleted, and directly A stack operation.
  • S310 when it is determined that the (i+1)th bit is a fixed bit, S312 is performed, the path is extended with fixed bits, and the path metric value of each candidate path in the stack is updated.
  • the sum is determined according to the sum of the path metric values of all candidate paths of the layer.
  • a pruning threshold of the layer and determining, according to the pruning threshold and the search width of each layer, a second decoding path set of the polarization code from the first decoding path set, where the second decoding path set has
  • the decoding path of the maximum path metric is determined as the decoding result of the polarization code, and since the pruning threshold of the layer can be determined according to the sum of the path metrics of all candidate paths of each layer of the decoding code tree, The decoding performance loss is controlled within a preset tolerable performance loss value, and the complexity of the polarization code decoding can be greatly reduced.
  • the SCL decoding (I) of the present invention in Table 1 refers to a decoding method for calculating a pruning threshold using Equation (1)
  • the SCL decoding (II) of the present invention refers to calculation using Equations (3) and (4).
  • the decoding method of the pruning threshold, the SCL decoding (III) of the present invention refers to a decoding method for calculating the pruning threshold according to the formulas (5) and (6).
  • the decoding method of the present invention can greatly reduce the complexity compared to the conventional CASCL decoding algorithm on the premise that the performance is hardly affected.
  • the SCL decoding (II) of the present invention can avoid about 90% of the sorting operation
  • the SCS decoding of the present invention can reduce the probability metric calculation and the 50% path copy operation by 45%.
  • the decoding method of the present invention can still achieve significant complexity gains at this operating point.
  • Figure 9 shows a comparison of the FER performance of the decoding method of the present invention and the prior art decoding method when Ptol is configured to different values, and the basic decoding scheme uses CASCL decoding.
  • the unpruned scheme in the figure refers to the SC decoding method in the prior art in Table 1.
  • the existing pruning scheme refers to the prior art pruning decoding method in Table 1
  • the pruning scheme of the present invention refers to The SCL decoding (III) method of the present invention in Table 1 is shown.
  • the pruning scheme of the present invention and the existing pruning scheme can both have and uncut.
  • Figure 10 shows the corresponding computational complexity curve (the average number of probability metric calculation operations required per frame decoding).
  • the unpruned scheme in the figure refers to the SC decoding method in the prior art in Table 1.
  • the existing pruning scheme refers to the prior art pruning decoding method in Table 1
  • the pruning scheme of the present invention refers to The SCL decoding (III) method of the present invention in Table 1 is shown.
  • Figure 11 shows the FER performance and performance loss values for different P tol settings at a signal-to-noise ratio of 1.5 dB.
  • the unpruned scheme in the figure refers to the SC decoding method in the prior art in Table 1.
  • the existing pruning scheme refers to the prior art pruning decoding method in Table 1
  • the layer is determined according to the sum of the path metric values of all candidate paths of the layer. a pruning threshold, and determining, according to a pruning threshold of each layer, a second set of decoding paths of the polarization code from the first set of decoding paths, and having a maximum path metric in the second decoding path set
  • the decoding path is determined as the decoding result of the polarization code, and the decoding performance loss can be determined because the pruning threshold of the layer can be determined according to the sum of the path metrics of all candidate paths of each layer of the decoding code tree.
  • the control is within the preset tolerable performance loss value, which greatly reduces the complexity of the polarization code decoding.
  • the method for decoding the polarization code of the embodiment of the present invention is described in detail above with reference to FIG. 2 to FIG. 11.
  • the decoding device for the polarization code of the embodiment of the present invention will be described in detail below with reference to FIG.
  • the decoding apparatus 10 for the polarization code decoding includes:
  • the processing module 11 is configured to determine, according to a pruning threshold and a search width L of each layer of the decoding code tree of the polarization code, a second decoding path set of the polarization code from the first decoding path set,
  • the pruning threshold of each layer of the decoding code tree is determined according to a sum of path metric values of all candidate paths of the layer, where the first decoding path set is from the root node to the decoding code tree. Any leaf node a collection of all the shortest paths that make up;
  • the determining module 12 is configured to determine, as the decoding result of the polarization code, a bit estimation sequence corresponding to the decoding path having the largest path metric value in the second decoding path set determined by the processing module 11.
  • the decoding process of the polarization code when the decoding path is extended to each layer of the decoding code tree corresponding to the polarization code, the sum is determined according to the sum of the path metric values of all candidate paths of the layer.
  • the pruning threshold of the layer and determining the surviving path and the deleting path of the layer according to the pruning threshold and the search width L, splitting the surviving path and deleting the deleted path, wherein the path metric of the surviving path is greater than or equal to the The pruning threshold, the path metric of the deleted path is smaller than the pruning threshold.
  • the set of surviving paths of the number of layers of the decoding code tree in which the leaf node is located is determined as the second decoding path set, and the second decoding is performed.
  • the bit estimation sequence corresponding to the decoding path having the largest path metric value in the path set is determined as the decoding result of the polarization code.
  • the decoding path when the decoding path is extended to each layer of the decoding code tree in the decoding process, the sum is determined according to the sum of the path metric values of all candidate paths of the layer.
  • a pruning threshold of the layer and determining, according to the pruning threshold and the search width of each layer, a second decoding path set of the polarization code from the first decoding path set, where the second decoding path set has
  • the bit estimation sequence corresponding to the decoding path of the maximum path metric is determined as the decoding result of the polarization code, since the pruning of the layer can be determined according to the sum of the path metrics of all candidate paths of each layer of the decoding code tree.
  • the threshold enables the loss of decoding performance to be controlled within a predetermined tolerable performance loss value, and can greatly reduce the complexity of polarization code decoding.
  • the processing module 11 when the decoding apparatus is applied to the serial cancellation list SCL, the processing module 11 is specifically configured to: when the decoding path is extended to each layer of the decoding code tree, Determining, in the candidate path set of the layer, a set of candidate path components whose path metric value is greater than a pruning threshold of the layer is a first candidate path set of the layer, where the candidate path set of the first layer of the decoding code tree a set of all shortest paths formed from the root node to any node of the first layer on the decoding code tree; when the length of the candidate path in the first candidate path set is less than the code length of the polarization code, Determining, according to the search width L, a candidate path set of the next layer of the layer, and extending the decoding path to the next layer of the layer, or the length of the candidate path in the first candidate path set is equal to the When the code length of the polarization code is long, a second decoding path set of the polarization code is determined from the first candidate path set
  • the processing module 11 when the decoding apparatus is applied to the serial cancellation list SCL, the processing module 11 is specifically configured to: when the decoding path is extended to each layer of the decoding code tree, Determining, according to the search width L, a second candidate path set of the layer from the candidate paths of the layer, where the candidate path set of the first layer of the decoding code tree is from the root node to the decoding code tree a set of all shortest paths formed by any node of the first layer; when the length of the candidate path in the second candidate path set is less than the code length of the polarization code, the path metric value in the second candidate path set is greater than And a set of subsequent paths of candidate paths equal to the pruning threshold of the layer is determined as a candidate path set of the next layer of the layer, and the decoding path is extended to the next layer of the layer, or, in the When the length of the candidate path in the second candidate path set is equal to the code length of the polarization code, the set of candidate path paths whose path metric value is greater than
  • the processing module 11 when the decoding apparatus is applied to the serial cancellation stack SCS decoding, the processing module 11 is specifically configured to:
  • the path metric value of the pop-up path is greater than or equal to the pruning threshold corresponding to the number of layers of the decoding code tree corresponding to the pop-up path, and the length of the pop-up path is less than the code length of the polarization code, determining the a surviving candidate path set in the candidate path stack, adding the subsequent path corresponding to the pop-up path to the candidate path stack, and performing the next pop-up operation, or
  • the pop-up path is determined as the decoding path in the second decoding path set of the polarization code, and the next pop-up operation is performed.
  • the determining module 12 is specifically configured to: have the maximum path metric value in the second decoding path set, and pass the CRC calibration The bit estimation sequence corresponding to the decoded decoding path is determined as the decoding result of the polarization code.
  • the processing module 11 is specifically configured to: determine a pruning threshold of each layer of the decoding code tree according to the following formula:
  • ⁇ i is the pruning threshold of the i-th layer
  • P tol is a preset tolerable performance loss value
  • K is the length of the information block corresponding to the polarization code
  • L is the search width.
  • the processing module 11 is specifically configured to: determine, according to the following formula, a pruning threshold of each layer of the decoding code tree:
  • ⁇ i is the pruning threshold of the i-th layer
  • L is the search width
  • P tol is the preset tolerable performance loss value, a sequence number set of candidate paths that are deleted among all candidate paths of the i'th layer-1, The path metric of the candidate path in which the kth row is deleted among all candidate paths of the i'th layer-1, The sum of the path metrics for all candidate paths of the i''th layer.
  • the processing module 11 is specifically configured to: determine, according to the following formula, a pruning threshold of each layer of the decoding code tree:
  • c i is a set of candidate paths that are all or partially deleted in the previous i-1 layer decoding process.
  • the processing module 11 is specifically configured to: determine, according to the following formula, a pruning threshold of each layer of the decoding code tree:
  • ⁇ i,t is the pruning threshold of the i-th layer after the t-th stack operation
  • P tol is the preset tolerable performance loss value.
  • the coding apparatus 10 in accordance with an embodiment of the present invention may correspond to the method 100 of performing the coding in the embodiments of the present invention, and that the above and other operations and/or functions of the various modules in the decoding apparatus 10 are respectively implemented for The corresponding processes in FIG. 2 and FIG. 4 to FIG. 6 are not described herein again for the sake of brevity.
  • the decoding path is expanded in the decoding process.
  • the pruning threshold of the layer is determined according to the sum of the path metric values of all candidate paths of the layer, and the first decoding path is determined according to the pruning threshold and the search width of each layer.
  • Determining, in the set, a second set of decoding paths of the polarization code determining a bit estimation sequence corresponding to the decoding path having the largest path metric value in the second decoding path set as a decoding result of the polarization code, Since the pruning threshold of the layer can be determined according to the sum of the path metrics of all candidate paths of each layer of the decoding code tree, the decoding performance loss can be controlled within a preset tolerable performance loss value, and The complexity of polarization code decoding is greatly reduced.
  • FIG. 13 is a schematic block diagram of an apparatus in accordance with another embodiment of the present invention.
  • the apparatus 20 of FIG. 13 can be used to implement the steps and methods of the above method embodiments.
  • the device 20 is applicable to base stations or terminals in various communication systems.
  • device 20 includes a transmit circuit 202, a receive circuit 203, a decode processor 204, a processing unit 205, a memory 206, and an antenna 201.
  • Processing unit 205 controls the operation of device 20 and is operable to process signals.
  • the processing unit 205 may also be referred to as a Central Processing Unit ("CPU").
  • Memory 206 can include read only memory and random access memory and provides instructions and data to processing unit 205.
  • a portion of memory 206 may also include non-volatile line random access memory (NVRAM).
  • device 20 may be embedded or may itself be a wireless communication device such as a mobile telephone, and may also include a carrier that houses transmit circuitry 202 and receive circuitry 203 to allow for data transmission between device 20 and a remote location. receive. Transmit circuitry 202 and receive circuitry 203 may be coupled to antenna 201.
  • the various components of device 20 are coupled together by a bus system 209, which in addition to the data bus includes a power bus, a control bus, and a status signal bus. However, for clarity of description, various buses are labeled as bus system 209 in the figure.
  • Decoding processor 204 may be an integrated circuit chip with signal processing capabilities. In an implementation process, the steps of the above method may be completed by an integrated logic circuit of the hardware in the decoding processor 204 or an instruction in the form of software. These instructions can be implemented and controlled by processing unit 205.
  • the above decoding processor may be a general purpose processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), an off-the-shelf programmable gate array (FPGA), or other programmable Logic devices, discrete gates or transistor logic devices, discrete hardware components.
  • DSP digital signal processor
  • ASIC application specific integrated circuit
  • FPGA off-the-shelf programmable gate array
  • the general purpose processor may be a microprocessor or the processor or any conventional processor, decoder or the like.
  • the steps of the method disclosed in connection with the embodiments of the present invention may be straight
  • the implementation is performed by the hardware decoding processor, or by a combination of hardware and software modules in the decoding processor.
