CN107431559B - method and device for data transmission by using multi-polarization code - Google Patents

method and device for data transmission by using multi-polarization code Download PDF

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CN107431559B
CN107431559B CN201580078059.5A CN201580078059A CN107431559B CN 107431559 B CN107431559 B CN 107431559B CN 201580078059 A CN201580078059 A CN 201580078059A CN 107431559 B CN107431559 B CN 107431559B
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CN107431559A (en
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塔尔·爱德
瓦迪·亚历山大
沈晖
李斌
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Huawei Technologies Co Ltd
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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
    • H03M13/03—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
    • 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
    • H03M13/25—Error detection or forward error correction by signal space coding, i.e. adding redundancy in the signal constellation, e.g. Trellis Coded Modulation [TCM]
    • H03M13/251—Error detection or forward error correction by signal space coding, i.e. adding redundancy in the signal constellation, e.g. Trellis Coded Modulation [TCM] with block coding

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Abstract

The invention discloses a method for data transmission by using a multi-element polarization code, which comprises the steps of merging a plurality of channels of a basic unit of the multi-element polarization code, then updating the transition probability of the merged channels, obtaining the upper limit of the error probability of the merged channels according to the transition probability, transmitting information bits by using K channels with the minimum upper limit of the error probability in the merged channels, and controlling the complexity of coding in the data transmission process by combining the channels of the multi-element polarization code under high-order modulation, wherein the information loss during the high-order modulation and demodulation can be reduced because the multi-element polarization code is used.

Description

method and device for data transmission by using multi-polarization code
Technical Field
The present invention relates to the field of communications, and more particularly, to methods and apparatuses for data transmission using a multi-polarization code.
Background
Recently, th polarization Code (English: Polar Code; Polar Code for short) theoretically proves that Shannon capacity can be obtained and good Code with Low coding complexity (O (NlogN), wherein N is Code length) is provided by Arikan.
Polar code encoding
Polar code is linear block code, and the encoding process is as follows:
wherein the content of the first and second substances,
Figure GPA0000233673180000022
in order to encode the bits that have been encoded,
Figure GPA0000233673180000023
to code bits, GNTo generate a matrix, wherein,
Figure GPA0000233673180000024
wherein N is 2n，n≥1，BNAs a transpose matrix, such as a bit reversal matrix (english),is the Kronecker product, which is defined as
Figure GPA0000233673180000026
Figure GPA0000233673180000027
Polar codes may be represented as coset codes (N, K, a,
Figure GPA0000233673180000028
) Wherein, K is the number of information bits, and the encoding process is as follows:wherein A is an information bit indexSet of (2), GN(A) Is GNIn which a sub-matrix is formed by the rows corresponding to the indices in the set A, GN(Ac) Is GNIn (A) is setcThe sub-matrix is composed of rows corresponding to the indexes in (1),
Figure GPA00002336731800000210
is a fixed bit (English: free bit) with the number of (N-K).
Figure GPA00002336731800000211
For known bits, the fixed bits may all be set to 0 for simplicity.
When N is 8, the Polar code is encoded as shown in fig. 1.
Two, Polar code decoding
Suppose (y)1，y2，...，yN) Is received as
Figure GPA00002336731800000212
SC decoder 1) first calculates u1Log likelihood ratio of
Figure GPA0000233673180000031
Wherein the content of the first and second substances,
Figure GPA0000233673180000032
then u is obtained from the symbol decision of the value1Evaluation of
Figure GPA0000233673180000033
2) According to what has been obtained
Figure GPA0000233673180000034
Calculating u2Log likelihood ratio ofThen u is obtained from the symbol decision of the value2Evaluation of
Figure GPA0000233673180000036
3) Thus translating one by oneGo out u3，u4，...，uNIn the decision process, if the bit is a fixed bit, the bit is decided to be 0. Wherein, if
Figure GPA0000233673180000037
Then a decision is made as follows:
Figure GPA0000233673180000038
if it is not
Figure GPA0000233673180000039
Simple order
Figure GPA00002336731800000310
Like SC coding, List coding is also sequential coding, and the process is briefly described as follows:
to avoid too many reserved sequences, the decoder will reserve up to fixed number of sequences, which may avoid or reduce the decisions in the SC decoder for the newly decoded information bits.
