WO2019080912A1 - Turbo乘积码的译码方法、装置和计算机可读存储介质 - Google Patents

Turbo乘积码的译码方法、装置和计算机可读存储介质

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Publication number
WO2019080912A1
WO2019080912A1 PCT/CN2018/111970 CN2018111970W WO2019080912A1 WO 2019080912 A1 WO2019080912 A1 WO 2019080912A1 CN 2018111970 W CN2018111970 W CN 2018111970W WO 2019080912 A1 WO2019080912 A1 WO 2019080912A1
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codeword
decoding
external information
optimal
received
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PCT/CN2018/111970
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English (en)
French (fr)
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孙二坤
蔡轶
王卫明
殷俊杰
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中兴通讯股份有限公司
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Application filed by 中兴通讯股份有限公司 filed Critical 中兴通讯股份有限公司
Priority to KR1020207011509A priority Critical patent/KR102326491B1/ko
Priority to JP2020523258A priority patent/JP2021500814A/ja
Priority to EP18870539.6A priority patent/EP3678297A4/en
Priority to US16/756,367 priority patent/US20200252086A1/en
Publication of WO2019080912A1 publication Critical patent/WO2019080912A1/zh

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    • 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
    • H03M13/29—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 combining two or more codes or code structures, e.g. product codes, generalised product codes, concatenated codes, inner and outer codes
    • H03M13/2906—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 combining two or more codes or code structures, e.g. product codes, generalised product codes, concatenated codes, inner and outer codes using block codes
    • H03M13/2927—Decoding strategies
    • 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
    • H03M13/29—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 combining two or more codes or code structures, e.g. product codes, generalised product codes, concatenated codes, inner and outer codes
    • H03M13/2957—Turbo codes and decoding
    • 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
    • H03M13/29—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 combining two or more codes or code structures, e.g. product codes, generalised product codes, concatenated codes, inner and outer codes
    • H03M13/2906—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 combining two or more codes or code structures, e.g. product codes, generalised product codes, concatenated codes, inner and outer codes using block codes
    • H03M13/2909—Product codes
    • 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
    • H03M13/29—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 combining two or more codes or code structures, e.g. product codes, generalised product codes, concatenated codes, inner and outer codes
    • H03M13/2957—Turbo codes and decoding
    • H03M13/296—Particular turbo code structure
    • H03M13/2963—Turbo-block codes, i.e. turbo codes based on block codes, e.g. turbo decoding of product codes
    • 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
    • H03M13/37—Decoding methods or techniques, not specific to the particular type of coding provided for in groups H03M13/03 - H03M13/35
    • H03M13/3784—Decoding methods or techniques, not specific to the particular type of coding provided for in groups H03M13/03 - H03M13/35 for soft-output decoding of block codes
    • 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
    • H03M13/37—Decoding methods or techniques, not specific to the particular type of coding provided for in groups H03M13/03 - H03M13/35
    • H03M13/45—Soft decoding, i.e. using symbol reliability information
    • H03M13/451—Soft decoding, i.e. using symbol reliability information using a set of candidate code words, e.g. ordered statistics decoding [OSD]
    • H03M13/453—Soft decoding, i.e. using symbol reliability information using a set of candidate code words, e.g. ordered statistics decoding [OSD] wherein the candidate code words are obtained by an algebraic decoder, e.g. Chase decoding
    • 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
    • H03M13/65—Purpose and implementation aspects
    • H03M13/6502—Reduction of hardware complexity or efficient processing

Definitions

  • the present disclosure relates to, but is not limited to, the field of error correction control coding techniques.
  • Kaneko algorithm is an algorithm proposed to reduce the search space dynamically when generating candidate codewords in order to reduce the complexity. This algorithm uses the condition of the optimal candidate codeword correlation difference to direct the direction of further search or to terminate the decoding process when the most likely codeword is found.
  • the Kaneko algorithm implements maximum likelihood decoding. Although the Kaneko algorithm can dynamically reduce the search space, the complexity of the algorithm is high.
  • a decoding method of a turbo product code including: acquiring a received codeword and a code pattern of a turbo product code; determining a reduction according to the pattern, an unreliable number of bits, and a reduced number of error bits. a set of error patterns, wherein the reduced number of error bits is less than the unreliable number of bits; an optimal codeword is calculated according to the reduced error mode set and the received codeword; and decoding is performed according to the optimal codeword
  • the algorithm calculates external information; and performs iterative calculation according to the external information and a preset number of iterations to obtain a decoding result of the received codeword.
  • the present disclosure also provides a decoding apparatus for a turbo product code, comprising: an obtaining module configured to acquire a received codeword and a code pattern of a turbo product code; and a reduced error mode determining module configured to be according to the pattern, not Determining a reduced error mode set, wherein the reduced error bit number is less than the unreliable number of bits; the optimal codeword calculation module is set to be based on the reduced error mode set and Deriving a codeword to calculate an optimal codeword; an external information calculation module configured to calculate external information by using a decoding algorithm according to the optimal codeword; and a decoding result output module configured to be based on the external information and The preset number of iterations is iteratively calculated to obtain the decoding result of the received codeword.
  • the present disclosure also provides a decoding device for a turbo product code, comprising a memory and a processor, the memory storing a computer program, the processor executing the Turbo according to the present disclosure when the computer program is executed by the processor The decoding method of the product code.
  • the present disclosure also provides a computer readable storage medium having stored thereon one or more programs, the one or more programs being executed by one or more processors, the one or more processors executing according to the present A method of decoding a disclosed Turbo product code.
  • FIG. 1 is a flowchart of a decoding method of a turbo product code according to an embodiment of the present disclosure
  • FIG. 2 is a flowchart of processing an optimal codeword in a decoding method of a turbo product code according to an embodiment of the present disclosure
  • FIG. 3 is a flowchart of considering a contention codeword in a decoding method of a turbo product code according to an embodiment of the present disclosure
  • FIG. 4 is a flowchart of a decoding method of a turbo product code according to another embodiment of the present disclosure.