  • the software module can be located in a conventional storage medium such as random access memory, flash memory, read only memory, programmable read only memory or electrically erasable programmable memory, registers, and the like.
  • the storage medium is located in memory 206, and decoding processor 204 reads the information in memory 206 and, in conjunction with its hardware, performs the steps of the above method.
  • memory 206 may store instructions that cause decoding processor 204 or processing unit 205 to perform the following process:
  • the pruning threshold of each layer of the tree is determined according to the sum of path metrics of all candidate paths of the layer, and the first decoding path set is composed of the root node to any leaf node in the decoding code tree.
  • a set of all shortest paths; a bit estimation sequence corresponding to the coding path having the largest path metric value in the second coding path set is determined as a decoding result of the polarization code.
  • the pruning threshold of the layer is determined according to the sum of the path metric values of all the candidate paths of the layer, and according to each The pruning threshold and the search width of one layer determine a second decoding path set of the polarization code from the first decoding path set, and the decoding path with the largest path metric value in the second decoding path set corresponds to
  • the bit estimation sequence is determined as the decoding result of the polarization code, and the decoding performance loss can be determined because the pruning threshold of the layer can be determined according to the sum of the path metrics of all candidate paths of each layer of the decoding code tree.
  • the control is within the preset tolerable performance loss value and can greatly reduce the complexity of the polarization code decoding.
  • system and “network” are used interchangeably herein. It should be understood that the term “and/or” in this document is merely an association describing the associated object, indicating that there may be three types. Relationships, for example, A and/or B, may indicate that there are three cases where A exists separately, and both A and B exist, and B exists alone. In addition, the character “/" in this article generally indicates that the contextual object is an "or" relationship.
  • B corresponding to A means that B is associated with A, and B can be determined from A.
  • determining B from A does not mean that B is only determined based on A, and that B can also be determined based on A and/or other information.
  • the disclosed systems, devices, and methods may be implemented in other manners.
  • the device embodiments described above are merely illustrative.
  • the division of the unit is only a logical function division.
  • there may be another division manner for example, multiple units or components may be combined or Can be integrated into another system, or some features can be ignored or not executed.
  • the mutual coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection through some interface, device or unit, and may be in an electrical, mechanical or other form.
  • the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, may be located in one place, or may be distributed to multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of the embodiment.
  • each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.
  • the integrated unit is implemented as a software functional unit and sold as a standalone product or When used, it can be stored in a computer readable storage medium.
  • the technical solution of the present invention which is essential or contributes to the prior art, or a part of the technical solution, may be embodied in the form of a software product, which is stored in a storage medium, including
  • the instructions are used to cause a computer device (which may be a personal computer, server, or network device, etc.) to perform all or part of the steps of the methods described in various embodiments of the present invention.
  • the foregoing storage medium includes: a USB flash drive, a mobile hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a disk or a CD.
  • ROM Read-Only Memory
  • RAM Random Access Memory

Abstract

本发明实施例提供了一种极化码的译码方法和译码装置，该译码方法包括：根据极化码的译码码树的每一层的剪枝门限和搜索宽度L，从第一译码路径集合中确定出该极化码的第二译码路径集合，其中，该译码码树的每一层的剪枝门限是根据该层的所有候选路径的路径度量值之和确定的，该第一译码路径集合为该译码码树上从根节点到任一叶子节点构成的所有最短路径的集合；将该第二译码路径集合中具有最大路径度量值的译码路径对应的比特估计序列确定为该极化码的译码结果。由于根据译码码树的每一层的所有候选路径的路径度量之和确定该层的剪枝门限，使得能够将译码性能损失控制在预先设定的可容忍性能损失值以内，并能大幅度降低极化码译码的复杂度。

Description

极化码的译码方法和译码装置 技术领域
本发明涉及通信领域，并且更具体地，涉及极化码的译码方法和译码装置。
背景技术
通信系统通常采用信道编码提高数据传输的可靠性，保证通信的质量。最近，Arikan提出的极化码是第一个理论上证明可以取得香农容量且具有低编译码复杂度的好码。当码长较短的时候，传统的串行抵消译码(Successive Cancellation decoding，简称为“SC”)译码的性能并不理想，其性能不如目前已广泛使用的低密度奇偶校验码(Low Density Parity Check，简称为“LDPC”)码或Turbo码。最新的研究表明，基于SC算法改进得到的串行抵消列表译码(Successive Cancellation List decoding，简称为“SCL”)、串行抵消堆栈译码(Successive Cancellation Stack decoding，“SCS”)和串行抵消混合译码(Successive Cancellation Hybrid decoding，简称为“SCH”)算法能够显著提高极化码的误帧率(Frame Error Rate，简称为“FER”)性能，这类算法统称为增强SC译码算法。并且，在循环冗余校验(Cyclic Redundancy Check，简称为“CRC”)辅助的增强SC译码算法下，极化码能够获得优于LDPC与Turbo码的FER性能。然而，为达到较为理想的性能，增强SC译码算法的搜索宽度需要设定为一个较大的值，从而导致译码复杂度较高。
由于增强SC译码算法本质上是译码码树上的路径搜索过程，于是能够在搜索过程中通过剪枝算法及时地删除度量值较小的候选路径，避免不必要的路径扩展过程，从而达到降低复杂度的目的。现有技术给出了一种针对SCL译码算法的剪枝方案。该方法在SCL译码的每一次路径扩展之后根据路径度量值的最大值确定剪枝门限：给定某一个能够容忍的误帧率(Frame ErrorRate，简称为“FER”)性能损失值Ptol，在译码过程(即路径搜索过程)中，列表中的候选路径经过排序之后，若某一长度为i的候选路径度量值满足：
Figure PCTCN2015076958-appb-000001
则删除该候选路径，其中，
Figure PCTCN2015076958-appb-000002
为长度为i的候选路径组成的集合，j为该候选 路径在集合
Figure PCTCN2015076958-appb-000003
中的序号，K为信息块大小，L为SCL译码的搜索宽度，