1) (path splitting) each time ifIs information bit or free bit, and splits the current decoding path into two paths:
Figure GPA00002336731800000312
pieces of
Figure GPA00002336731800000313
, discarding the least reliable paths when the total number of paths exceeds a predefined limit of , L, keeping only the L most reliable paths, and updating the probability values or log-likelihood ratios (english: L) on all pathsAn og Likelihood Ratio; for short: LLR).
2) (without path splitting) if
Figure GPA00002336731800000314
Is a fixed bit, all decoding paths are not split, setKeeping the path number unchanged and updating probability values or LLRs of all paths;
when L is 4, decoding paths of non-fixed bits are as shown in fig. 2, and a flow chart of List decoding in case of cascade connection of Polar codes with a survivor path number of L and Cyclic Redundancy Check (CRC) is as shown in fig. 3.
Thus, Polar code pairProcessed sequentially one by one, the complexity of SC coding is O (N log)2N), the complexity of List coding is O (L × N × log)2N)。
Although the SC decoding can achieve good performance approaching to the shannon limit under the condition of long code length N, when N is short or medium, the SC decoding performance of Polar code does not exceed the performance of Turbo code and LDPC code, and it is necessary to further to improve the decoding performance.
The performance of List coding is -fold higher than SC coding, which is about L times more complex than SC coding, and needs to be simplified.
The scheme of Polar code combining the existing and high-order modulation is a scheme of multilayer code, namely, the high-order modulation is regarded as a plurality of binary White Gaussian Noise (AWGN) channels, and Polar codes are used for the AWGN channel of each bin;
the scheme combining Polar codes of multilayer codes and high-order modulation has information loss during high-order modulation and demodulation, and finally the whole scheme has constant information loss, so that constant loss is required for the performance relative to the optimal scheme.
Disclosure of Invention
The embodiment of the invention provides methods for data transmission by using multi-element polarization codes, which can realize controllable channel number of the multi-element polarization codes under high-order modulation, thereby controlling the complexity of coding in the data transmission process.
, an embodiment of the present invention provides methods for data transmission using a multi-polarization code, including:
combining a plurality of channels of a basic unit of a multi-component polarization code, wherein the size of an alphabet of the plurality of channels is greater than 2;
updating the transition probabilities of the combined channels;
obtaining the upper limit of the error probability of the combined channels according to the transition probability;
and transmitting information bits by using K channels with the minimum upper limit of the error probability in the combined plurality of channels.
With reference to the , in an possible implementation manner of the , the combining multiple channels of a basic unit of a multi-component polarization code includes:
and performing pre-combination or greedy combination on a plurality of channels of the elementary units with the multi-polarization.
With reference to the possible implementation manner of the , in a second possible implementation manner of the , the pre-combining multiple channels of a multi-polarization basic unit includes:
and combining the plurality of channels according to the posterior probability distance between two letters of the plurality of channels.
With reference to the possible implementation manner of the , in a third possible implementation manner of the , the merging the multiple channels according to the posterior probability distance between two letters of the multiple channels includes:
and when the posterior probability distance between the two letters is smaller than a preset confidence parameter, combining the channels corresponding to the two letters, and adding the channel transfer probabilities corresponding to the two combined letters.
With reference to the second or third possible implementation manner of the aspect, in a fourth possible implementation manner of the aspect, the posterior probability distance is obtained according to the following method:
channels W, y of input alphabet size q and output alphabet size M1、y2For two letter indices, then y is received1、y2The probabilities of (c) are respectively:
Figure GPA0000233673180000051
will receive y1、y2The probabilities of (A) and (B) are respectively classified into and 1/2, the results after classification into are as follows:
Figure GPA0000233673180000052
when y is calculated1、y2Capacity difference at merging:
Figure GPA0000233673180000053
the capacity difference is then: 1+ σ/q where σ is the noise variance.