  • FIG. 5 is a diagram of external information calculation in a decoding method of a turbo product code according to an embodiment of the present disclosure
  • FIG. 6 is a schematic block diagram of a decoding apparatus for a turbo product code in accordance with an embodiment of the present disclosure.
  • FIG. 1 is a flow chart of a method of decoding a turbo product code in accordance with an embodiment of the present disclosure.
  • a decoding method of a turbo product code may include steps 100 to 500.
  • the received codeword and pattern of the Turbo product code are obtained.
  • the Turbo product code constructs a product code having a minimum distance characteristic by sub-arranging two or more component code code codes into a two-dimensional or multi-dimensional matrix.
  • the pattern of the turbo product code includes (128, 120) ⁇ (128, 120), (128, 127) ⁇ (128, 127), (64, 57) ⁇ (64, 57), (32, 26) ⁇ ( 16,15) ⁇ (8, 7) and so on.
  • the Turbo product code is transmitted serially bit by bit.
  • the received serial sequence is converted into a two-dimensional matrix form and decoded by a matrix structure.
  • the complexity and decoding delay of Turbo product code decoding depends on the subcode pattern and increases linearly with the construction complexity and decoding complexity of the subcode.
  • the pattern of the received codeword cannot be discriminated according to the received codeword, so it is necessary to acquire the received codeword and pattern at the same time for subsequent decoding.
  • a reduced set of error patterns is determined based on the pattern, the number of unreliable bits, and the number of bits of error reduction, wherein the number of reduced errors is less than the number of unreliable bits.
  • the error mode set is obtained according to the pattern and the unreliable number of bits, and then the reduced error mode set is obtained in the error mode set according to the reduced error bit number.
  • the number of error modes in the reduced error mode set can be controlled according to the number of unreliable bits and the number of reduced error bits. For example, if n unreliable bits are selected according to the pattern (ie, the number of unreliable bits is n), the unreliable mode (ie, the set of error patterns) has 2 n possibilities and can be performed without affecting performance.
  • the error mode is reduced. Select the least reliable error 1 bit, the least reliable error 2 bits, ..., the most unreliable error k bit for each error mode (k ⁇ n, ie, reduce the number of error bits to k), making the error mode The number is reduced to
  • an optimal codeword is calculated based on the reduced error mode set and the received codeword.
  • step 400 external information is computed using a decoding algorithm based on the optimal codeword.
  • the decoding algorithm may include a soft input soft output algorithm (SISO algorithm) and an Euclidean distance based algorithm (DBD algorithm).
  • SISO algorithm soft input soft output algorithm
  • DBD algorithm Euclidean distance based algorithm
  • the external information is the decoded soft output information.
  • an iterative calculation is performed according to the external information and a preset number of iterations to obtain a decoding result of the received codeword.
  • the row and column decoding iterative calculation is performed according to the external information and the preset number of iterations, and the received codeword is hardly judged and the decoding result is output after the iteration is completed.
  • the soft input formula for a row or column iterative decoder is as follows, where m is the preset number of iterations:
  • the reduced error mode set can be determined according to the unreliable number of bits and the reduced number of error bits, and the optimal codeword is obtained according to the received codeword and the reduced error mode set, and the decoding algorithm is used. After the external information is calculated, and the iterative calculation is performed using the external information, the decoding result is obtained. Since the number of error modes is reduced, the complexity of the Turbo product code decoding algorithm is reduced, and the Kaneko algorithm using maximum likelihood decoding improves the decoding performance.
  • FIG. 2 is a flow diagram of processing an optimal codeword in a method of decoding a turbo product code in accordance with an embodiment of the present disclosure.
  • the decoding method of the turbo product code may include steps 310 to 390.
  • step 310 after hard-segmenting the received codeword, the hard-coded code is obtained, and the hard-coded code is assigned to the first codeword.
  • the received codeword is decoded based on the hard-coded and reduced error mode sets.
  • BCH decoding may be performed separately after bitwise exclusive OR of each error mode in the hard coded and reduced error mode sets.
  • step 330 it is determined whether all decoding of the received codeword has failed, and if so, proceeds to step 340, and if not, proceeds to step 350.
  • the first codeword is determined to be the optimal codeword.
  • the first codeword assigned a hard code can be used as the final optimal codeword.
  • step 350 a decoded codeword that was successfully decoded is obtained.
  • step 360 it is determined whether the decoded codeword satisfies the sufficient condition of the Kaneko algorithm, and if so, proceeds to step 370, and if not, proceeds to step 380.
  • the decoded codeword is assigned to the first codeword to update the first codeword, and then proceeds to step 340.
  • a decoded codeword that satisfies the sufficient condition of the Kaneko algorithm can be assigned to the first codeword as the optimal codeword.
  • step 380 when the respective decoded codewords obtained by traversing the reduced error mode set do not satisfy the sufficient condition of the Kaneko algorithm, the intra-distance product value of each decoded codeword and the hard-coded code is calculated.
  • the decoded codeword corresponding to the minimum distance inner product value is assigned to the first codeword to update the first codeword, and then proceeds to step 340.
  • the decoding method of the turbo product code of the embodiment when all the decoding of the received codeword is unsuccessful, the hard decision code of the received codeword is assigned to the optimal codeword.
  • the decoded codeword with the smallest hard coded distance is assigned to the optimal codeword. Therefore, in the case that the error mode is reduced, the decoding complexity of the Turbo product code is greatly reduced, and the acquisition of the optimal codeword is more perfect and reliable.
  • FIG. 3 is a flow diagram of considering a competing codeword in a decoding method of a turbo product code in accordance with an embodiment of the present disclosure.
  • the decoding method of the turbo product code may include steps 410A to 430A.
  • the received codeword is decoded according to the hard-coded and reduced error mode set, and when the decoding of the received codeword fails, the hard-coded is determined as the candidate codeword set, otherwise the decoded decoded codeword is determined. It is a set of candidate codewords until a decoded codeword that satisfies the sufficient condition of the Kaneko algorithm is obtained.