Figure PCTCN2015076958-appb-000004
为序号为j的候选序列
Figure PCTCN2015076958-appb-000005
根据
Figure PCTCN2015076958-appb-000006
计算得到的路径度量值：
Figure PCTCN2015076958-appb-000007
现有技术中的剪枝方案能够很好地将由于引入剪枝操作而带来的性能损失控制在Ptol以内。
然而现有技术的剪枝方案过于保守，在中、低信噪比时，复杂度降低效果不明显。该信噪比区间正是在CRC辅助增强SC译码下，FER在0.1～0.0001附近的工作区间，此时为了获得与LDPC码或Turbo码相当、甚至更优的性能，译码复杂度依然非常高。
发明内容
本发明提供一种极化码译码的方法和装置，在译码过程中能够将译码性能损失控制在预先设定的可容忍性能损失值以内，并能大幅度降低极化码译码的复杂度。
第一方面，提供了一种极化码译码的方法，包括：根据极化码的译码码树的每一层的剪枝门限和搜索宽度L，从第一译码路径集合中确定出该极化码的第二译码路径集合，其中，该译码码树的每一层的剪枝门限是根据该层的所有候选路径的路径度量值之和确定的，该第一译码路径集合为该译码码树上从根节点到任一叶子节点构成的所有最短路径的集合；将该第二译码路径集合中具有最大路径度量值的译码路径对应的比特估计序列确定为该极化码的译码结果。
结合第一方面，在第一方面的第一种可能的实现方式中，在该译码方法应用于串行抵消列表SCL译码时，该根据极化码的译码码树的每一层的剪枝门限和搜索宽度L，从第一译码路径集合中确定出该极化码的第二译码路径集合，包括：在译码路径扩展到该译码码树的每一层时，将该层的候选路径集合中路径度量值大于该层的剪枝门限的候选路径组成的集合确定为该层的第一候选路径集合，其中，该译码码树的第一层的候选路径集合为该译码码树上从根结点到第一层的任一节点构成的所有最短路径的集合；在该第一候选路径集合中的候选路径的长度小于该极化码的码长时，根据该搜索宽度L，确定该层的下一层的候选路径集合，并将译码路径扩展到该该层的下 一层，或，在该第一候选路径集合中的候选路径的长度等于该极化码的码长时，根据该搜索宽度L，从该第一候选路径集合中确定出该极化码的第二译码路径集合。
结合第一方面，在第一方面的第二种可能的实现方式中，在该译码方法应用于串行抵消列表SCL译码时，该根据极化码的译码码树的每一层的剪枝门限和搜索宽度L，从第一译码路径集合中确定出该极化码的第二译码路径集合，包括：在译码路径扩展到该译码码树的每一层时，根据该搜索宽度L从该层的候选路径集合中确定出该层的第二候选路径集合，其中，该译码码树的第一层的候选路径集合为该译码码树上从根结点到第一层的任一节点构成的所有最短路径的集合；在该第二候选路径集合中的候选路径的长度小于该极化码的码长时，将该第二候选路径集合中路径度量值大于或等于该层的剪枝门限的候选路径的后继路径组成的集合确定为该层的下一层的候选路径集合，并将译码路径扩展到该该层的下一层，或，在该第二候选路径集合中的候选路径的长度等于该极化码的码长时，将该第二候选路径集合中路径度量值大于或等于该层的剪枝门限的候选路径组成的集合确定为该极化码的第二译码路径集合。
结合第一方面，在第一方面的第三种可能的实现方式中，在该译码方法应用于串行抵消堆栈SCS译码时，该根据极化码的译码码树的每一层的剪枝门限和搜索宽度L，从第一译码路径集合中确定出该极化码的第二译码路径集合，包括：
在弹出路径的路径度量值小于该弹出路径对应的译码码树的层数对应的剪枝门限时，删除该弹出路径和候选路径堆栈中长度小于或等于该弹出路径的长度的候选路径，并直接进入到下一次弹栈操作，或，
在弹出路径的路径度量值大于或等于该弹出路径对应的译码码树的层数对应的剪枝门限且该弹出路径的长度小于该极化码的码长时，根据该搜索宽度L确定候选路径堆栈中的幸存候选路径集合，将该弹出路径的后继路径加入到该候选路径堆栈中，并进行下一次弹栈操作，或，
在弹出路径的长度等于该极化码的码长时，将该弹出路径确定为该极化码的第二译码路径集合中的译码路径，并进行下一次弹栈操作。
结合第一方面，第一方面的第一至第三种可能的实现方式中任一可能的实现方式，在第一方面的第四种可能的实现方式中，在采用循环冗余校验 CRC辅助译码时，该将第二译码路径集合中具有最大路径度量值的译码路径对应的比特估计序列确定为该极化码的译码结果，包括：将该第二译码路径集合中具有最大路径度量值，且能通过CRC校验的译码路径对应的比特估计序列确定为该极化码的译码结果。
结合第一方面的第二种可能的实现方式，在第一方面的第五种可能的实现方式中，该译码码树的每一层的剪枝门限是根据该层的所有候选路径的路径度量值之和确定的，包括：该译码码树的每一层的剪枝门限是根据下式确定的：
Figure PCTCN2015076958-appb-000008
其中，τi为第i层的剪枝门限，
Figure PCTCN2015076958-appb-000009
为第i层的所有候选路径的路径度量值之和，Ptol为预设可容忍性能损失值，K为该极化码对应的信息块的长度，L为搜索宽度。
结合第一方面的第二种可能的实现方式，在第一方面的第六种可能的实现方式中，该译码码树的每一层的剪枝门限是根据该层的所有候选路径的路径度量值之和确定的，包括：该译码码树的每一层的剪枝门限是根据下式确定的：
Figure PCTCN2015076958-appb-000010
其中，τi为第i层的剪枝门限，
Figure PCTCN2015076958-appb-000011
为第i层的所有候选路径的路径度量值之和，
Figure PCTCN2015076958-appb-000012
为第i层的可容忍性能损失值，L为搜索宽度；Ptol为预设可容忍性能损失值，
Figure PCTCN2015076958-appb-000013
为第i'-1层的所有候选路径中被删除的候选路径的序号集合，
Figure PCTCN2015076958-appb-000014
为第i'-1层的所有候选路径中第k条被删除的候选路径的路径度量值，
Figure PCTCN2015076958-appb-000015
为第i'-1层的所有候选路径的路径度量值之和。
结合第一方面的第三种可能的实现方式，在第一方面的第七种可能的实现方式中，该译码码树的每一层的剪枝门限是根据该层的所有候选路径的路径度量值之和确定的，包括：该译码码树的每一层的剪枝门限是根据下式确定的：
Figure PCTCN2015076958-appb-000016
其中，j的取值满足下式：
Figure PCTCN2015076958-appb-000017
Figure PCTCN2015076958-appb-000018
为第i层的所有候选路径的序号组成的集合，
Figure PCTCN2015076958-appb-000019
为第i层的可容忍性能损失 值，Ptol为预设可容忍性能损失值，(j,k)表示第j层被删除的候选路径的序号为k，
Figure PCTCN2015076958-appb-000020
为在第j层删除序号为k的候选路径造成的性能损失，ci为所有或部分在前i-1层译码过程中被删除的候选路径组成的集合。
结合第一方面的第四种可能的实现方式，在第一方面的第八种可能的实现方式中，该译码码树的每一层的剪枝门限是根据该层的所有候选路径的路径度量值之和确定的，包括：该译码码树的每一层的剪枝门限是根据下式确定的：
Figure PCTCN2015076958-appb-000021
其中，τi,t为第t次弹栈操作后第i层的剪枝门限，Ptol为预设可容忍性能损失值，
Figure PCTCN2015076958-appb-000022
为在前t-1次弹栈操作中弹出的长度为i的所有候选路径的路径度量值之和，K为该极化码对应的信息块的长度，L为搜索宽度。
第二方面，提供了一种极化码的译码装置，包括：处理模块，用于根据极化码的译码码树的每一层的剪枝门限和搜索宽度L，从第一译码路径集合中确定出该极化码的第二译码路径集合，其中，该译码码树的每一层的剪枝门限是根据该层的所有候选路径的路径度量值之和确定的，该第一译码路径集合为该译码码树上从根节点到任一叶子节点构成的所有最短路径的集合；确定模块，用于将该处理模块确定出的该第二译码路径集合中具有最大路径度量值的译码路径对应的比特估计序列确定为该极化码的译码结果。
结合第二方面，在第二方面的第一种可能的实现方式中，在该译码装置应用于串行抵消列表SCL译码时，该处理模块具体用于：在译码路径扩展到该译码码树的每一层时，将该层的候选路径集合中路径度量值大于该层的剪枝门限的候选路径组成的集合确定为该层的第一候选路径集合，其中，该译码码树的第一层的候选路径集合为该译码码树上从根结点到第一层的任一节点构成的所有最短路径的集合；在该第一候选路径集合中的候选路径的长度小于该极化码的码长时，根据该搜索宽度L，确定该层的下一层的候选路径集合，并将译码路径扩展到该该层的下一层，或，在该第一候选路径集合中的候选路径的长度等于该极化码的码长时，根据该搜索宽度L，从该第一候选路径集合中确定出该极化码的第二译码路径集合。
结合第二方面，在第二方面的第二种可能的实现方式中，在该译码装置应用于串行抵消列表SCL译码时，该处理模块具体用于：在译码路径扩展到该译码码树的每一层时，根据该搜索宽度L从该层的候选路径集合中确定 出该层的第二候选路径集合，其中，该译码码树的第一层的候选路径集合为该译码码树上从根结点到第一层的任一节点构成的所有最短路径的集合；在该第二候选路径集合中的候选路径的长度小于该极化码的码长时，将该第二候选路径集合中路径度量值大于或等于该层的剪枝门限的候选路径的后继路径组成的集合确定为该层的下一层的候选路径集合，并将译码路径扩展到该该层的下一层，或，在该第二候选路径集合中的候选路径的长度等于该极化码的码长时，将该第二候选路径集合中路径度量值大于或等于该层的剪枝门限的候选路径组成的集合确定为该极化码的第二译码路径集合。
结合第二方面，在第二方面的第三种可能的实现方式中，在该译码装置应用于串行抵消堆栈SCS译码时，该处理模块具体用于：
在弹出路径的路径度量值小于该弹出路径对应的译码码树的层数对应的剪枝门限时，删除该弹出路径和候选路径堆栈中长度小于或等于该弹出路径的长度的候选路径，并直接进入到下一次弹栈操作，或，
在弹出路径的路径度量值大于或等于该弹出路径对应的译码码树的层数对应的剪枝门限且该弹出路径的长度小于该极化码的码长时，根据该搜索宽度L确定候选路径堆栈中的幸存候选路径集合，将该弹出路径对应的后继路径加入到该候选路径堆栈中，并进行下一次弹栈操作，或，
在弹出路径的长度等于该极化码的码长时，将该弹出路径确定为该极化码的第二译码路径集合中的译码路径，并进行下一次弹栈操作。
结合第二方面，第二方面的第一种至第三种可能的实现方式中任一可能的实现方式，在第二方面的第四种可能的实现方式中，在采用循环冗余校验CRC辅助译码时，该确定模块具体用于：将该第二译码路径集合中具有最大路径度量值，且能通过CRC校验的译码路径对应的比特估计序列确定为该极化码的译码结果。
结合第二方面的第一种可能的实现方式，在第二方面的第五种可能的实现方式中，该处理模块具体用于：根据下式确定该译码码树的每一层的剪枝门限：
Figure PCTCN2015076958-appb-000023
其中，τi为第i层的剪枝门限，
Figure PCTCN2015076958-appb-000024
为第i层的所有候选路径的路径度量值之和，Ptol为预设可容忍性能损失值，K为该极化码对应的信息块的长度，L为搜索宽度。
结合第二方面的第一种可能的实现方式中，在第二方面的第六种可能的实现方式中，该处理模块具体用于：根据下式确定该译码码树的每一层的剪枝门限：
Figure PCTCN2015076958-appb-000025
其中，τi为第i层的剪枝门限，
Figure PCTCN2015076958-appb-000026
为第i层的所有候选路径的路径度量值之和，
Figure PCTCN2015076958-appb-000027
为第i层的可容忍性能损失值，L为搜索宽度；Ptol为预设可容忍性能损失值，
Figure PCTCN2015076958-appb-000028
为第i'-1层的所有候选路径中被删除的候选路径的序号集合，
Figure PCTCN2015076958-appb-000029
为第i'-1层的所有候选路径中第k条被删除的候选路径的路径度量值，
Figure PCTCN2015076958-appb-000030
为第i'-1层的所有候选路径的路径度量值之和。
结合第二方面的第二种可能的实现方式，在第二方面的第七种可能的实现方式中，该处理模块具体用于：根据下式确定该译码码树的每一层的剪枝门限：
Figure PCTCN2015076958-appb-000031
其中，j的取值满足下式：
Figure PCTCN2015076958-appb-000032
Figure PCTCN2015076958-appb-000033
为第i层的所有候选路径的序号组成的集合，
Figure PCTCN2015076958-appb-000034
为第i层的可容忍性能损失值，Ptol为预设可容忍性能损失值，(j,k)表示第j层被删除的候选路径的序号为k，
Figure PCTCN2015076958-appb-000035