Then y is1、y2The posterior probability distance between them is:
APPdistance(y1，y2)＝1+σ/q。
with reference to the th aspect or the th to the fourth th possible implementation manner of the th aspect, in a fifth possible implementation manner of the th aspect, the merging of the multiple channels is implemented by:
for two letters y1、y2Merging, wherein u is 1,2, …, q, for every u:
W(y1|u)＝W(y1|u)+W(y2|u)
W(y2|u)＝W(yM|u)
wherein, after the above operation is completed for all u, the value of M is reduced by 1; and by analogy, combining any plurality of channels by combining two letter classes.
With reference to the possible implementation manner of the aspect of , in a sixth possible implementation manner of the aspect of , the greedy combining and merging the multiple channels of the multi-polarization basic unit includes:
and combining the plurality of channels according to the combination distance between two letters of the plurality of channels.
With reference to the sixth possible implementation manner of the , in a seventh possible implementation manner of the , the merging the multiple channels according to a merging distance between two letters of the multiple channels includes:
when the combination distance between two letters is smaller than the optimal limit, combining the pre-combined channels corresponding to the two letters, and so on until the size of the output alphabet is smaller than or equal to the preset reliability parameter, wherein the initial value of the optimal limit is 0, and then the combination distance between the two letters with the minimum combination distance of times is included.
With reference to the sixth or seventh possible implementation manner of the aspect , in an eighth possible implementation manner of the aspect , the combining distance is obtained according to the following method:
channels W, y of input alphabet size q and output alphabet size M1、y2For the index of two letters (in the output alphabet), then y is received1The probabilities of (c) are:
Figure GPA0000233673180000061
calculating an entropy difference:
then y is1、y2The merging distance between them is:
Figure GPA0000233673180000063
with reference to the aspect or the to the eighth possible implementation manners of the aspect, in a ninth possible implementation manner of the aspect, the transmitting information bits by using the K channels with the minimum upper limit of the error probability in the combined multiple channels may specifically include calculating the error probability of each symbol channel by using the upper limit of the error probability of the combined multiple channels, and selecting the K symbol channels with the minimum error probability to transmit information bits.
In a second aspect, an embodiment of the present invention provides an apparatus for data transmission using a multi-polarization code, including:
a merging unit, configured to merge multiple channels of a basic unit of a multi-component polarization code, where the size of an alphabet of the multiple channels is greater than 2;
an updating unit, configured to update transition probabilities of the combined multiple channels;
a processing unit, configured to obtain an upper limit of the error probability of the combined multiple channels according to the transition probability;
and a transmission unit, configured to transmit information bits using the K channels with the minimum upper limit of the error probability in the combined multiple channels.
With reference to the second aspect, in an th possible implementation manner of the second aspect, the merging unit includes a pre-merging unit or a greedy merging unit;
the pre-combining unit is used for pre-combining a plurality of channels of the basic unit with multi-polarization; the greedy merging unit is used for greedy merging of a plurality of channels of the multi-polarization basic unit.
With reference to the th possible implementation manner of the second aspect, in a second possible implementation manner of the second aspect, the pre-combining unit is configured to:
and combining the plurality of channels according to the posterior probability distance between two letters of the plurality of channels.
With reference to the th possible implementation manner of the second aspect, in a third possible implementation manner of the second aspect, the merging the multiple channels according to a posterior probability distance between two letters of the multiple channels includes:
and when the posterior probability distance between the two letters is smaller than a preset confidence parameter, combining the channels corresponding to the two letters, and adding the channel transfer probabilities corresponding to the two combined letters.