  • the hard code can be assigned to the optimal codeword, and the hard code and the error mode in the reduced error mode set are XORed and then BCH decoded. If all decoding fails, the optimal codeword is hard-coded, and the candidate codeword set includes only hard-coded. If the decoded decoded codeword satisfies the sufficient condition of the Kaneko algorithm, the decoded codeword is assigned to the optimal codeword and output, and the candidate codeword set is a decoding code that all BCH decoding succeeds before finding the optimal codeword. word. If there is no qualified decoding codeword, the decoded codeword with the smallest hard-coded distance is assigned to the optimal codeword and output, and the candidate codeword set includes all decoded codewords whose BCH decoding is successful.
  • a contention codeword is derived from the set of candidate codewords.
  • the contention codeword needs to satisfy two conditions simultaneously: condition 1, the Euclidean distance from the received codeword is the smallest; and condition 2, cj ⁇ dj , where cj is the contention codeword at the jth The symbol of the bit, d j is the symbol of the j-th bit of the optimal codeword.
  • condition 2 is judged, and each sequence of c j ⁇ d j is found in the candidate code word set, and then the sequence having the largest correlation value with the received code word is searched for as a contention code word in each of the found sequences.
  • step 430A external information is calculated based on the received codeword, the optimal codeword, and the contention codeword.
  • w j is the symbol of the jth bit of the external information
  • r j is the symbol of the jth bit of the received codeword
  • R is the received codeword
  • C is the contention codeword
  • D is the optimal codeword.
  • the optimal codeword and the contention codeword are obtained in the reduced error mode, and various failures in the decoding process, especially all decoding of the received codeword, are considered, and are calculated by the SISO algorithm.
  • the external information realizes the decoding of Turbo product code in the reduced error mode, which reduces the complexity of the operation, improves the performance of decoding, and achieves a good compromise in complexity and performance, which is very suitable for high performance. High throughput system.
  • FIG. 4 is a flowchart of a decoding method of a turbo product code according to another embodiment of the present disclosure.
  • the decoding method of the turbo product code may include steps 410B to 450B.
  • step 410B a first correspondence is obtained according to the pattern, where the first correspondence is a correspondence between the corrupted Euclidean distance of the pattern and the trust value.
  • Table 1 is a table showing the extended BCH code (64, 51) destroying the Euclidean distance and the trust value:
  • the corrupted Euclidean distance of the received codeword is calculated based on the received codeword.
  • the trust value of the received codeword is determined based on the corrupted Euclidean distance and the first correspondence.
  • an external information comparison value is calculated based on the received codeword, the optimal codeword, and the preset noise.
  • the external information comparison value may be exp(2r j d j / ⁇ 2 ), where d j is the symbol of the jth bit of the optimal codeword, r j is the symbol of the jth bit of the received codeword, ⁇ is Preset noise.
  • the traditional SISO algorithm does not have competitive codewords in most cases, so the computational complexity is low when calculating external information, and the DBD algorithm is a unified formula in calculation, and the calculation is complicated. Higher degrees.
  • the formula for calculating external information by the DBD algorithm is:
  • ⁇ is the trust value.
  • d j is the same as r j , ) is very large, and ⁇ is a positive value less than 1.
  • step 450B when the external information comparison value is greater than or equal to the preset external information threshold, the external information output value is calculated according to the optimal codeword, the preset noise, and the trust value.
  • the external information threshold can be set.
  • the formula for calculating the external information by the DBD algorithm can be simplified as:
  • FIG. 5 is a diagram of external information calculation in a decoding method of a turbo product code according to an embodiment of the present disclosure, which can clearly describe division of steps of an external information calculation method according to an embodiment of the present disclosure.
  • the decoding process of calculating the external information according to the optimal codeword first, the correspondence between the corrupted Euclidean distance and the trust value is obtained according to the pattern, and then the received codeword is determined according to the optimal codeword.
  • the trust value is used to calculate a simplified external information comparison value based on the trust value. When the calculated external information comparison value is greater than a preset threshold, the calculation formula of the external information is simplified.
  • the computational complexity of decoding is further reduced, the performance of decoding is improved, and a good compromise between complexity and performance is achieved, which is very suitable for high performance and high throughput.
  • the amount of the system is very suitable for high performance and high throughput.
  • FIG. 6 is a schematic block diagram of a decoding apparatus for a turbo product code in accordance with an embodiment of the present disclosure.
  • the decoding apparatus of the turbo product code may include an acquisition module 10, a reduced error mode determination module 20, an optimal codeword calculation module 30, an external information calculation module 40, and a decoding result output. Module 50.
  • the acquisition module 10 is arranged to obtain the received codeword and pattern of the Turbo product code.
  • the reduced error mode determination module 20 is configured to determine a reduced error mode set based on the pattern, the number of unreliable bits, and the number of reduced errors, wherein the reduced number of bits is less than the unreliable number of bits.
  • the reduced error mode determining module 20 may be configured to: obtain the unreliable number of bits according to the pattern, and obtain an unreliable mode set according to the unreliable number of bits; and the unreliable according to the reduced number of bits Get a collection of reduced error patterns in the pattern collection.
  • the optimal codeword calculation module 30 is arranged to calculate an optimal codeword based on the reduced error mode set and the received codeword.
  • the optimal codeword calculation module 30 may be configured to: after performing a hard decision on the received codeword, obtain a hard decision code, and assign the hard code to the first codeword; according to the hard code and the Decoding the error mode set to decode the received codeword; when all decoding of the received codeword fails, determining the first codeword as an optimal codeword; when the received codeword is successfully decoded, Obtaining a decoded codeword; determining whether the decoded codeword satisfies a sufficient condition of the Kaneko algorithm, and if so, assigning the decoded codeword to the first codeword to update the first codeword, and after updating The first codeword is determined as the optimal codeword; when each of the decoded codewords obtained by traversing the reduced error mode set does not satisfy the sufficient condition of the Kaneko algorithm, calculating each decoded codeword and the hard-coded a distance inner product
  • the external information calculation module 40 is configured to calculate external information using a decoding algorithm based on the optimal codeword.