为在第j层删除序号为k的候选路径造成的性能损失，ci为所有或部分在前i-1层译码过程中被删除的候选路径组成的集合。
结合第二方面的第三种可能的实现方式，在第二方面的第四种可能的实现方式中，该处理模块具体用于：根据下式确定该译码码树的每一层的剪枝门限：
Figure PCTCN2015076958-appb-000036
其中，τi,t为第t次弹栈操作后第i层的剪枝门限，Ptol为预设可容忍性能损失值，
Figure PCTCN2015076958-appb-000037
为在前t-1次弹栈操作中弹出的长度为i的所有候选路径的路径度量值之和，K为该极化码对应的信息块的长度，L为搜索宽度。
基于上述技术特征，本发明实施例提供的极化码的译码方法和译码装置，在译码过程中路径扩展到译码码树的每一层时，根据该层的所有候选路径的路径度量值之和确定该层的剪枝门限，并根据每一层的剪枝门限和搜索宽度从第一译码路径集合中确定出该极化码的第二译码路径集合，将该第二 译码路径集合中具有最大路径度量值的译码路径确定为该极化码的译码结果，由于根据译码码树的每一层的所有候选路径的路径度量之和确定该层的剪枝门限，使得能够将译码性能损失控制在预先设定的可容忍性性能损失值以内，并能大幅度降低极化码译码的复杂度。
附图说明
为了更清楚地说明本发明实施例的技术方案，下面将对实施例或现有技术描述中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动性的前提下，还可以根据这些附图获得其他的附图。
图1示出了根据本文所述的各个实施例的无线通信系统；
图2是根据本发明实施例的极化码的译码方法的示意性流程图；
图3是根据本发明实施例的码长为4的极化码的译码码树；
图4是根据本发明实施例的极化码译码方法的另一示意性流程图；
图5是根据本发明实施例的极化码译码方法的再一示意性流程图；
图6是根据本发明实施例的极化码译码方法的再一示意性流程图；
图7是根据本发明另一实施例的极化码译码方法的示意性流程图；
图8是根据本发明再一实施例的极化码译码方法的示意性流程图；
图9是本发明实施例的译码方法与现有技术的译码方法在FER性能上的比较的示意图；
图10是本发明实施例的译码方法与现有技术的译码方法对应的计算复杂度曲线；
图11是在信噪比为1.5dB时，FER性能及性能损失值与预设可容忍性能损失值之间的关系曲线；
图12是根据本发明实施例的译码装置的示意性框图；
图13是根据本发明实施例的装置的示意性框图。
具体实施方式
下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有付出创 造性劳动的前提下所获得的所有其他实施例，都属于本发明保护的范围。
本发明实施例可应用于各种通信系统，因此，下面的描述不限制于特定通信系统。全球移动通讯(Global System of Mobile communication，简称“GSM”)系统、码分多址(Code Division Multiple Access，简称“CDMA”)系统、宽带码分多址(Wideband Code Division Multiple Access，简称“WCDMA”)系统、通用分组无线业务(General Packet Radio Service，简称“GPRS”)、长期演进(Long Term Evolution，简称“LTE”)系统、LTE频分双工(Frequency Division Duplex，简称“FDD”)系统、LTE时分双工(Time Division Duplex，简称“TDD”)、通用移动通信系统(Universal Mobile Telecommunication System，简称“UMTS”)等。在上述的系统中的基站或者终端使用传统Turbo码、LDPC码编码处理的信息或者数据都可以使用本实施例中的极化码编码。
图1示出了根据本文所述的各个实施例的无线通信系统100。系统100包括基站102，后者可包括多个天线组。例如，一个天线组可包括天线104和106，另一个天线组可包括天线108和110，附加组可包括天线112和114。对于每个天线组示出了2个天线，然而可对于每个组使用更多或更少的天线。基站102可附加地包括发射机链和接收机链，本领域普通技术人员可以理解，它们均可包括与信号发送和接收相关的多个部件(例如处理器、调制器、复用器、解调器、解复用器或天线等)。
基站102可以与一个或多个接入终端(例如接入终端116和接入终端122)通信。然而，可以理解，基站102可以与类似于接入终端116和122的基本上任意数目的接入终端通信。接入终端116和122可以是例如蜂窝电话、智能电话、便携式电脑、手持通信设备、手持计算设备、卫星无线电装置、全球定位系统、PDA和/或用于在无线通信系统100上通信的任意其它适合设备。如图所示，接入终端116与天线112和114通信，其中天线112和114通过前向链路118向接入终端116发送信息，并通过反向链路120从接入终端116接收信息。此外，接入终端122与天线104和106通信，其中天线104和106通过前向链路124向接入终端122发送信息，并通过反向链路126从接入终端122接收信息。在频分双工(Frequency Division Duplex，简称为“FDD”)系统中，例如，前向链路118可利用与反向链路120所使用的不同频带，前向链路124可利用与反向链路126所使用的不同频带。此 外，在时分双工(Time Division Duplex，简称为“TDD”)系统中，前向链路118和反向链路120可使用共同频带，前向链路124和反向链路126可使用共同频带。
被设计用于通信的每组天线和/或区域称为基站102的扇区。例如，可将天线组设计为与基站102覆盖区域的扇区中的接入终端通信。在通过前向链路118和124的通信中，基站102的发射天线可利用波束成形来改善针对接入终端116和122的前向链路118和124的信噪比。此外，与基站通过单个天线向它所有的接入终端发送相比，在基站102利用波束成形向相关覆盖区域中随机分散的接入终端116和122发送时，相邻小区中的移动设备会受到较少的干扰。
在给定时间，基站102、接入终端116和/或接入终端122可以是发送无线通信装置和/或接收无线通信装置。当发送数据时，发送无线通信装置可对数据进行编码以用于传输。具体地，发送无线通信装置可具有(例如生成、获得、在存储器中保存等)要通过信道发送至接收无线通信装置的一定数目的信息比特。这种信息比特可包含在数据的传输块(或多个传输块)中，其可被分段以产生多个码块。此外，发送无线通信装置可使用极化码编码器(未示出)来对每个码块编码，以提高数据传输的可靠性，进而保证通信质量。
对于串行抵消列表SCL译码，所有的候选路径与其对应的路径度量值都被存储在一个列表中。列表中所有的候选路径被同步地扩展，所以每次扩展之后，列表中候选路径数量就会翻倍。丢弃那可靠性度量值较小的部分候选路径，以保证候选路径数始终不大于列表大小的一半。在译码结束时，从列表中找出可靠性度量值最大的那条路径，其对应的比特估计序列即为译码结果。
对于串行抵消堆栈译码SCS译码使用一个有序堆栈，而不是列表，去存储候选路径。SCS译码过程中，每次都只基于可靠性度量最大的那一条候选路径(位于堆栈的栈顶)进行扩展。当出现栈顶路径到达码树的某一个叶子节点时，停止译码过程，并且将该路径所对应的比特估计序列输出，作为译码结果。
SCL译码可以看作是在码树上做广度优先搜索，而SCS译码则是在码树上做最佳优先搜索。SCL译码允许较低的空间复杂度，而SCS译码的计算复杂度较低。将两种模式混合，即为SCH译码。SCH译码的实现机构类 似SCS译码，也使用一个有序堆栈存储候选路径。所不同的是，SCH的堆栈深度远远小于SCS译码，并且通过灵活地在两种模式下切换，使得候选路径数始终不会使堆栈溢出。SCH译码的计算复杂度稍高于SCS译码、远小于SCL译码；空间复杂度稍高于SCL译码远小于SCS译码。
无论是何种实现方式，增强SC译码的本质就是搜索得到一组具有较大路径度量值的候选路径集合，并从中选择路径度量值最大的一条作为译码输出。
如果信息块包含了循环冗余校验信息，即信息块序列的CRC结果为全零序列，那么就可以使用CRC辅助的增强SC译码算法进行译码，即从最终得到的候选路径集合中选择具有最大路径度量值且能够通过CRC校验的一条候选路径作为译码输出。同样地，根据在码树上的搜索策略不同，有CASCL、CASCS以及CASCH三种实现方法。采用这类译码方法时，有限码长极化码的抗噪性能可以得到很大幅度的提高，并且能够显著优于现广泛应用于各通信系统的LDPC码与Turbo码。
图2是本发明一个实施例的极化码的译码方法的流程图。图1的方法由译码端执行。如图1所示，该方法100包括：
S110，根据极化码的译码码树的每一层的剪枝门限和搜索宽度L，从第一译码路径集合中确定出该极化码的第二译码路径集合，其中，该译码码树的每一层的剪枝门限是根据该层的所有候选路径的路径度量值之和确定的，该第一译码路径集合为该译码码树上从根节点到任一叶子节点构成的所有最短路径的集合；
S120，将该第二译码路径集合中具有最大路径度量值的译码路径对应的比特估计序列确定为该极化码的译码结果。
具体而言，在极化码的译码过程中，在译码路径扩展到极化码对应的译码码树的每一层时，根据该层的所有候选路径的路径度量值之和确定该层的剪枝门限，并根据该剪枝门限和搜索宽度L确定该层的幸存路径和删除路径，将幸存路径进行路径分裂且将删除路径删除，其中，幸存路径的路径度量值大于或等于该剪枝门限，删除路径的路径度量值小于该剪枝门限。在译码路径扩展到译码码树的叶子节点时，将该叶子节点所在的译码码树的层数的幸存路径组成的集合确定为第二译码路径集合，并将该第二译码路径集合中具有最大路径度量值的译码路径对应的比特估计序列确定为该极化码的 译码结果。
因此，本发明实施例的极化码的译码方法，在译码过程中译码路径扩展到译码码树的每一层时，根据该层的所有候选路径的路径度量值之和确定该层的剪枝门限，并根据每一层的剪枝门限和搜索宽度从第一译码路径集合中确定出该极化码的第二译码路径集合，将该第二译码路径集合中具有最大路径度量值的译码路径对应的比特估计序列确定为该极化码的译码结果，由于能够根据译码码树的每一层的所有候选路径的路径度量之和确定该层的剪枝门限，使得能够将译码性能损失控制在预先设定的可容忍性能损失值以内，并能大幅度降低极化码译码的复杂度。
应理解，在本发明实施例中，删除候选路径的操作可以被称为剪枝操作，但本发明并不限于此。
应理解，在本发明实施例中，一个码长为N的极化码可以对应一个由N层边构成的二叉译码码树，第一译码路径集合是指极化码的译码码树上从根节点到任一叶子节点构成的所有最短路径的集合，若为CRC辅助增强SC译码，更要求第一译码路径集合中的译码路径所对应的信息比特序列能够通过CRC校验。除叶子节点外，译码码树中各节点均有2条后继节点，与该节点和该节点的两个后继节点相关联的两条边分别被标记为0和1。所有的边根据与其相关联的、远离根节点的那个节点到根节点的距离被分为N层，最靠近根节点的为第1层，与叶子节点相关联的为第N层，图3所示是一个码长为4的极化码的译码码树，该译码码树共有4层。
在本发明实施例中，可选地，在采用循环冗余校验CRC辅助译码时，在S120中，将该第二译码路径集合中具有最大路径度量值且能通过CRC校验的译码路径对应的比特估计序列确定为该极化码的译码结果。
在本发明实施例中，可选地，如图4所示，在应用于串行抵消列表SCL译码时，S110具体包括以下步骤：
S111，在译码路径扩展到所述译码码树的每一层时，将该层的候选路径集合中路径度量值大于该层的剪枝门限的候选路径组成的集合确定为该层的第一候选路径集合，其中，该译码码树的第一层的候选路径集合为该译码码树上从根结点到第一层的任一节点构成的所有最短路径的集合；
S112，在该第一候选路径集合中的候选路径的长度小于该极化码的码长时，根据该搜索宽度L，确定该层的下一层的候选路径集合，并将译码路径 扩展到该该层的下一层，或，在该第一候选路径集合中的候选路径的长度等于该极化码的码长时，根据该搜索宽度L，从该第一候选路径集合中确定出该极化码的第二译码路径集合。
应理解，在本发明实施例中，候选路径的长度指的是候选路径对应的比特估计序列的长度。
还应理解，在S112中，在该第一候选路径集合中的候选路径的长度小于该极化码的码长时，将译码路径扩展到该该层的下一层后，再执行S111，循环执行S112和S111，直至在S112中第一候选路径集合中的候选路径的长度等于该极化码的码长时，根据搜索宽度L从该第一候选路径集合中确定出该极化码的第二译码路径集合。
可选地，在S112中，在该第一候选路径集合中的候选路径的长度小于该极化码的码长时，根据该搜索宽度L，确定该层的下一层的候选路径集合，并将译码路径扩展到该该层的下一层，具体步骤为：在第一候选路径集合中的候选路径的条数大于该搜索宽度L时，将该第一候选路径集合中具有最大路径度量值的L条候选路径的后继路径组成的集合确定为该层的下一层的候选路径集合，并将译码路径扩展到该该层的下一层；在第一候选路径集合中的候选路径的条数小于或等于该搜索宽度L时，将该第一候选路径集合中所有候选路径的后继路径组成的集合确定为该层的下一层的候选路径集合，并将译码路径扩展到该该层的下一层。