With reference to the second or third possible implementation manner of the second aspect, in a fourth possible implementation manner of the second aspect, the posterior probability distance is obtained according to the following method:
channels W, y of input alphabet size q and output alphabet size M1、y2For two letter indices, then y is received1、y2The probabilities of (c) are respectively:
Figure GPA0000233673180000071
will receive y1、y2The probabilities of (A) and (B) are respectively classified into and 1/2, the results after classification into are as follows:
Figure GPA0000233673180000072
when y is calculated1、y2Capacity difference at merging:
Figure GPA0000233673180000073
the capacity difference is then: 1+ σ/q where σ is the noise variance.
Then y is1、y2The posterior probability distance between them is:
APPdistance(y1，y2)＝1+σ/q。
with reference to the second aspect or any one of th through fourth possible implementations of the second aspect, in a fifth possible implementation of the second aspect, the combining multiple channels is implemented by:
for two letters y1、y2Merging, wherein u is 1,2, …, q, for every u:
W(y1|u)＝W(y1|u)+W(y2|u)
W(y2|u)＝W(yM|u)
wherein, after the above operation is completed for all u, the value of M is reduced by 1; and by analogy, combining any plurality of channels by combining two letter classes.
With reference to the possible implementation manners of the second aspect, in a sixth possible implementation manner of the second aspect, the greedy merging unit is configured to:
and combining the plurality of channels according to the combination distance between two letters of the plurality of channels.
With reference to the sixth possible implementation manner of the second aspect, in a seventh possible implementation manner of the second aspect, the merging the multiple channels according to a merging distance between two letters of the multiple channels includes:
when the combination distance between two letters is smaller than the optimal limit, combining the pre-combined channels corresponding to the two letters, and so on until the size of the output alphabet is smaller than or equal to the preset reliability parameter, wherein the initial value of the optimal limit is 0, and then the combination distance between the two letters with the minimum combination distance of times is included.
With reference to the sixth or seventh possible implementation manner of the second aspect, in an eighth possible implementation manner of the second aspect, the combining distance is obtained according to the following method:
channels W of alphabet size q for input and alphabet size M for output,y1、y2for the index of two letters (in the output alphabet), then y is received1The probabilities of (c) are:
Figure GPA0000233673180000081
calculating an entropy difference:
Figure GPA0000233673180000082
then y is1、y2The merging distance between them is:
Figure GPA0000233673180000083
with reference to the second aspect or any one of th through th possible implementations of the second aspect, in a ninth possible implementation of the second aspect, the transmitting information bits using the K channels with the minimum upper limit of the error probability in the combined multiple channels may specifically include calculating the error probability of each symbol channel using the upper limit of the error probability of the combined multiple channels, and selecting the K symbol channels with the minimum error probability to transmit information bits.
The method for transmitting data by utilizing the multi-element polarization code comprises the steps of combining a plurality of channels of a basic unit of the multi-element polarization code, then updating the transition probability of the combined plurality of channels, obtaining the upper limit of the error probability of the combined plurality of channels according to the transition probability, transmitting information bits by utilizing K channels with the minimum upper limit of the error probability in the combined plurality of channels, controlling the channel number of the multi-element polarization code under high-order modulation by combining, thereby being capable of controlling the complexity of coding in the data transmission process, and reducing the information loss in the high-order modulation demodulation process due to the fact that the multi-element polarization code is used, is capable of controlling the capacity difference of the combined channels by utilizing the posterior probability distance or the combining distance, thereby being capable of controlling the information loss in the data transmission process.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments of the present invention or the description of the prior art will be briefly described below, and it is obvious that the drawings described below are only embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a schematic diagram of an encoding process of Polar code when N is 8;
FIG. 2 is a schematic diagram of a decoding path of non-fixed bits when L is 4;
FIG. 3 is a flow chart of List decoding in case of cascade of Polar code with L survivor path number and CRC;
FIG. 4 is a basic unit of multi-element Polar codes provided by the embodiment of the present invention;
FIG. 5 is a definition of types of "add operations" under 16QAM that can result in channel polarization, provided by an embodiment of the present invention;
fig. 6 illustrates methods for data transmission using multi-polarization codes according to an embodiment of the present invention;
fig. 7 illustrates apparatuses for data transmission using multi-polarization codes according to an embodiment of the present invention;
fig. 8 shows kinds of devices for data transmission by using multi-polarization codes according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are partial embodiments of the present invention, rather than all embodiments.