  • the external information calculation module 40 may be configured to: decode the received codeword according to the hard code and the reduced error mode set; when all decoding of the received codeword fails, the hard code is determined Determining to be a candidate codeword set, otherwise determining a decoded decoded codeword as a candidate codeword set until a decoded codeword satisfying a sufficient condition of the Kaneko algorithm is obtained; obtaining a contention codeword according to the candidate codeword set; The external information is calculated based on the received codeword, the optimal codeword, and the contention codeword.
  • the external information calculation module 40 may be further configured to: obtain a first correspondence between the corrupted Euclidean distance and the trust value of the pattern according to the pattern; according to the received codeword, the first correspondence, and Presetting noise, calculating an external information comparison value; and when the external information comparison value is greater than or equal to a preset external information threshold, according to the optimal codeword, the preset noise, and the trust value, Calculate the external information output value.
  • the external information calculation module 40 may be further configured to: calculate a corrupted Euclidean distance of the received codeword according to the received codeword; determine the received codeword according to the corrupted Euclidean distance and the first correspondence a trust value; and calculating an external information comparison value based on the received codeword, the optimal codeword, and the preset noise.
  • the decoding result output module 50 is configured to perform an iterative calculation according to the external information and a preset number of iterations to obtain a decoding result of the received codeword.
  • the reduced error mode set is determined according to the unreliable number of bits and the reduced number of error bits, and the optimal codeword is obtained according to the received codeword and the reduced error mode set, and then the decoding algorithm is used to calculate After the external information, and using the external information for iterative calculation, the decoding result is obtained. Since the number of error modes is reduced, the complexity of the Turbo product code decoding algorithm is reduced, and the Kaneko algorithm using maximum likelihood decoding improves the decoding performance.