具体而言，在该第一候选路径集合中的候选路径的长度小于该极化码的码长且该第一候选路径集合中的候选路径的条数大于该搜索宽度L时，可以对该第一候选路径集合中的每条候选路径按照路径度量值的大小进行排序，保留路径度量值最大的L条候选路径，并将该L条候选路径的后继路径组成的集合确定为该层的下一层的候选路径集合，同时将第一候选路径集合中除该L条候选路径外的候选路径删除；在该第一候选路径集合中的候选路径的条数小于或等于该搜索宽度L时，可以对该第一候选路径集合中的每条候选路径按照路径度量值的大小进行排序，也可以不进行排序，直接将该第一候选路径集合中所有候选路径的后继路径确定为该层的下一层的候选路径集合，本发明对此不作限定。
可选地，在S112中，在该第一候选路径集合中的候选路径的长度等于该极化码的码长时，根据该搜索宽度L，从该第一候选路径集合中确定出该 极化码的第二译码路径集合，具体步骤为：在该第一候选路径集合中的候选路径的条数大于该搜索宽度L时，将该第一候选路径集合中具有最大路径度量值的L条候选路径组成的集合确定为该极化码的第二译码路径集合；在该第一候选路径集合中的候选路径的条数小于或等于该搜索宽度L时，将该第一候选路径集合确定为该极化码的第二译码路径集合。
具体而言，在该第一候选路径集合中的候选路径的长度等于该极化码的码长且在该第一候选路径集合中的候选路径的条数大于该搜索宽度L时，可以对该第一候选路径集合中的每条候选路径按照路径度量值的大小进行排序，将路径度量值最大的L条候选路径组成的集合确定为该极化码的第二译码路径集合，并将第一候选路径集合中除该L条候选路径外的候选路径删除；在该第一候选路径集合中的候选路径的条数小于或等于该搜索宽度L时，可以对该第一候选路径集合中的每条候选路径按照路径度量值的大小进行排序，也可以不进行排序，直接将该第一候选路径集合确定为该极化码的第二译码路径集合，本发明对此不作限定。
在本发明实施例中，可选地，可以根据公式(1)确定该译码码树的每一层的剪枝门限：
Figure PCTCN2015076958-appb-000038
其中，τi为第i层的剪枝门限，
Figure PCTCN2015076958-appb-000039
为第i层的所有候选路径的路径度量值之和，Ptol为预设可容忍性能损失值，K为该极化码对应的信息块的长度，L为搜索宽度。
具体而言，在译码开始之前可以根据实际需要预先设定整个译码过程中能够容忍的性能损失值Ptol(例如：误帧率)，并且
Figure PCTCN2015076958-appb-000040
可以根据公式(2)具体计算得到：
Figure PCTCN2015076958-appb-000041
其中，
Figure PCTCN2015076958-appb-000042
表示第i-1层路径扩展结束后的候选路径的列表，即
Figure PCTCN2015076958-appb-000043
中包括第i层的所有候选路径，
Figure PCTCN2015076958-appb-000044
表示序号为k的候选路径的路径度量值，可以根据现有技术中的计算方法计算每条候选路径的路径度量值，本发明对此不作限定。
在本发明实施例中，可选地，可以根据公式(3)和(4)确定译码码树的每一层的剪枝门限：
Figure PCTCN2015076958-appb-000045
Figure PCTCN2015076958-appb-000046
其中，τi为第i层的剪枝门限，
Figure PCTCN2015076958-appb-000047
为第i层的所有候选路径的路径度量值之和，
Figure PCTCN2015076958-appb-000048
为第i层的可容忍性能损失值，L为搜索宽度；Ptol为预设可容忍性能损失值，
Figure PCTCN2015076958-appb-000049
为第i'-1层的所有候选路径中被删除的候选路径的序号集合，
Figure PCTCN2015076958-appb-000050
为第i'-1层的所有候选路径中第k条被删除的候选路径的路径度量值，
Figure PCTCN2015076958-appb-000051
为第i'-1层的所有候选路径的路径度量值之和。
因此，本发明实施例的极化码译码的方法，在译码过程中译码路径扩展到译码码树的每一层时，根据该层的所有候选路径的路径度量值之和确定该层的剪枝门限，并根据该剪枝门限确定该层的第一候选路径集合之后，根据搜索宽度确定该层的下一层的候选路径集合或极化码的第二译码路径集合，能够减少候选路径的路径度量值的计算操作、候选路径的复制操作和对候选路径的路径度量值的排序操作，由此，能够将译码性能损失控制在预先设定的可容忍性能损失值以内，并能大幅度降低极化码译码的复杂度。
在本发明实施例中，可选地，如图5所示，在应用于串行抵消列表SCL译码时，S110具体包括以下步骤：
S113，在译码路径扩展到该译码码树的每一层时，根据该搜索宽度L从该层的候选路径集合中确定出该层的第二候选路径集合，其中，该译码码树的第一层的候选路径集合为该译码码树上从根结点到第一层的任一节点构成的所有最短路径的集合；
S114，在该第二候选路径集合中的候选路径的长度小于该极化码的码长时，将该第二候选路径集合中路径度量值大于或等于该层的剪枝门限的候选路径的后继路径组成的集合确定为该层的下一层的候选路径集合，并将译码路径扩展到该该层的下一层，或，在该第二候选路径集合中的候选路径的长度等于该极化码的码长时，将该第二候选路径集合中路径度量值大于或等于该层的剪枝门限的候选路径组成的集合确定为该极化码的第二译码路径集合。
应理解，在S114中，在该第二候选路径集合中的候选路径的长度小于该极化码的码长时，将译码路径扩展到该该层的下一层后，再执行S113，循 环执行S113和S114，直至在S114中第二候选路径集合中的候选路径的长度等于该极化码的码长时，将该第二候选路径集合中路径度量值大于或等于该层的剪枝门限的候选路径组成的集合确定为该极化码的第二译码路径集合。
可选地，在S113中，在译码路径扩展到该译码码树的每一层时，根据该搜索宽度L从该层的候选路径集合中确定该层的第二候选路径集合，具体步骤为：在该层的候选路径集合中的候选路径的条数大于该搜索宽度L时，将该层的候选路径集合中具有最大路径度量值的L条候选路径组成的集合确定为该层的第二候选路径集合；在该层的候选路径集合中的候选路径的条数小于或等于该搜索宽度L时，将该层的候选路径集合确定为该层的第二候选路径集合。
具体而言，在译码路径扩展到该译码码树的每一层且该层的候选路径集合中的候选路径的条数大于该搜索宽度L时，可以对该候选路径集合中的每条候选路径按照路径度量值的大小进行排序，将路径度量值最大的L条候选路径组成的集合确定为该层的第二候选路径集合，同时将除该L条候选路径外的候选路径删除；在该层的候选路径集合中的候选路径的条数小于或等于该搜索宽度L时，可以对该层的候选路径集合中的每条候选路径按照路径度量值的大小进行排序，也可以不进行排序，直接将该层的候选路径集合确定为该层的第二候选路径集合，本发明对此不作限定。
在本发明实施例中，可选地，可以根据公式(5)确定译码码树的每一层的剪枝门限：
Figure PCTCN2015076958-appb-000052
其中，j的取值满足公式(6)：
Figure PCTCN2015076958-appb-000053
Figure PCTCN2015076958-appb-000054
为第i层的所有候选路径的序号组成的集合，
Figure PCTCN2015076958-appb-000055
为第i层的可容忍性能损失值，Ptol为预设可容忍性能损失值，(j,k)表示第j层被删除的候选路径的序号为k，
Figure PCTCN2015076958-appb-000056
为在第j层删除序号为k的候选路径造成的性能损失，ci为所有或部分在前i-1层译码过程中被删除的候选路径组成的集合。
具体而言，
Figure PCTCN2015076958-appb-000057
依据预先设定的可容忍性能损失值Ptol以及在前i-1层中部分因剪枝操作删除的路径决定，该部分被剪枝的路径为：在第i层的路径度量估计值大于第i层幸存路径中的最小路径度量值的被剪枝路径中，性能损 失估计值最大的若干条路径所组成的集合，其计算方法如下：
在译码达到译码码树第i层时在剪枝步骤被删除的候选路径在列表
Figure PCTCN2015076958-appb-000058
中的序号为j，路径度量值为
Figure PCTCN2015076958-appb-000059
在译码达到码树第i层时在剪枝步骤被删除的候选路径的序号集合为
Figure PCTCN2015076958-appb-000060
第j层被剪枝删除的候选路径(序号为k)，该路径的后继在第i层时的度量上界为
Figure PCTCN2015076958-appb-000061
该路径的删除对性能造成的影响值为
Figure PCTCN2015076958-appb-000062
定义集合
Figure PCTCN2015076958-appb-000063
该集合指示了所有在前(i-1)层译码时通过剪枝操作删除的候选路径；令集合
Figure PCTCN2015076958-appb-000064
满足：对任意
Figure PCTCN2015076958-appb-000065
有
Figure PCTCN2015076958-appb-000066
且对任意
Figure PCTCN2015076958-appb-000067
有
Figure PCTCN2015076958-appb-000068
Figure PCTCN2015076958-appb-000069
表示由所有属于集合
Figure PCTCN2015076958-appb-000070
但不属于集合
Figure PCTCN2015076958-appb-000071
的元素组成的
Figure PCTCN2015076958-appb-000072
的子集。
若
Figure PCTCN2015076958-appb-000073
则
Figure PCTCN2015076958-appb-000074
否则，
Figure PCTCN2015076958-appb-000075
应当满足
Figure PCTCN2015076958-appb-000076
且对任意
Figure PCTCN2015076958-appb-000077
与任意
Figure PCTCN2015076958-appb-000078
有
Figure PCTCN2015076958-appb-000079
从而，
Figure PCTCN2015076958-appb-000080
上述过程中，
Figure PCTCN2015076958-appb-000081
的值根据以下方法得到：
通过密度进化或高斯近似，可以得到序号为i的比特对应的极化信道在发送比特0时，接收信号对数似然比LLRi＝ln(W(i)(y|0)/W(i)(y|1))的概率密度分布函数pi(l)；
定义函数
Figure PCTCN2015076958-appb-000082
自变量t≥0，其反函数为f-1(s)；
计算vi＝f-1(εPtol)，设置为ε＝0.00001；
则在译码达到译码码树第i层时路径度量值的上界为：
Figure PCTCN2015076958-appb-000083
因此，本发明实施例的极化码译码的方法，在译码过程中译码路径扩展到译码码树的每一层时，根据搜索宽度L确定该层的第二候选路径集合之后，根据该层的所有候选路径的路径度量值之和确定该层的剪枝门限，并根据该剪枝门限确定该层的下一层的候选路径集合或极化码的第二译码路径集合，能够减少候选路径的路径度量值的计算操作、候选路径的复制操作和对候选路径的路径度量值的排序操作，由此，能够将译码性能损失控制在预先设定的可容忍性能损失值以内，并能大幅度降低极化码译码的复杂度。
在本发明实施例中，可选地，如图6所示，在应用于串行抵消堆栈SCS译码时，S110具体包括以下步骤：
S115，在弹出路径的路径度量值小于该弹出路径对应的译码码树的层数对应的剪枝门限时，删除该弹出路径和该候选路径堆栈中长度小于或等于该 弹出路径的长度的候选路径，并直接进入到下一次弹栈操作，或，
在弹出路径的路径度量值大于或等于该弹出路径对应的译码码树的层数对应的剪枝门限且该弹出路径的长度小于该极化码的码长时，根据该搜索宽度L确定该候选路径堆栈中的幸存候选路径集合，将该弹出路径的后继路径加入到该候选路径堆栈中，并进行下一次弹栈操作，或，
在弹出路径的长度等于该极化码的码长时，将该弹出路径确定为该极化码的第二译码路径集合中的译码路径，并进行下一次弹栈操作。
应理解，在S115中，在候选路径堆栈为空时，结束弹栈操作。
还应理解，在S115中，该弹出路径对应的译码码树的层数对应的剪枝门限是根据该层数的所有候选路径的路径度量值之和确定的，该层数的所有候选路径指的是在该次弹栈操作之前的弹栈操作过程中弹出的长度与此次弹栈操作弹出的弹出路径的长度相同的所有弹出路径。
在本发明实施例中，可选地，可以根据公式(7)确定译码码树每一层的剪枝门限：
Figure PCTCN2015076958-appb-000084
其中，τi,t为第t次弹栈操作后第i层的剪枝门限，Ptol为预设可容忍性能损失值，
Figure PCTCN2015076958-appb-000085