The technical scheme provided by the embodiment of the invention can be applied to various communication systems, such as: a Global System for Mobile communications (GSM) System, a Code Division Multiple Access (CDMA) System, a Wideband Code Division Multiple Access (WCDMA) System, a General Packet Radio Service (GPRS), a Long Term Evolution (Long Term Evolution, LTE) System, a Frequency Division Duplex (FDD) System, a Time Division Duplex (TDD), a Universal Mobile Telecommunications System (UMTS), a world wide Mobile Access (WiMAX) communication System, or a Public Land Mobile Network (PLMN) 5 (Public Land Mobile network).
User Equipment (UE), also referred to as Mobile Terminal (Mobile Terminal), Mobile User Equipment (UE), and so on, may communicate with or more core networks via a Radio Access Network (RAN, Radio Access Network, for example), where the UE may be a Mobile Terminal, such as a Mobile phone (or referred to as a "cellular" phone) and a computer having a Mobile Terminal, such as a portable, pocket, hand-held, computer-included, or vehicle-mounted Mobile device, which exchange languages and/or data with the Radio Access Network.
The Base Station may be a Base Transceiver Station (BTS) in GSM or CDMA, a Base Station (NodeB) in WCDMA, an evolved node b (eNB or e-NodeB) in LTE, or a Base Station in a 5G network, and the present invention is not limited thereto.
According to the principle of coded modulation, if q-ary Polar codes adopted during data transmission are not matched with M-order modulation (for example, q ≠ M), the problem of conversion of multi-system and binary soft information is introduced, so that loss is caused in the information reprocessing process and the Polar codes are generally used for binary channels, and even if a scheme of multi-layer codes is adopted, high-order modulation is considered as a plurality of binary channels, so that loss is caused.
In order to apply Polar codes to the situation of high-price modulation, the embodiment of the invention provides construction algorithms of multi-element Polar codes applied to high-order modulation, wherein an alphabet is merged and output by using a greedy principle in each basic unit polarization transformations, so that the number of the sizes of the alphabets is controllable after each levels of basic polarization transformations, and the complexity is also controllable, and therefore, the construction algorithms of the multi-element Polar codes with the complexity of polynomials are designed, and the performance of the Polar codes and the high-order modulation when combined can be greatly improved by the construction algorithms of the multi-element Polar codes described in the patent, namely, the information loss and the control algorithm complexity are reduced.
FIG. 4 shows the basic units of multi-element Polar codes provided by the embodiment of the present invention, as shown in FIG. 4, let W1：x1→y1And W2：x2→y2；
The corresponding transformation of the basic unit of the multi-element Polar code is as follows:
wherein, W-、W+The probability of (c) is obtained by the following formula,
Figure GPA0000233673180000111
W+(y1y2u1|u2)＝W1(y1|u1+u2)W2(y2|u2)
it should be noted that, where u1、u2Is defined in a multivariate field (e.g., q-ary or q-ary), u1、u2The addition between is a modulo q addition. In particular, for two unpolarized signalsWay W1、W2Performing a single step poling operation, wherein x1、x2Is a channel input symbol, y1、y2Is a channel output symbol; will u2Direct assignment to x2，Wherein the content of the first and second substances,
Figure GPA0000233673180000113
although generally, addition modulo q (or mod q) or addition in the Galois Field GF (q) generally does not result in channel polarization.
Taking 16QAM as an example, it is necessary to define an addition operation that can cause channel polarization for 16 QAM. Let the input alphabet set of 16QAM be as follows:
χ＝{(x1，x2)：x1，x2∈{-3，-1，+1，+3}}
then, the definition of "addition" under 16QAM that can cause channel polarization is shown in fig. 5, and it should be noted that fig. 5 shows
Figure GPA0000233673180000114
The expression "3" indicates that,it should be understood that fig. 4 is only expressions of basic units of the multi-Polar code provided by the embodiment of the present invention, and other manners capable of realizing polarization can be applied to the method provided by the embodiment of the present invention, and thus all manners capable of realizing polarization are within the scope of the embodiment of the present invention.