  • Embodiments of the present disclosure also provide a computer readable storage medium having stored thereon one or more programs, the one or more programs being executed by one or more processors, the one or more processors executing The following method steps: obtaining a received codeword and a code pattern of a Turbo product code; determining a reduced error mode set according to the pattern, an unreliable number of bits, and a reduced number of error bits, wherein the reduced error bit number is smaller than the a reliable number of bits; calculating an optimal codeword according to the reduced error mode set and the received codeword; calculating external information by using a decoding algorithm according to the optimal codeword; and according to the external information and a preset iteration The number of times is iteratively calculated to obtain the decoded result of the received codeword.
  • the storage medium of this embodiment may include, but is not limited to, a ROM, a RAM, a magnetic disk, an optical disk, or the like.

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Abstract

本公开提供了一种Turbo乘积码的译码方法、装置和计算机可读存储介质。所述方法包括：获取Turbo乘积码的接收码字和码型；根据所述码型、不可靠位数和缩减错误位数，确定缩减错误模式集合，其中，所述缩减错误位数小于所述不可靠位数；根据所述缩减错误模式集合和所述接收码字计算最优码字；根据所述最优码字，利用译码算法计算外部信息；以及根据所述外部信息和预设的迭代次数进行迭代计算，得到所述接收码字的译码结果。

Description

Turbo乘积码的译码方法、装置和计算机可读存储介质 技术领域
本公开涉及(但不限于)纠错控制编码技术领域。
背景技术
在信道编码的发展过程中，人们一直在追寻误码率低、译码复杂度可以忍受的编码方法。作为基于软输入软输出迭代译码算法的代表之一，Turbo码由于其纠错性能非常接近香农极限，因此成为近二十年信道编码领域研究的热点。
在Turbo码的解码方法中，Kaneko算法是一种为了减少复杂度，提出的能在生成候选码字时动态减少搜索空间的算法。这个算法使用最优候选码字相关差的条件指导进一步搜索的方向或者当最可能的码字被找到时终止译码过程。Kaneko算法实现了最大似然译码。虽然Kaneko算法可以动态减少搜索空间，但是该算法的复杂度很高。
发明内容
依据本公开的一个方面，提供一种Turbo乘积码的译码方法，包括：获取Turbo乘积码的接收码字和码型；根据所述码型、不可靠位数和缩减错误位数，确定缩减错误模式集合，其中，所述缩减错误位数小于所述不可靠位数；根据所述缩减错误模式集合和所述接收码字计算最优码字；根据所述最优码字，利用译码算法计算外部信息；以及根据所述外部信息和预设的迭代次数进行迭代计算，得到所述接收码字的译码结果。
本公开还提供一种Turbo乘积码的译码装置，包括：获取模块，其设置为获取Turbo乘积码的接收码字和码型；缩减错误模式确定模块，其设置为根据所述码型、不可靠位数和缩减错误位数，确定缩减错误模式集合，其中，所述缩减错误位数小于所述不可靠位数；最优码字计算模块，其设置为根据所述缩减错误模式集合和所述接收码字计算最优码字；外部信息计算模块，其设置为根据所述最优码字，利 用译码算法计算外部信息；以及译码结果输出模块，其设置为根据所述外部信息和预设的迭代次数进行迭代计算，得到所述接收码字的译码结果。
本公开还提供一种Turbo乘积码的译码装置，包括存储器和处理器，所述存储器存储有计算机程序，所述计算机程序被所述处理器执行时，所述处理器执行根据本公开的Turbo乘积码的译码方法。
本公开还提供一种计算机可读存储介质，其上存储有一个或者多个程序，所述一个或者多个程序被一个或者多个处理器执行时，所述一个或者多个处理器执行根据本公开的Turbo乘积码的译码方法。
上述说明仅是本公开技术方案的概述，为了能够更清楚了解本公开的技术手段，而可依照说明书的内容予以实施，并且为了让本公开的上述和其它目的、特征和优点能够更明显易懂，以下特举本公开的具体实施方式。
附图说明
通过阅读下文优选实施方式的详细描述，各种其他的优点和益处对于本领域普通技术人员将变得清楚明了。附图仅用于示出优选实施方式的目的，而并不认为是对本公开的限制。而且在整个附图中，用相同的参考符号表示相同的部件。在附图中：
图1为根据本公开实施例的Turbo乘积码的译码方法的流程图；
图2为根据本公开实施例的Turbo乘积码的译码方法中对最优码字进行处理的流程图；
图3为根据本公开实施例的Turbo乘积码的译码方法中考虑竞争码字的流程图；
图4为根据本公开另一实施例的Turbo乘积码的译码方法的流程图；
图5为根据本公开实施例的Turbo乘积码的译码方法中外部信息计算的示图；以及
图6为根据本公开实施例的Turbo乘积码的译码装置的示意框图。
具体实施方式
下面将参照附图更详细地描述本公开的示例性实施例。虽然附图中显示了公开的示例性实施例，然而应当理解，可以以各种形式实现本公开而不应被这里阐述的实施例所限制。相反，提供这些实施例是为了能够更透彻地理解本公开，并且能够将本公开的范围完整的传达给本领域的技术人员。
图1为根据本公开实施例的Turbo乘积码的译码方法的流程图。
如图1所示，根据本公开实施例的Turbo乘积码的译码方法可以包括步骤100至500。
在步骤100，获取Turbo乘积码的接收码字和码型。
Turbo乘积码通过将两组或多组分组码字码排列到一个二维或多维矩阵中，构造子码具有最小距离特性的乘积码。Turbo乘积码的码型包括(128，120)×(128，120)、(128，127)×(128，127)、(64，57)×(64，57)、(32，26)×(16，15)×(8，7)等。在发送端发送信息时，Turbo乘积码按行逐比特串行发送。在接收端，将接收的串行序列转换成二维矩阵形式，并依靠矩阵结构进行译码。Turbo乘积码译码的复杂度和译码延时取决于子码码型，并且随着子码的构造复杂度和译码复杂度的增加而线性增加。根据接收码字无法判别接收码字的码型，因此需要同时获取接收码字和码型，以用于后续的解码。
在步骤200，根据所述码型、不可靠位数和缩减错误位数，确定缩减错误模式集合，其中，所述缩减错误位数小于所述不可靠位数。