为在前t-1次弹栈操作中弹出的长度为i的所有候选路径的路径度量值之和，K为所述极化码对应的信息块的长度，L为搜索宽度。
在本发明实施例中，可选地，可以根据公式(8)确定译码码树每一层的剪枝门限：
Figure PCTCN2015076958-appb-000086
其中，
Figure PCTCN2015076958-appb-000087
为第i层译码时允许由剪枝操作引入的性能损失，其值根据(4)或(6)确定，
Figure PCTCN2015076958-appb-000088
在SCS译码时定义为t次弹栈操作中弹出的、长度为i的候选路径所组成的集合，集合序列
Figure PCTCN2015076958-appb-000089
将随着t的增加而不断更新，因此在SCS译码时，不同t时的不尽相同。
在本发明实施例中，可选地，当本发明实施例的译码方法应用于SCH译码时，若SCH译码器工作在广度优先的搜索模式下，则采用当本发明实施例应用于SCL译码时的相关步骤进行操作，若SCH译码器工作在最佳有限搜索模式下，则采用当本发明实施例应用于SCS译码时的相关步骤进行操作。
因此，本发明实施例的极化码译码的方法，在应用于SCS译码时，在译码过程中，每一次弹栈操作之后根据之前弹栈操作弹出的长度与该次弹栈操作弹出的候选路径的长度相同的弹出路径的度量值之和确定此次弹栈操作弹出的弹出路径对应的层数的剪枝门限，并根据该剪枝门限和搜索宽度L执行后续译码操作，能够减少候选路径的路径度量值的计算操作和对候选路径的路径度量值的排序操作，由此，能够将译码性能损失控制在预先设定的可容忍性能损失值以内，并能大幅度降低极化码译码的复杂度。
下面将结合具体的例子详细描述本发明实施例，应注意，这些例子只是为了帮助本领域技术人员更好地理解本发明实施例，而非限制本发明实施例的范围。
图7是根据本发明另一实施例的极化码译码方法的示意性流程图。如图7所示，该方法200包括：
S201，初始化候选路径列表，填充一条空路径，并设置i＝1；
S202，计算列表中各候选路径的两条后继路径的路径度量值；
具体地，在S202中，可以根据现有技术中计算路径度量值的方法计算列表中个候选路径的两条后继路径的路径度量值，但本发明并不限于此。
S203，判断序号为i的比特是否为固定比特；
S204，删除路径度量值小于剪枝门限的候选路径；
具体而言，在S204中，采用本发明实施例的计算剪枝门限的公式(1)或公式(3)计算译码码树的每一层的剪枝门限，并删除候选路径中路径度量值小于剪枝门限的候选路径。
S205，对路径度量值排序；
具体地，将列表中所有没被删除的候选路径按照路径度量值的大小进行排序。
S206，保留具有最大路径度量值的L条候选路径的后继路径，删除其余的；
具体地，在S205中对列表中没被删除的候选路径按照路径度量值大小进行排序之后，保留具有最大路径度量值的L条候选路径，并进行路径扩展，同时删除该L条候选路径之外的候选路径。
S207，在需要时，进行路径复制；
S208，更新表中幸存路径的对第i个比特的判决值；
S209，判断i的取值是否等于极化码的码长N；
S210，从列表中选择具有最大路径度量值的路径，并将其对应的比特序列输出为译码判决序列；
应理解，如果采用CRC辅助译码，需要从表中选择能够通过CRC校验并且具有最大路径度量值的路径，将其对应的比特序列输出为译码判决序列。
可选地，在S203中，判断为i的比特为固定比特时，直接执行S208。在S209中i的取值与极化码的码长N不相等时，执行S211，将i的值增加1，之后重新执行S202及S202以后的步骤，直至i的取值与极化码的码长N相等。
可选地，在S204中，删除路径度量值小于剪枝门限的候选路径后，在没有被删除的候选路径的条数小于L时，可以不执行S205，相应的在S206中，将所有没被删除的候选路径进行路径扩展。
可选地，S204也可以在S206之后执行，在S204中可以根据本发明实施例的计算剪枝门限的公式(5)和公式(6)计算译码码树的每一层的剪枝门限。
图8是根据本发明再一实施例的极化码译码方法的示意性流程图。如图8所示，该方法300包括：
S301，初始化候选路径堆栈，填充一条空路径；
S302，弹出栈顶路径，路径长度为i；
S303，长度为i的弹出路径对应的计数器值加1；
S304，确定弹出路径的长度与极化码码长N是否相等；
S305，确定弹出路径的路径度量值小于剪枝门限；
具体而言，在确定弹出路径的长度与极化码码长N不相等时，可以根据本发明实施例的计算剪枝门限的公式(7)或(8)计算译码码树每一层的剪枝门限，并确定此次弹栈操作的弹出路径的路径度量值是否小于第i层的剪枝门限。
S306，确定计数器的值是否达到L；
具体而言，在弹出路径的路径度量值大于或等于第i层的剪枝门限时，确定计数器的值是否达到L。
S307，删除栈中所有长度小于或等于i的候选路径；
S310，确定第(i+1)比特是否为固定比特；
S311，扩展该路径，并更新度量；
具体而言，在第(i+1)比特不是固定比特时，用比特0和1分别扩展该路径，并更新栈中每条路径的路径度量值。
S313，将扩展后的路径入栈，保持栈内的路径按照路径度量值从大到小(栈顶到栈底)排列；
S314，确定站内路径数是否大于(D-2)条；
S315，从栈底删除路径直到栈内的路径数为(D-2)条；
应理解，在S315之后，继续执行S302及图7中的其他步骤，直到弹出路径的长度与极化码的码长相等且能通过CRC校验(S308)时，将该弹出路径对应的比特序列输出为译码判决序列(S309)。
可选地，在S305中确定的弹出路径的路径度量值小于第i(i为弹出路径的长度)层的剪枝门限时，删除栈内所有长度小于或等于i的候选路径，并直接进行下一次弹栈操作。
可选地，在S310中，确定第(i+1)比特为固定比特时，执行S312，用固定比特扩展该路径，并更新栈内每条候选路径的路径度量值。
可选地，在S314中确定栈内的路径数小于(D-2)时，直接进入下一次弹栈操作。
因此，本发明实施例的极化码的译码方法，在译码过程中译码路径扩展到译码码树的每一层时，根据该层的所有候选路径的路径度量值之和确定该层的剪枝门限，并根据每一层的剪枝门限和搜索宽度从第一译码路径集合中确定出该极化码的第二译码路径集合，将该第二译码路径集合中具有最大路径度量值的译码路径确定为该极化码的译码结果，由于能够根据译码码树的每一层的所有候选路径的路径度量之和确定该层的剪枝门限，使得能够将译码性能损失控制在预先设定的可容忍性能损失值以内，并能大幅度降低极化码译码的复杂度。
表1给出了极化码的码长N＝1024、信息块大小K＝512的Polar码在BPSK调制下通过AWGN信道传输时，根据本发明实施例的译码方法与传统的SC译码方法和SCL译码方法在译码过程中的计算复杂度，译码过程中预设可容忍性能损失值Ptol＝1×10-4，搜索宽度L＝32，比特信噪比为1.35dB。
Figure PCTCN2015076958-appb-000091
表1中的本发明SCL译码(I)指的是采用公式(1)计算剪枝门限的译码方法，本发明SCL译码(II)指的是采用公式(3)和(4)计算剪枝门限的译码方法，本发明SCL译码(III)指的是根据公式(5)和(6)计算剪枝门限的译码方法。
从表1中的数据可以看到，在CASCL工作在FER大约为0.01时，本发明译码方法能够在性能几乎不受影响的前提下，相比传统CASCL译码算法大大降低复杂度。其中本发明SCL译码(II)能够避免约90％的排序操作，本发明SCS译码能够减少45％的概率度量计算和50％的路径复制操作。相比现有技术的剪枝译码方法，本发明的译码方法在该工作点上依然能够获得显著的复杂度增益。
图9给出了当Ptol配置为不同值时本发明的译码方法与现有技术译码方法在FER性能上的比较，基本译码方案均使用CASCL译码。图中未剪枝方案指的是表1中的现有技术中的SC译码方法，已有剪枝方案指的是表1中的现有技术剪枝译码方法，本发明剪枝方案指的是表1中的本发明SCL译码(III)方法。从图中曲线可以看到，当搜索宽度L＝32且Ptol设置为小于0.1倍未剪枝CASCL译码的FER值时，本发明剪枝方案与已有剪枝方案都能够具有与未剪枝方案几乎相同的FER性能；当L＝32且Ptol设置为1倍的未剪枝CASCL(L＝32)方案的FER值时，本发明剪枝方案下性能较L＝16的未剪枝方案几乎相当，而较L＝8的未剪枝译方案多获得0.2dB增益。
图10给出了对应的计算复杂度曲线(平均每帧译码所需的概率度量计算操作的次数)。图中未剪枝方案指的是表1中的现有技术中的SC译码方法，已有剪枝方案指的是表1中的现有技术剪枝译码方法，本发明剪枝方案指的是表1中的本发明SCL译码(III)方法。在相同搜索宽度L＝32和Ptol的设置下，本发明剪枝方案的计算复杂度远低于已有剪枝方案；当L＝32且Ptol设置为0.1倍未剪枝CASCL译码的FER值时，本发明剪枝方案的复杂度仅为未剪枝方案的30％(1.5dB处)；当L＝32且Ptol设置为1倍未剪枝CASCL(L＝32)方案的FER值时，本发明剪枝方案较L＝8的未剪枝方案具有更低复杂度，同时有0.2dB的增益。
图11给出了在信噪比为1.5dB下，不同Ptol设置的FER性能及性能损失值。图中未剪枝方案指的是表1中的现有技术中的SC译码方法，已有剪枝方案指的是表1中的现有技术剪枝译码方法，本发明剪枝方案指的是表1中的本发明SCL译码(III)方法。图中所有涉及的译码方案搜索宽度均设置为L＝32。本发明的剪枝方案在Ptol的值设置为小于1倍的未剪枝CASCL译码的FER值时，实际性能损失非常接近可容忍性能损失值Ptol。因此，相比已有剪枝方案，本发明剪枝方案能够充分利用可容忍性能损失，更有效地进行剪枝，从而更显著地降低计算复杂度。
因此，本发明实施例的极化码的译码方法，在译码过程中，路径扩展到译码码树的每一层时，根据该层的所有候选路径的路径度量值之和确定该层的剪枝门限，并根据每一层的剪枝门限从第一译码路径集合中确定出该极化码的第二译码路径集合，将该第二译码路径集合中具有最大路径度量值的译码路径确定为该极化码的译码结果，由于能够根据译码码树的每一层的所有候选路径的路径度量之和确定该层的剪枝门限，使得能够将译码性能损失控制在预先设定的可容忍性能损失值以内，大幅度降低极化码译码的复杂度。
以上结合图2至图11详细描述了本发明实施例的极化码译码的方法，下面将结合图12详细描述本发明实施例的极化码的译码装置。
如图12所示，该极化码译码的译码装置10包括：
处理模块11，用于根据极化码的译码码树的每一层的剪枝门限和搜索宽度L，从第一译码路径集合中确定出该极化码的第二译码路径集合，其中，该译码码树的每一层的剪枝门限是根据该层的所有候选路径的路径度量值之和确定的，该第一译码路径集合为该译码码树上从根节点到任一叶子节点 构成的所有最短路径的集合；
确定模块12，用于将该处理模块11确定出的该第二译码路径集合中具有最大路径度量值的译码路径对应的比特估计序列确定为该极化码的译码结果。
具体而言，在极化码的译码过程中，在译码路径扩展到极化码对应的译码码树的每一层时，根据该层的所有候选路径的路径度量值之和确定该层的剪枝门限，并根据该剪枝门限和搜索宽度L确定该层的幸存路径和删除路径，将幸存路径进行路径分裂且将删除路径删除，其中，幸存路径的路径度量值大于或等于该剪枝门限，删除路径的路径度量值小于该剪枝门限。在译码路径扩展到译码码树的叶子节点时，将该叶子节点所在的译码码树的层数的幸存路径组成的集合确定为第二译码路径集合，并将该第二译码路径集合中具有最大路径度量值的译码路径对应的比特估计序列确定为该极化码的译码结果。
因此，本发明实施例的极化码的译码方法，在译码过程中译码路径扩展到译码码树的每一层时，根据该层的所有候选路径的路径度量值之和确定该层的剪枝门限，并根据每一层的剪枝门限和搜索宽度从第一译码路径集合中确定出该极化码的第二译码路径集合，将该第二译码路径集合中具有最大路径度量值的译码路径对应的比特估计序列确定为该极化码的译码结果，由于能够根据译码码树的每一层的所有候选路径的路径度量之和确定该层的剪枝门限，使得能够将译码性能损失控制在预先设定的可容忍性能损失值以内，并能大幅度降低极化码译码的复杂度。
可选地，作为一个实施例，在该译码装置应用于串行抵消列表SCL译码时，该处理模块11具体用于：在译码路径扩展到该译码码树的每一层时，将该层的候选路径集合中路径度量值大于该层的剪枝门限的候选路径组成的集合确定为该层的第一候选路径集合，其中，该译码码树的第一层的候选路径集合为该译码码树上从根结点到第一层的任一节点构成的所有最短路径的集合；在该第一候选路径集合中的候选路径的长度小于该极化码的码长时，根据该搜索宽度L，确定该层的下一层的候选路径集合，并将译码路径扩展到该该层的下一层，或，在该第一候选路径集合中的候选路径的长度等于该极化码的码长时，根据该搜索宽度L，从该第一候选路径集合中确定出该极化码的第二译码路径集合。
可选地，作为一个实施例，在该译码装置应用于串行抵消列表SCL译码时，该处理模块11具体用于：在译码路径扩展到该译码码树的每一层时，根据该搜索宽度L从该层的候选路径中确定出该层的第二候选路径集合，其中，该译码码树的第一层的候选路径集合为该译码码树上从根结点到第一层的任一节点构成的所有最短路径的集合；在该第二候选路径集合中的候选路径的长度小于该极化码的码长时，将该第二候选路径集合中路径度量值大于或等于该层的剪枝门限的候选路径的后继路径组成的集合确定为该层的下一层的候选路径集合，并将译码路径扩展到该该层的下一层，或，在该第二候选路径集合中的候选路径的长度等于该极化码的码长时，将该第二候选路径集合中路径度量值大于或等于该层的剪枝门限的候选路径组成的集合确定为该极化码的第二译码路径集合。