After defining the addition operation of the multivariate field, we can obtain the following construction algorithm of multivariate (also called multilevel, such as q-ary, English: q-ary) Polar code:
the Polar code construction means that under the condition that the matching of multi-Polar codes and high-order modulation is met, the number of channel transfer probabilities entering a construction algorithm is controlled by means of pre-combination or greedy combination, so that complexity is reduced, K channels with the minimum upper bound of channel error probability are selected for coding transmission, information loss can be reduced, and data transmission by means of the multi-Polar codes is completed.
Taking q-ary as an example, the construction algorithm of Polar code mainly comprises two stages: a pre-merge stage and a greedy merge stage; wherein the time complexity of the precombinations stage is O (M)2) (ii) a The temporal complexity of the greedy merge stage is O (M)3)。
channels W, y of input alphabet size q and output alphabet size M1、y2For an index of two letters (in the output alphabet) (where the input alphabet size q indicates that there are q possibilities for the input or out of q symbols for the input, the meaning of the output alphabet size M is similar.) taking as an example the basic unit shown in fig. 4, let u be the input1、u2With 16 different values ({ -3, -1, +1, +3}, -3, -1, +1, +3}) respectively, the input alphabet size is 16, and y is1，y2There are M kinds of values, the output alphabet size is M, and y is used1、y2Representing two letters in the M values.
Step 601 a: pre-combining a plurality of channels;
when the posterior probability distance between two letters is smaller than the preset confidence parameter, the channels corresponding to the two letters are merged, the channel transition probabilities corresponding to the two letters are added, and letters are selected by the alphabet after merging.
The merging in the embodiment of the present invention is performed for a plurality of channels, where the plurality of channels refers to that the input channels W with an alphabet size q and an output channel W with an alphabet size M output an alphabet size M, and there are possible values in M, so that a plurality of different channels may be formed, and these channels may be pre-merged or greedy merged to reduce complexity.
Wherein the posterior probability distance between two letters is defined as follows:
channels W, y of input alphabet size q and output alphabet size M1、y2For the index of two letters (in the output alphabet), then y is received1、y2The probabilities of (c) are respectively:
Figure GPA0000233673180000121
will receive y1、y2The probabilities of (A) and (B) are respectively classified into and 1/2, the results after classification into are as follows:
Figure GPA0000233673180000122
when y is calculated1、y2Capacity difference at merging:
Figure GPA0000233673180000123
the capacity difference is then: 1+ σ/q where σ is the noise variance.
Then y is1、y2The posterior probability distance between them is:
APPdistance(y1，y2)＝1+σ/q，
that is, when y1、y2Merging y under the condition of when the received probabilities are all 1/21、y2The difference in capacity generated is y1、y2The posterior probability distance between.
step, when APPdistance(y1，y2) E.g. when y is ≦ epsilon1、y2When the posterior probability distance between the two is less than or equal to the preset confidence parameter epsilon, for y1、y2Merging;
specifically, for y1、y2The merging can be realized by the following processes:
1,2, …, q, for every u:
W(y1|u)＝W(y1|u)+W(y2|u)
W(y2|u)＝W(yM|u)
after the above operations are performed on all u, the value of M is decreased by 1, that is, as long as merging operations are performed, the value of M is decreased by 1 accordingly, that is, the size of the output alphabet is 1 less than the size before merging.
According to the above steps, all y can be traversed1、y2To implement pre-combining of multiple channels; for example, when y 11,2, …, M, for y2＝y1+1，y1+2, …, M performs the above steps to achieve precombining of multiple channels it should be noted that each time combining operations are performed, y2Is reduced by 1 (i.e., y is included) accordingly based on the value at the time of merging2＝y2-1 this step).