首先根据码型以及不可靠位数获取错误模式集合，然后根据缩减错误位数在错误模式集合中获取缩减错误模式集合。在实际应用中，可根据不可靠位数和缩减错误位数对于缩减错误模式集合的中的错误模式的个数进行控制。例如，根据码型选择了n个不可靠位(即，不可靠位数为n)，则不可靠模式(即，错误模式集合)有2 n种可能，并且可以在不影响性能的情况下对错误模式进行缩减。选择最不可靠的错误1位、最不可靠的错误2位，……，最不可靠的错误k位的各 个错误模式(k＜n,即，缩减错误位数为k)，使得错误模式的个数缩减为
Figure PCTCN2018111970-appb-000001
假设，根据复杂度将不可靠位数确定为8(即，n＝8)，未缩减时，错误模式的个数为2 8＝256个。缩减错误位数为4(即，k＝4)，加上全为0的码字后，缩减后的错误模式的个数为
Figure PCTCN2018111970-appb-000002
Figure PCTCN2018111970-appb-000003
在步骤300，根据所述缩减错误模式集合和所述接收码字计算最优码字。
由于缩减错误模式集合中的错误模式大大减少，为提高得到的最优码字的准确率，在根据缩减错误模式集合和接收码字计算最优码字时，需要在遍历所有缩减错误模式后均不能进行解码时，增加对最优码字的处理。下面将参照图2对该处理进行详细描述。
在步骤400，根据所述最优码字，利用译码算法计算外部信息。
译码算法可以包括软输入软输出算法(SISO算法)和基于欧氏距离的算法(DBD算法)。外部信息为译码后的软输出信息。
在步骤500，根据所述外部信息和预设的迭代次数进行迭代计算，得到所述接收码字的译码结果。
根据外部信息和预设的迭代次数进行行列译码迭代计算，并且在迭代完成后对接收码字进行硬判决并输出译码结果。行或列迭代译码器的软输入公式如下，其中m为预设的迭代次数：
[R(m)]＝[R]+α(m)[W(m)]。
根据本实施例的Turbo乘积码的译码方法，可以根据不可靠位数和缩减错误位数确定缩减错误模式集合，根据接收码字和缩减错误模式集合得到最优码字后，利用译码算法计算外部信息后，并且利用外部信息进行迭代计算后获取译码结果。由于缩减了错误模式的个数，从而降低了Turbo乘积码译码算法的复杂性，并且使用了最大似然译码的Kaneko算法提高了译码性能。
图2为根据本公开实施例的Turbo乘积码的译码方法中对最优码字进行处理的流程图。
如图2所示，根据本公开实施例的Turbo乘积码的译码方法可 以包括步骤310至390。
在步骤310，对接收码字进行硬判后，获取硬判码，并将硬判码赋值给第一码字。
在步骤320，根据硬判码和缩减错误模式集合对接收码字进行解码。
例如，可以在硬判码与缩减错误模式集合中的各个错误模式按位异或后分别进行BCH解码。
在步骤330，判断是否接收码字的所有解码均失败，若是，则前进至步骤340，若否，则前进至步骤350。
在步骤340，将第一码字确定为最优码字。
例如，在接收码字的所有解码均失败的情况下，可以将被赋值为硬判码的第一码字作为最终的最优码字。
在步骤350，获取解码成功的解码码字。
在步骤360，判断解码码字是否满足Kaneko算法的充分条件，若是，则前进步骤370，若否，则前进至步骤380。
在步骤370，将解码码字赋值给第一码字，以更新第一码字，随后前进至步骤340。
例如，可以将满足Kaneko算法的充分条件的解码码字赋值给第一码字，以作为最优码字。
在步骤380，当遍历缩减错误模式集合获取的各个解码码字均不满足Kaneko算法的充分条件时，计算各个解码码字与硬判码的距离内积值。
在步骤390，将与最小的距离内积值对应的解码码字赋值给第一码字，以更新第一码字，随后前进至步骤340。
根据本实施例的Turbo乘积码的译码方法，在接收码字的所有解码均不成功时，将接收码字的硬判码赋值给最优码字。此外，当遍历缩减错误模式集合获取的各个解码码字均不满足Kaneko算法的充分条件时，将与硬判码距离最小的解码码字赋值给最优码字。从而，在缩减了错误模式的情况下，在大大降低了Turbo乘积码译码复杂性的同时，使得最优码字的获取更加完善可靠。
图3为根据本公开实施例的Turbo乘积码的译码方法中考虑竞争码字的流程图。
如图3所示，根据本公开实施例的Turbo乘积码的译码方法可以包括步骤410A至430A。
在步骤410A，根据硬判码和缩减错误模式集合对接收码字进行解码，当接收码字的解码均失败时，将硬判码确定为候选码字集合，否则将解码成功的解码码字确定为候选码字集合，直至获取到满足Kaneko算法的充分条件的解码码字为止。
可以将硬判码赋值给最优码字，并且将硬判码与缩减错误模式集合中的各个错误模式按位异或后分别进行BCH解码。若所有解码均失败，则最优码字为硬判码，并且候选码字集合仅包括硬判码。若解码成功的解码码字满足Kaneko算法的充分条件的码字，则将这个解码码字赋值给最优码字并输出，候选码字集合为找到最优码字之前所有BCH解码成功的解码码字。若没有符合条件的解码码字，则将与硬判码距离最小的解码码字赋值给最优码字并输出，并且候选码字集合包括所有BCH解码成功的解码码字。
在步骤420A，根据候选码字集合得到竞争码字。
根据本公开实施例，竞争码字需要同时满足两个条件：条件1，与接收码字的欧氏距离最小；以及条件2、c j≠d j，其中，c j为竞争码字在第j位的码元，d j为最优码字在第j位的码元。
首先判断条件2，在候选码字集合中找到c j≠d j的各个序列，然后在各个找到的序列中查找与接收码字有最大相关值的序列作为竞争码字。
在步骤430A，根据接收码字、最优码字和竞争码字计算外部信息。
若存在竞争码字，则：
Figure PCTCN2018111970-appb-000004
若不存在竞争码字，则：
ω j＝d j-r j
其中，w j为外部信息在第j位的码元，r j为接收码字在第j位的 码元，R为接收码字，C为竞争码字，D为最优码字。
在本实施例中，在缩减错误模式下获取最优码字和竞争码字，对解码过程中的各种情况，尤其是接收码字的所有解码均失败情况进行了考量，通过SISO算法，计算外部信息，实现了在缩减错误模式下的Turbo乘积码的译码，降低了运算的复杂度，提高了译码的性能，在复杂度和性能上达到了很好的折衷，非常适合高性能、高吞吐量的系统。
图4为根据本公开另一实施例的Turbo乘积码的译码方法的流程图。
如图4所示，根据本公开实施例的Turbo乘积码的译码方法可以包括步骤410B至450B。
在步骤410B，根据码型获取第一对应关系，所述第一对应关系为码型的破坏欧氏距离和信任值之间的对应关系。
表1为示出了扩展的BCH码(64,51)破坏欧氏距离与信任值之间表格：
表1：
Figure PCTCN2018111970-appb-000005
在步骤420B，根据接收码字计算接收码字的破坏欧氏距离。
在步骤430B，根据破坏欧氏距离和所述第一对应关系，确定接收码字的信任值。
在步骤440B，根据接收码字、最优码字和预设的噪声，计算外部信息比较值。