可选地，作为一个实施例，在该译码装置应用于串行抵消堆栈SCS译码时，该处理模块11具体用于：
在弹出路径的路径度量值小于该弹出路径对应的译码码树的层数对应的剪枝门限时，删除该弹出路径和该候选路径堆栈中长度小于或等于该弹出路径的长度的候选路径，并直接进入到下一次弹栈操作，或，
在弹出路径的路径度量值大于或等于该弹出路径对应的译码码树的层数对应的剪枝门限且该弹出路径的长度小于该极化码的码长时，根据该搜索宽度L确定该候选路径堆栈中的幸存候选路径集合，将该弹出路径对应的后继路径加入到该候选路径堆栈中，并进行下一次弹栈操作，或，
在弹出路径的长度等于该极化码的码长时，将该弹出路径确定为该极化码的第二译码路径集合中的译码路径，并进行下一次弹栈操作。
可选地，作为一个实施例，在采用循环冗余校验CRC辅助译码时，该确定模块12具体用于：将该第二译码路径集合中具有最大路径度量值，且能通过CRC校验的译码路径对应的比特估计序列确定为该极化码的译码结果。
在本发明实施例中，可选地，该处理模块11具体用于：根据下式确定该译码码树的每一层的剪枝门限：
Figure PCTCN2015076958-appb-000092
其中，τi为第i层的剪枝门限，
Figure PCTCN2015076958-appb-000093
为第i层的所有候选路径的路径度量 值之和，Ptol为预设可容忍性能损失值，K为该极化码对应的信息块的长度，L为搜索宽度。
可选地，作为一个实施例，该处理模块11具体用于：根据下式确定该译码码树的每一层的剪枝门限：
Figure PCTCN2015076958-appb-000094
其中，τi为第i层的剪枝门限，
Figure PCTCN2015076958-appb-000095
为第i层的所有候选路径的路径度量值之和，
Figure PCTCN2015076958-appb-000096
为第i层的可容忍性能损失值，L为搜索宽度；Ptol为预设可容忍性能损失值，
Figure PCTCN2015076958-appb-000097
为第i'-1层的所有候选路径中被删除的候选路径的序号集合，
Figure PCTCN2015076958-appb-000098
为第i'-1层的所有候选路径中第k条被删除的候选路径的路径度量值，
Figure PCTCN2015076958-appb-000099
为第i'-1层的所有候选路径的路径度量值之和。
可选地，作为一个实施例，该处理模块11具体用于：根据下式确定该译码码树的每一层的剪枝门限：
Figure PCTCN2015076958-appb-000100
其中，j的取值满足下式：
Figure PCTCN2015076958-appb-000101
Figure PCTCN2015076958-appb-000102
为第i层的所有候选路径的序号组成的集合，
Figure PCTCN2015076958-appb-000103
为第i层的可容忍性能损失值，Ptol为预设可容忍性能损失值，(j,k)表示第j层被删除的候选路径的序号为k，
Figure PCTCN2015076958-appb-000104
为在第j层删除序号为k的候选路径造成的性能损失，ci为所有或部分在前i-1层译码过程中被删除的候选路径组成的集合。
可选地，作为一个实施例，该处理模块11具体用于：根据下式确定该译码码树的每一层的剪枝门限：
Figure PCTCN2015076958-appb-000105
其中，τi,t为第t次弹栈操作后第i层的剪枝门限，Ptol为预设可容忍性能损失值，
Figure PCTCN2015076958-appb-000106
为在前t-1次弹栈操作中弹出的长度为i的所有候选路径的路径度量值之和，K为该极化码对应的信息块的长度，L为搜索宽度。
应理解，根据本发明实施例的译码装置10可对应于执行本发明实施例中的译码的方法100，并且译码装置10中的各个模块的上述和其它操作和/或功能分别为了实现图2，图4至图6中的相应流程，为了简洁，在此不再赘述。
因此，本发明实施例的极化码的译码方法，在译码过程中译码路径扩展 到译码码树的每一层时，根据该层的所有候选路径的路径度量值之和确定该层的剪枝门限，并根据每一层的剪枝门限和搜索宽度从第一译码路径集合中确定出该极化码的第二译码路径集合，将该第二译码路径集合中具有最大路径度量值的译码路径对应的比特估计序列确定为该极化码的译码结果，由于能够根据译码码树的每一层的所有候选路径的路径度量之和确定该层的剪枝门限，使得能够将译码性能损失控制在预先设定的可容忍性能损失值以内，并能大幅度降低极化码译码的复杂度。
图13是本发明另一实施例的装置的示意框图。图13的装置20可用于实现上述方法实施例中各步骤及方法。装置20可应用于各种通信系统中的基站或者终端。图13的实施例中，装置20包括发射电路202、接收电路203、译码处理器204、处理单元205，存储器206及天线201。处理单元205控制装置20的操作，并且可用于处理信号。处理单元205还可以称为中央处理单元(Central Processing Unit，简称为“CPU”)。存储器206可以包括只读存储器和随机存取存储器，并向处理单元205提供指令和数据。存储器206的一部分还可以包括非易失行随机存取存储器(NVRAM)。具体的应用中，装置20可以嵌入或者本身可以就是例如移动电话之类的无线通信设备，还可以包括容纳发射电路202和接收电路203的载体，以允许装置20和远程位置之间进行数据发射和接收。发射电路202和接收电路203可以耦合到天线201。装置20的各个组件通过总线系统209耦合在一起，其中总线系统209除包括数据总线之外，还包括电源总线、控制总线和状态信号总线。但是为了清楚说明起见，在图中将各种总线都标为总线系统209。
上述本发明实施例揭示的方法可以应用于译码处理器204中，或者由译码处理器204实现。译码处理器204可能是一种集成电路芯片，具有信号的处理能力。在实现过程中，上述方法的各步骤可以通过译码处理器204中的硬件的集成逻辑电路或者软件形式的指令完成。这些指令可以通过处理单元205以配合实现及控制。用于执行本发明实施例揭示的方法，上述的译码处理器可以是通用处理器、数字信号处理器(DSP)、专用集成电路(ASIC)、现成可编程门阵列(FPGA)或者其他可编程逻辑器件、分立门或者晶体管逻辑器件、分立硬件组件。可以实现或者执行本发明实施例中的公开的各方法、步骤及逻辑框图。通用处理器可以是微处理器或者该处理器也可以是任何常规的处理器，译码器等。结合本发明实施例所公开的方法的步骤可以直 接体现为硬件译码处理器执行完成，或者用译码处理器中的硬件及软件模块组合执行完成。软件模块可以位于随机存储器，闪存、只读存储器，可编程只读存储器或者电可擦写可编程存储器、寄存器等本领域成熟的存储介质中。该存储介质位于存储器206，译码处理器204读取存储器206中的信息，结合其硬件完成上述方法的步骤。
具体地，存储器206可存储使得译码处理器204或处理单元205执行以下过程的指令：
根据极化码的译码码树的每一层的剪枝门限和搜索宽度L，从第一译码路径集合中确定出该极化码的第二译码路径集合，其中，该译码码树的每一层的剪枝门限是根据该层的所有候选路径的路径度量值之和确定的，该第一译码路径集合为该译码码树上从根节点到任一叶子节点构成的所有最短路径的集合；将该第二译码路径集合中具有最大的路径度量值的译码路径对应的比特估计序列确定为该极化码的译码结果。
本发明实施例中，在译码过程中译码路径扩展到译码码树的每一层时，根据该层的所有候选路径的路径度量值之和确定该层的剪枝门限，并根据每一层的剪枝门限和搜索宽度从第一译码路径集合中确定出该极化码的第二译码路径集合，将该第二译码路径集合中具有最大路径度量值的译码路径对应的比特估计序列确定为该极化码的译码结果，由于能够根据译码码树的每一层的所有候选路径的路径度量之和确定该层的剪枝门限，使得能够将译码性能损失控制在预先设定的可容忍性能损失值以内，并能大幅度降低极化码译码的复杂度。
应理解，说明书通篇中提到的“一个实施例”或“一实施例”意味着与实施例有关的特定特征、结构或特性包括在本发明的至少一个实施例中。因此，在整个说明书各处出现的“在一个实施例中”或“在一实施例中”未必一定指相同的实施例。此外，这些特定的特征、结构或特性可以任意适合的方式结合在一个或多个实施例中。
在本发明的各种实施例中，应理解，上述各过程的序号的大小并不意味着执行顺序的先后，各过程的执行顺序应以其功能和内在逻辑确定，而不应对本发明实施例的实施过程构成任何限定。
另外，本文中术语“系统”和“网络”在本文中常可互换使用。应理解，本文中术语“和/或”，仅仅是一种描述关联对象的关联关系，表示可以存在三种 关系，例如，A和/或B，可以表示：单独存在A，同时存在A和B，单独存在B这三种情况。另外，本文中字符“/”，一般表示前后关联对象是一种“或”的关系。
在本申请所提供的实施例中，应理解，“与A相应的B”表示B与A相关联，根据A可以确定B。但还应理解，根据A确定B并不意味着仅仅根据A确定B，还可以根据A和/或其它信息确定B。
本领域普通技术人员可以意识到，结合本文中所公开的实施例描述的各示例的单元及算法步骤，能够以电子硬件、计算机软件或者二者的结合来实现，为了清楚地说明硬件和软件的可互换性，在上述说明中已经按照功能一般性地描述了各示例的组成及步骤。这些功能究竟以硬件还是软件方式来执行，取决于技术方案的特定应用和设计约束条件。专业技术人员可以对每个特定的应用来使用不同方法来实现所描述的功能，但是这种实现不应认为超出本发明的范围。
所属领域的技术人员可以清楚地了解到，为描述的方便和简洁，上述描述的系统、装置和单元的具体工作过程，可以参考前述方法实施例中的对应过程，在此不再赘述。
在本申请所提供的几个实施例中，应该理解到，所揭露的系统、装置和方法，可以通过其它的方式实现。例如，以上所描述的装置实施例仅仅是示意性的，例如，所述单元的划分，仅仅为一种逻辑功能划分，实际实现时可以有另外的划分方式，例如多个单元或组件可以结合或者可以集成到另一个系统，或一些特征可以忽略，或不执行。另一点，所显示或讨论的相互之间的耦合或直接耦合或通信连接可以是通过一些接口，装置或单元的间接耦合或通信连接，可以是电性，机械或其它的形式。
所述作为分离部件说明的单元可以是或者也可以不是物理上分开的，作为单元显示的部件可以是或者也可以不是物理单元，即可以位于一个地方，或者也可以分布到多个网络单元上。可以根据实际的需要选择其中的部分或者全部单元来实现本实施例方案的目的。
另外，在本发明各个实施例中的各功能单元可以集成在一个处理单元中，也可以是各个单元单独物理存在，也可以两个或两个以上单元集成在一个单元中。
集成的单元如果以软件功能单元的形式实现并作为独立的产品销售或 使用时，可以存储在一个计算机可读取存储介质中。基于这样的理解，本发明的技术方案本质上或者说对现有技术做出贡献的部分或者该技术方案的部分可以以软件产品的形式体现出来，该计算机软件产品存储在一个存储介质中，包括若干指令用以使得一台计算机设备(可以是个人计算机，服务器，或者网络设备等)执行本发明各个实施例所述方法的全部或部分步骤。而前述的存储介质包括：U盘、移动硬盘、只读存储器(Read-Only Memory，简称为“ROM”)、随机存取存储器(Random Access Memory，简称为“RAM”)、磁碟或者光盘等各种可以存储程序代码的介质。
以上所述，仅为本发明的具体实施方式，但本发明的保护范围并不局限于此，任何熟悉本技术领域的技术人员在本发明揭露的技术范围内，可轻易想到变化或替换，都应涵盖在本发明的保护范围之内。因此，本发明的保护范围应以所述权利要求的保护范围为准。

Claims (18)

  1. 一种极化码的译码方法，其特征在于，包括：
    根据极化码的译码码树的每一层的剪枝门限和搜索宽度L，从第一译码路径集合中确定出所述极化码的第二译码路径集合，其中，所述译码码树的每一层的剪枝门限是根据该层的所有候选路径的路径度量值之和确定的，所述第一译码路径集合为所述译码码树上从根节点到任一叶子节点构成的所有最短路径的集合；
    将所述第二译码路径集合中具有最大路径度量值的译码路径对应的比特估计序列确定为所述极化码的译码结果。
  2. 根据权利要求1所述的译码方法，其特征在于，在所述译码方法应用于串行抵消列表SCL译码时，所述根据极化码的译码码树的每一层的剪枝门限和搜索宽度L，从第一译码路径集合中确定出所述极化码的第二译码路径集合，包括：
    在译码路径扩展到所述译码码树的每一层时，将该层的候选路径集合中路径度量值大于该层的剪枝门限的候选路径组成的集合确定为该层的第一候选路径集合，其中，所述译码码树的第一层的候选路径集合为所述译码码树上从根结点到第一层的任一节点构成的所有最短路径的集合；
    在所述第一候选路径集合中的候选路径的长度小于所述极化码的码长时，根据所述搜索宽度L，确定该层的下一层的候选路径集合，并将译码路径扩展到所述该层的下一层，或，
    在所述第一候选路径集合中的候选路径的长度等于所述极化码的码长时，根据所述搜索宽度L，从所述第一候选路径集合中确定出所述极化码的第二译码路径集合。