Step 602 a: greedy merging is carried out on a plurality of channels;
when the combination distance between the two letters is smaller than the optimal limit value, combining the channels corresponding to the two letters, and repeating the steps until the size of the output alphabet is smaller than or equal to the preset reliability parameter, wherein the optimal limit value is the combination distance between the two letters with the minimum combination distance for the upper times, and the initial value can be set to 1.
Wherein the merging distance between two letters is defined as follows:
channels W, y of input alphabet size q and output alphabet size M1、y2For the index of two letters (in the output alphabet), then y is received1The probabilities of (c) are:
Figure GPA0000233673180000131
calculating an entropy difference:
then y is1、y2The merging distance between them is:
Figure GPA0000233673180000142
, all y's can be traversed according to the definition of the merge distance described above1、y2To find the two letters with the smallest merging distance; for example, when y 11,2, …, M, for y2＝y1+1，y1+2, …, M performs: if MergeDistance (y)1，y2)＜ε(best)Then y at this time1、y2To merge two letters with the smallest distance and limit the optimum to epsilon(best)Update to MergeDistance (y)1，y2). So that the two letters with the minimum merging distance can be found and merged, wherein the merging operation method is the same as the merging operation method in the pre-merging (i.e. the same as the merging operation method in step 601 a), but the two letters with the minimum merging distance are merged. In addition, the merging distance defined in the embodiment of the present invention is a capacity difference after merging.
Alternatively, the above construction algorithm can also be implemented by the following five algorithms:
algorithm 1 is used to implement the steps of precombinations: for y 11,2, …, each value of M and y2＝y1+1，y1+2, …, each value of M when y is1、y2When the posterior probability distance between the y and y is less than or equal to the preset confidence parameter epsilon, merging the y1、y2Wherein the merging method is the same as the merging method in the step 601a, and in addition, merging y is performed every time times2Is reduced by 1 on the basis of the value at the time of combining algorithm 1 is mainly based on combining the original channels (x- > y) reducing the number of samples of channel transition probability entering the construction algorithm, thus reducing complexity, specifically possible implementations of algorithm 1 are as follows:
algorithm 2 is used to define the combining step of the pre-combining stage, and the basic implementation is to combine the alphabet pairs of the combined received signals, add the combined probabilities, and select from the combined alphabets.
Figure GPA0000233673180000151
Algorithm 3 is used to define the merging criterion (or a posteriori probability distance) of the pre-merging phase, i.e. the (letters) selected for merging are chosen by the posteriori probability distance, algorithm 3 gives a definition of the posteriori probability distance, the definition of the particular posteriori probability distance being the same as in step 601 a. in particular, possible implementations of algorithm 3 are as follows:
algorithm 4 is used to define the steps of the greedy merging phase, which merges greedily according to the merging distance, i.e., the smaller the merging distance, the more preferential merging is performed, until the size of the output alphabet reaches a given parameter.
Figure GPA0000233673180000161
Algorithm 5 is used to define the merge criterion (or merge distance) of the greedy merge stage, i.e. the merge is selected by the merge distance, and Algorithm 5 gives a definition of the merge distance, which is the capacity difference after the merge, and the definition of the specific merge distance is the same as the definition in step 602 a. specifically, possible implementations of Algorithm 5 are as follows:
Figure GPA0000233673180000162
optionally, the above-mentioned construction method may also omit pre-merging and directly perform greedy merging to simplify the operation steps, thereby reducing the complexity; or pre-merge directly and omit greedy merge to simplify operations. For the situations of both pre-merging and greedy merging, it is necessary to simply deform the two or simply process the intermediate data, but the basic principle is the same as the above method, and is not described herein again.
In addition, the above construction method is mainly designed for the basic unit of Polar code, and the whole Polar code can be completely constructed according to the basic unit, which can be obtained according to the prior art, and is not described herein again.