外部信息比较值可以为exp(2r jd j/σ 2)，其中，d j为最优码字在第j位的码元，r j为接收码字在第j位的码元，σ为预设的噪声。
在实际的译码过程中，传统SISO算法在大部分的情况下是不存在竞争码字的，所以计算外部信息时计算复杂度较低，而DBD算法在计算时是统一的公式，计算的复杂度较高。DBD算法计算外部信息的 公式为：
Figure PCTCN2018111970-appb-000006
其中，Ф为信任值。
上述公式可化简为：
Figure PCTCN2018111970-appb-000007
大部分情况下，d j与r j同号，
Figure PCTCN2018111970-appb-000008
)非常大，而Ф为小于1的正值。
在步骤450B，当外部信息比较值大于或等于预设的外部信息阈值时，根据最优码字、预设的噪声和信任值，计算外部信息输出值。
即，可以设定外部信息阈值，当外部信息比较值超过外部信息阈值时，上述DBD算法计算外部信息的公式可以简化为：
Figure PCTCN2018111970-appb-000009
另一方面，当外部信息比较值小于阈值时，上述DBD算法计算外部信息的公式不变。
图5为根据本公开实施例的Turbo乘积码的译码方法中外部信息计算的示图，能够清晰地描述根据本公开实施例的外部信息计算方法的步骤的划分。
在本实施例中，在根据最优码字计算外部信息的译码过程中，首先根据码型获取破坏欧氏距离和信任值之间的对应关系，然后根据最优码字确定接收码字的信任值，再根据所述信任值计算简化的外部信息比较值。当计算得到的外部信息比较值大于预设的阈值时，将外部信息的计算公式进行简化。
根据本实施例的Turbo乘积码的译码方法，进一步降低了译码的运算复杂度，提高了译码的性能，在复杂度和性能上达到了很好的折衷，非常适合高性能、高吞吐量的系统。
图6为根据本公开实施例的Turbo乘积码的译码装置的示意框图。
如图6所示，根据本公开实施例的Turbo乘积码的译码装置可 以包括获取模块10、缩减错误模式确定模块20、最优码字计算模块30、外部信息计算模块40和译码结果输出模块50。
获取模块10设置为获取Turbo乘积码的接收码字和码型。
缩减错误模式确定模块20设置为根据所述码型、不可靠位数和缩减错误位数，确定缩减错误模式集合，其中，所述缩减错误位数小于所述不可靠位数。缩减错误模式确定模块20可以设置为：根据所述码型获取所述不可靠位数，并根据所述不可靠位数获取不可靠模式集合；以及根据所述缩减错误位数在所述不可靠模式集合中获取缩减错误模式集合。
最优码字计算模块30设置为根据所述缩减错误模式集合和所述接收码字计算最优码字。最优码字计算模块30可以设置为：对所述接收码字进行硬判后，获取硬判码，并将所述硬判码赋值给第一码字；根据所述硬判码和所述缩减错误模式集合对所述接收码字进行解码；当所述接收码字的所有解码均失败时，将所述第一码字确定为最优码字；当所述接收码字解码成功时，获取解码码字；判断所述解码码字是否满足Kaneko算法的充分条件，若满足，将所述解码码字赋值给所述第一码字，以更新所述第一码字，并将更新后的第一码字确定为所述最优码字；当遍历所述缩减错误模式集合获取的各个解码码字均不满足Kaneko算法的充分条件时，计算各个解码码字与所述硬判码的距离内积值；以及将与最小的距离内积值对应的解码码字赋值给所述第一码字，以更新所述第一码字，并将更新后的第一码字确定为所述最优码字。
外部信息计算模块40设置为根据所述最优码字，利用译码算法计算外部信息。外部信息计算模块40可以设置为：根据所述硬判码和所述缩减错误模式集合对所述接收码字进行解码；当所述接收码字的所有解码均失败时，将所述硬判码确定为候选码字集合，否则将解码成功的解码码字确定为候选码字集合，直至获取到满足Kaneko算法的充分条件的解码码字为止；根据所述候选码字集合得到竞争码字；以及根据所述接收码字、所述最优码字和所述竞争码字计算所述外部信息。外部信息计算模块40还可以设置为：根据所述码型获取所述 码型的破坏欧氏距离和信任值之间的第一对应关系；根据所述接收码字、所述第一对应关系和预设的噪声，计算外部信息比较值；以及当所述外部信息比较值大于或等于预设的外部信息阈值时，根据所述最优码字、所述预设的噪声和所述信任值，计算外部信息输出值。外部信息计算模块40还可以设置为：根据所述接收码字计算所述接收码字的破坏欧氏距离；根据所述破坏欧氏距离和所述第一对应关系，确定所述接收码字的信任值；以及根据所述接收码字、所述最优码字和所述预设的噪声，计算外部信息比较值。
译码结果输出模块50设置为根据所述外部信息和预设的迭代次数进行迭代计算，得到所述接收码字的译码结果。
根据本实施例的Turbo乘积码的译码装置，根据不可靠位数和缩减错误位数确定缩减错误模式集合，根据接收码字和缩减错误模式集合得到最优码字后，利用译码算法计算外部信息后，并且利用外部信息进行迭代计算后获取译码结果。由于缩减了错误模式的个数，从而降低了Turbo乘积码译码算法的复杂性，并且使用了最大似然译码的Kaneko算法提高了译码性能。
本公开实施例还提供一种计算机可读存储介质，其上存储有一个或者多个程序，所述一个或者多个程序被一个或者多个处理器执行时，所述一个或者多个处理器执行以下方法步骤：获取Turbo乘积码的接收码字和码型；根据所述码型、不可靠位数和缩减错误位数，确定缩减错误模式集合，其中，所述缩减错误位数小于所述不可靠位数；根据所述缩减错误模式集合和所述接收码字计算最优码字；根据所述最优码字，利用译码算法计算外部信息；以及根据所述外部信息和预设的迭代次数进行迭代计算，得到所述接收码字的译码结果。
本实施例所述存储介质可以包括(但不限于)ROM、RAM、磁盘或光盘等。
以上所述仅为本公开的示例实施例，并非用于限定本公开的保护范围。凡在本公开的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本公开的保护范围之内。

Claims (18)

  1. 一种Turbo乘积码的译码方法，包括：
    获取Turbo乘积码的接收码字和码型；
    根据所述码型、不可靠位数和缩减错误位数，确定缩减错误模式集合，其中，所述缩减错误位数小于所述不可靠位数；
    根据所述缩减错误模式集合和所述接收码字计算最优码字；
    根据所述最优码字，利用译码算法计算外部信息；以及
    根据所述外部信息和预设的迭代次数进行迭代计算，得到所述接收码字的译码结果。
  2. 如权利要求1所述的Turbo乘积码的译码方法，其中，所述根据所述码型、不可靠位数和缩减错误位数，确定缩减错误模式集合的步骤包括：
    根据所述码型获取所述不可靠位数，并根据所述不可靠位数获取不可靠模式集合；以及
    根据所述缩减错误位数在所述不可靠模式集合中获取缩减错误模式集合。
  3. 如权利要求1所述的Turbo乘积码的译码方法，其中，所述根据所述缩减错误模式集合和所述接收码字计算最优码字的步骤包括：