  3. 根据权利要求1所述的译码方法，其特征在于，在所述译码方法应用于串行抵消列表SCL译码时，所述根据极化码的译码码树的每一层的剪枝门限和搜索宽度L，从第一译码路径集合中确定出所述极化码的第二译码路径集合，包括：
    在译码路径扩展到所述译码码树的每一层时，根据所述搜索宽度L从该层的候选路径集合中确定出该层的第二候选路径集合，其中，所述译码码树的第一层的候选路径集合为所述译码码树上从根结点到第一层的任一节点构成的所有最短路径的集合；
    在所述第二候选路径集合中的候选路径的长度小于所述极化码的码长时，将所述第二候选路径集合中路径度量值大于或等于该层的剪枝门限的候选路径的后继路径组成的集合确定为该层的下一层的候选路径集合，并将译码路径扩展到所述该层的下一层，或，
    在所述第二候选路径集合中的候选路径的长度等于所述极化码的码长时，将所述第二候选路径集合中路径度量值大于或等于该层的剪枝门限的候选路径组成的集合确定为所述极化码的第二译码路径集合。
  4. 根据权利要求1所述的译码方法，其特征在于，在所述译码方法应用于串行抵消堆栈SCS译码时，所述根据极化码的译码码树的每一层的剪枝门限和搜索宽度L，从第一译码路径集合中确定出所述极化码的第二译码路径集合，包括：
    在弹出路径的路径度量值小于所述弹出路径对应的译码码树的层数对应的剪枝门限时，删除所述弹出路径和候选路径堆栈中长度小于或等于所述弹出路径的长度的候选路径，并直接进入到下一次弹栈操作，或，
    在弹出路径的路径度量值大于或等于所述弹出路径对应的译码码树的层数对应的剪枝门限且所述弹出路径的长度小于所述极化码的码长时，根据所述搜索宽度L确定候选路径堆栈中的幸存候选路径集合，将所述弹出路径的后继路径加入到所述候选路径堆栈中，并进行下一次弹栈操作，或，
    在弹出路径的长度等于所述极化码的码长时，将所述弹出路径确定为所述极化码的第二译码路径集合中的译码路径，并进行下一次弹栈操作。
  5. 根据权利要求1至4中任一项所述的译码方法，其特征在于，在采用循环冗余校验CRC辅助译码时，所述将第二译码路径集合中具有最大路径度量值的译码路径对应的比特估计序列确定为所述极化码的译码结果，包括：
    将所述第二译码路径集合中具有最大路径度量值，且能通过CRC校验的译码路径对应的比特估计序列确定为所述极化码的译码结果。
  6. 根据权利要求3所述的译码方法，其特征在于，所述译码码树的每一层的剪枝门限是根据该层的所有候选路径的路径度量值之和确定的，包括：
    所述译码码树的每一层的剪枝门限是根据下式确定的：
    Figure PCTCN2015076958-appb-100001
    其中，τi为第i层的剪枝门限，
    Figure PCTCN2015076958-appb-100002
    为第i层的所有候选路径的路径度量值之和，Ptol为预设可容忍性能损失值，K为所述极化码对应的信息块的长度，L为搜索宽度。
  7. 根据权利要求3所述的译码方法，其特征在于，所述译码码树的每一层的剪枝门限是根据该层的所有候选路径的路径度量值之和确定的，包括：
    所述译码码树的每一层的剪枝门限是根据下式确定的：
    Figure PCTCN2015076958-appb-100003
    Figure PCTCN2015076958-appb-100004
    其中，τi为第i层的剪枝门限，
    Figure PCTCN2015076958-appb-100005
    为第i层的所有候选路径的路径度量值之和，
    Figure PCTCN2015076958-appb-100006
    为第i层的可容忍性能损失值，L为搜索宽度；Ptol为预设可容忍性能损失值，
    Figure PCTCN2015076958-appb-100007
    为第i'-1层的所有候选路径中被删除的候选路径的序号集合，
    Figure PCTCN2015076958-appb-100008
    为第i'-1层的所有候选路径中第k条被删除的候选路径的路径度量值，
    Figure PCTCN2015076958-appb-100009
    为第i'-1层的所有候选路径的路径度量值之和。
  8. 根据权利要求4所述的译码方法，其特征在于，所述译码码树的每一层的剪枝门限是根据该层的所有候选路径的路径度量值之和确定的，包括：
    所述译码码树的每一层的剪枝门限是根据下式确定的：
    Figure PCTCN2015076958-appb-100010
    其中，j的取值满足下式：
    Figure PCTCN2015076958-appb-100011
    Figure PCTCN2015076958-appb-100012
    为第i层的所有候选路径的序号组成的集合，
    Figure PCTCN2015076958-appb-100013
    为第i层的可容忍性能损失值，Ptol为预设可容忍性能损失值，(j,k)表示第j层被删除的候选路径的序号为k，
    Figure PCTCN2015076958-appb-100014
    为在第j层删除序号为k的候选路径造成的性能损失，ci为所有或部分在前i-1层译码过程中被删除的候选路径组成的集合。
  9. 根据权利要求5所述的译码方法，其特征在于，所述译码码树的每一层的剪枝门限是根据该层的所有候选路径的路径度量值之和确定的，包括：
    所述译码码树的每一层的剪枝门限是根据下式确定的：
    Figure PCTCN2015076958-appb-100015
    其中，τi,t为第t次弹栈操作后第i层的剪枝门限，Ptol为预设可容忍性能损失值，
    Figure PCTCN2015076958-appb-100016
    为在前t-1次弹栈操作中弹出的长度为i的所有候选路径的路径度量值之和，K为所述极化码对应的信息块的长度，L为搜索宽度。
  10. 一种极化码的译码装置，其特征在于，包括：
    处理模块，用于根据极化码的译码码树的每一层的剪枝门限和搜索宽度L，从第一译码路径集合中确定出所述极化码的第二译码路径集合，其中，所述译码码树的每一层的剪枝门限是根据该层的所有候选路径的路径度量值之和确定的，所述第一译码路径集合为所述译码码树上从根节点到任一叶子节点构成的所有最短路径的集合；
    确定模块，用于将所述处理模块确定出的所述第二译码路径集合中具有最大路径度量值的译码路径对应的比特估计序列确定为所述极化码的译码结果。
  11. 根据权利要求10所述的译码装置，其特征在于，在所述译码装置应用于串行抵消列表SCL译码时，所述处理模块具体用于：
    在译码路径扩展到所述译码码树的每一层时，将该层的候选路径集合中路径度量值大于该层的剪枝门限的候选路径组成的集合确定为该层的第一候选路径集合，其中，所述译码码树的第一层的候选路径集合为所述译码码树上从根结点到第一层的任一节点构成的所有最短路径的集合；
    在所述第一候选路径集合中的候选路径的长度小于所述极化码的码长时，根据所述搜索宽度L，确定该层的下一层的候选路径集合，并将译码路径扩展到所述该层的下一层，或，
    在所述第一候选路径集合中的候选路径的长度等于所述极化码的码长时，根据所述搜索宽度L，从所述第一候选路径集合中确定出所述极化码的第二译码路径集合。
  12. 根据权利要求10所述的译码装置，其特征在于，在所述译码装置应用于串行抵消列表SCL译码时，所述处理模块具体用于：
    在译码路径扩展到所述译码码树的每一层时，根据所述搜索宽度L从该层的候选路径集合中确定出该层的第二候选路径集合，其中，所述译码码树的第一层的候选路径集合为所述译码码树上从根结点到第一层的任一节点 构成的所有最短路径的集合；
    在所述第二候选路径集合中的候选路径的长度小于所述极化码的码长时，将所述第二候选路径集合中路径度量值大于或等于该层的剪枝门限的候选路径的后继路径组成的集合确定为该层的下一层的候选路径集合，并将译码路径扩展到所述该层的下一层，或，
    在所述第二候选路径集合中的候选路径的长度等于所述极化码的码长时，将所述第二候选路径集合中路径度量值大于或等于该层的剪枝门限的候选路径组成的集合确定为所述极化码的第二译码路径集合。
  13. 根据权利要求10所述的译码装置，其特征在于，在所述译码装置应用于串行抵消堆栈SCS译码时，所述处理模块具体用于：
    在弹出路径的路径度量值小于所述弹出路径对应的译码码树的层数对应的剪枝门限时，删除所述弹出路径和候选路径堆栈中长度小于或等于所述弹出路径的长度的候选路径，并直接进入到下一次弹栈操作，或，
    在弹出路径的路径度量值大于或等于所述弹出路径对应的译码码树的层数对应的剪枝门限且所述弹出路径的长度小于所述极化码的码长时，根据所述搜索宽度L确定候选路径堆栈中的幸存候选路径集合，将所述弹出路径对应的后继路径加入到所述候选路径堆栈中，并进行下一次弹栈操作，或，
    在弹出路径的长度等于所述极化码的码长时，将所述弹出路径确定为所述极化码的第二译码路径集合中的译码路径，并进行下一次弹栈操作。
  14. 根据权利要求10至13中任一项所述的译码装置，其特征在于，在采用循环冗余校验CRC辅助译码时，所述确定模块具体用于：
    将所述第二译码路径集合中具有最大路径度量值，且能通过CRC校验的译码路径对应的比特估计序列确定为所述极化码的译码结果。
  15. 根据权利要求11所述的译码装置，其特征在于，所述处理模块具体用于：根据下式确定所述译码码树的每一层的剪枝门限：
    Figure PCTCN2015076958-appb-100017
    其中，τi为第i层的剪枝门限，
    Figure PCTCN2015076958-appb-100018
    为第i层的所有候选路径的路径度量值之和，Ptol为预设可容忍性能损失值，K为所述极化码对应的信息块的长度，L为搜索宽度。
  16. 根据权利要求11所述的译码装置，其特征在于，所述处理模块具体用于：根据下式确定所述译码码树的每一层的剪枝门限：
    Figure PCTCN2015076958-appb-100019
    Figure PCTCN2015076958-appb-100020
    其中，τi为第i层的剪枝门限，
    Figure PCTCN2015076958-appb-100021
    为第i层的所有候选路径的路径度量值之和，
    Figure PCTCN2015076958-appb-100022
    为第i层的可容忍性能损失值，L为搜索宽度；Ptol为预设可容忍性能损失值，
    Figure PCTCN2015076958-appb-100023
    为第i'-1层的所有候选路径中被删除的候选路径的序号集合，
    Figure PCTCN2015076958-appb-100024
    为第i'-1层的所有候选路径中第k条被删除的候选路径的路径度量值，
    Figure PCTCN2015076958-appb-100025
    为第i'-1层的所有候选路径的路径度量值之和。
  17. 根据权利要求12所述的译码装置，其特征在于，所述处理模块具体用于：根据下式确定所述译码码树的每一层的剪枝门限：
    Figure PCTCN2015076958-appb-100026
    其中，j的取值满足下式：
    Figure PCTCN2015076958-appb-100027
    为第i层的所有候选路径的序号组成的集合，
    Figure PCTCN2015076958-appb-100029
    为第i层的可容忍性能损失值，Ptol为预设可容忍性能损失值，(j,k)表示第j层被删除的候选路径的序号为k，
    Figure PCTCN2015076958-appb-100030
    为在第j层删除序号为k的候选路径造成的性能损失，ci为所有或部分在前i-1层译码过程中被删除的候选路径组成的集合。
  18. 根据权利要求13所述的译码装置，其特征在于，所述处理模块具体用于：根据下式确定所述译码码树的每一层的剪枝门限：
    Figure PCTCN2015076958-appb-100031
    其中，τi,t为第t次弹栈操作后第i层的剪枝门限，Ptol为预设可容忍性能损失值，
    Figure PCTCN2015076958-appb-100032
    为在前t-1次弹栈操作中弹出的长度为i的所有候选路径的路径度量值之和，K为所述极化码对应的信息块的长度，L为搜索宽度。
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CN112118013A (zh) * 2019-06-20 2020-12-22 南京大学 一种适用于多进制ldpc码的高性能、低复杂度的迭代大数逻辑译码方法
CN110852101A (zh) * 2019-11-06 2020-02-28 北京儒博科技有限公司 一种路径解码方法、装置、计算机设备及存储介质
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