    对所述接收码字进行硬判后，获取硬判码，并将所述硬判码赋值给第一码字；
    根据所述硬判码和所述缩减错误模式集合对所述接收码字进行解码；以及
    当所述接收码字的所有解码均失败时，将所述第一码字确定为最优码字。
  4. 如权利要求3所述的Turbo乘积码的译码方法，其中，所述 根据所述缩减错误模式集合和所述接收码字计算最优码字的步骤还包括：
    当所述接收码字解码成功时，获取解码码字；以及
    判断所述解码码字是否满足Kaneko算法的充分条件，若满足，将所述解码码字赋值给所述第一码字，以更新所述第一码字，并将更新后的第一码字确定为所述最优码字。
  5. 如权利要求4所述的Turbo乘积码的译码方法，其中，所述根据所述缩减错误模式集合和所述接收码字计算最优码字的步骤还包括：
    当遍历所述缩减错误模式集合获取的各个解码码字均不满足Kaneko算法的充分条件时，计算各个解码码字与所述硬判码的距离内积值；以及
    将与最小的距离内积值对应的解码码字赋值给所述第一码字，以更新所述第一码字，并将更新后的第一码字确定为所述最优码字。
  6. 如权利要求5所述的Turbo乘积码的译码方法，其中，所述根据所述最优码字，利用译码算法计算外部信息的步骤包括：
    根据所述硬判码和所述缩减错误模式集合对所述接收码字进行解码；
    当所述接收码字的所有解码均失败时，将所述硬判码确定为候选码字集合，否则将解码成功的解码码字确定为候选码字集合，直至获取到满足Kaneko算法的充分条件的解码码字为止；
    根据所述候选码字集合得到竞争码字；以及
    根据所述接收码字、所述最优码字和所述竞争码字计算所述外部信息。
  7. 如权利要求1所述的Turbo乘积码的译码方法，其中，所述根据所述最优码字，利用译码算法计算外部信息的步骤包括：
    根据所述码型获取所述码型的破坏欧氏距离和信任值之间的第 一对应关系；
    根据所述接收码字、所述第一对应关系和预设的噪声，计算外部信息比较值；以及
    当所述外部信息比较值大于或等于预设的外部信息阈值时，根据所述最优码字、所述预设的噪声和所述信任值，计算外部信息输出值。
  8. 如权利要求7所述的Turbo乘积码的译码方法，其中，所述根据所述接收码字、所述第一对应关系和预设的噪声，计算外部信息比较值的步骤包括：
    根据所述接收码字计算所述接收码字的破坏欧氏距离；
    根据所述破坏欧氏距离和所述第一对应关系，确定所述接收码字的信任值；以及
    根据所述接收码字、所述最优码字和所述预设的噪声，计算外部信息比较值。
  9. 一种Turbo乘积码的译码装置，包括：
    获取模块，其设置为获取Turbo乘积码的接收码字和码型；
    缩减错误模式确定模块，其设置为根据所述码型、不可靠位数和缩减错误位数，确定缩减错误模式集合，其中，所述缩减错误位数小于所述不可靠位数；
    最优码字计算模块，其设置为根据所述缩减错误模式集合和所述接收码字计算最优码字；
    外部信息计算模块，其设置为根据所述最优码字，利用译码算法计算外部信息；以及
    译码结果输出模块，其设置为根据所述外部信息和预设的迭代次数进行迭代计算，得到所述接收码字的译码结果。
  10. 如权利要求9所述的Turbo乘积码的译码装置，其中，所述缩减错误模式确定模块设置为：
    根据所述码型获取所述不可靠位数，并根据所述不可靠位数获取不可靠模式集合；以及
    根据所述缩减错误位数在所述不可靠模式集合中获取缩减错误模式集合。
  11. 如权利要求9所述的Turbo乘积码的译码装置，其中，所述最优码字计算模块设置为：
    对所述接收码字进行硬判后，获取硬判码，并将所述硬判码赋值给第一码字；
    根据所述硬判码和所述缩减错误模式集合对所述接收码字进行解码；以及
    当所述接收码字的所有解码均失败时，将所述第一码字确定为最优码字。
  12. 如权利要求11所述的Turbo乘积码的译码装置，其中，所述最优码字计算模块还设置为：
    当所述接收码字解码成功时，获取解码码字；以及
    判断所述解码码字是否满足Kaneko算法的充分条件，若满足，将所述解码码字赋值给所述第一码字，以更新所述第一码字，并将更新后的第一码字确定为所述最优码字。
  13. 如权利要求12所述的Turbo乘积码的译码装置，其中，所述最优码字计算模块还设置为：
    当遍历所述缩减错误模式集合获取的各个解码码字均不满足Kaneko算法的充分条件时，计算各个解码码字与所述硬判码的距离内积值；以及
    将与最小的距离内积值对应的解码码字赋值给所述第一码字，以更新所述第一码字，并将更新后的第一码字确定为所述最优码字。
  14. 如权利要求13所述的Turbo乘积码的译码装置，其中，所 述外部信息计算模块设置为：
    根据所述硬判码和所述缩减错误模式集合对所述接收码字进行解码；
    当所述接收码字的所有解码均失败时，将所述硬判码确定为候选码字集合，否则将解码成功的解码码字确定为候选码字集合，直至获取到满足Kaneko算法的充分条件的解码码字为止；
    根据所述候选码字集合得到竞争码字；以及
    根据所述接收码字、所述最优码字和所述竞争码字计算所述外部信息。
  15. 如权利要求9所述的Turbo乘积码的译码装置，其中，所述外部信息计算模块设置为：
    根据所述码型获取所述码型的破坏欧氏距离和信任值之间的第一对应关系；
    根据所述接收码字、所述第一对应关系和预设的噪声，计算外部信息比较值；以及
    当所述外部信息比较值大于或等于预设的外部信息阈值时，根据所述最优码字、所述预设的噪声和所述信任值，计算外部信息输出值。
  16. 如权利要求15所述的Turbo乘积码的译码装置，其中，所述外部信息计算模块还设置为：
    根据所述接收码字计算所述接收码字的破坏欧氏距离；
    根据所述破坏欧氏距离和所述第一对应关系，确定所述接收码字的信任值；以及
    根据所述接收码字、所述最优码字和所述预设的噪声，计算外部信息比较值。
  17. 一种Turbo乘积码的译码装置，包括存储器和处理器，所述存储器存储有计算机程序，所述计算机程序被所述处理器执行时， 所述处理器执行如权利要求1至8任意一项所述的Turbo乘积码的译码方法。
  18. 一种计算机可读存储介质，其上存储有一个或者多个程序，所述一个或者多个程序被一个或者多个处理器执行时，所述一个或者多个处理器执行如权利要求1至8中任意一项所述的Turbo乘积码的译码方法。
PCT/CN2018/111970 2017-10-25 2018-10-25 Turbo乘积码的译码方法、装置和计算机可读存储介质 WO2019080912A1 (zh)

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