In the construction algorithm provided by the embodiment of the present invention, the error probability of the ith symbol channel (actually, q-ary symbol channel) can be calculated by using a similar procedure to SC decoding as follows: respectively updating the transition probability W according to the formulas (2) (3) and the algorithms 4-5 according to the parity condition corresponding to the symbol sequence number i at the stage by utilizing a flow (recursive calculation on a factor graph of a Polar code) similar to the SC decoding; finally, obtaining an upper bound of the error probability of each symbol channel; and obtaining the upper bound of the error probability of each symbol channel, sequencing the error probability, and selecting K channels with the minimum upper bound of the error probability of the symbol channels to transmit information bits, wherein K is determined according to the information bits which need to be transmitted actually, namely the construction of the multi-element Polar code is completed and the multi-element Polar code is used for data transmission. The Polar code construction method provided by the embodiment of the invention can improve the Frame Error rate (FER for short) of the Polar code combined with high-order modulation (such as QAM).
Further , fig. 6 shows methods for data transmission by using multi-polarization codes according to the embodiments of the present invention, as shown in fig. 6, the methods include:
step 601: combining a plurality of channels of a basic unit of a multi-element polarization code, wherein the size of an alphabet of the plurality of channels is larger than 2;
step 602: updating the transition probabilities of the combined channels;
step 603: obtaining the upper limit of the error probability of the combined channels according to the transition probability;
step 604: and transmitting the information bits by using K channels with the minimum upper limit of the error probability in the combined plurality of channels.
It should be understood that combining the multiple channels of the basic unit of the multi-component polarization code and then updating the transition probabilities of the combined multiple channels, the above two steps can be performed recursively or repeatedly to complete the construction of the whole polarization code (or the encoder of the polarization code) according to actual needs, and the most reliable K channels are selected to transmit information bits according to the upper limit of the error probability of the multiple channels of the encoder of the constructed polarization code. Where K is any positive integer, and the most reliable K channels are the K channels with the smallest upper limit of error probability.
Optionally, the information bits are transmitted by using the K channels with the minimum upper limit of the error probability in the merged multiple channels, which specifically includes calculating the error probability of each symbol channel by using the upper limit of the error probability of the merged multiple channels, and selecting the K symbol channels with the minimum error probability (or the upper limit of the error probability) to transmit the information bits.
, combining the multiple channels of the basic unit of the multi-component polarization code includes pre-combining or greedy combining, and the specific implementation flow is the same as the method provided above, and is not described herein again.
The method for transmitting data by utilizing the multi-element polarization code comprises the steps of combining a plurality of channels of a basic unit of the multi-element polarization code, then updating the transition probability of the combined plurality of channels, obtaining the upper limit of the error probability of the combined plurality of channels according to the transition probability, transmitting information bits by utilizing K channels with the minimum upper limit of the error probability in the combined plurality of channels, controlling the channel number of the multi-element polarization code under high-order modulation by combining, thereby being capable of controlling the complexity of coding in the data transmission process, and reducing the information loss in the high-order modulation demodulation process due to the fact that the multi-element polarization code is used, is capable of controlling the capacity difference of the combined channels by utilizing the posterior probability distance or the combining distance, thereby being capable of controlling the information loss in the data transmission process.
Corresponding to the above method embodiment, the embodiment of the present invention further provides apparatuses for data transmission by using multi-polarization codes, as shown in fig. 7, including:
a combining unit 701, configured to combine multiple channels of a basic unit of a multi-component polarization code, where the size of an alphabet of the multiple channels is greater than 2;
an updating unit 702, configured to update transition probabilities of the combined multiple channels;
a processing unit 703, configured to obtain an upper limit of the error probability of the combined multiple channels according to the transition probability obtained by the updating unit 702;
a transmission unit 704, configured to transmit information bits using the K channels with the minimum upper limit of the error probability in the combined multiple channels obtained by the processing unit 703.
Further , the merging unit 701 includes a pre-merging unit or a greedy merging unit, where the specific implementation flows of pre-merging and greedy merging are the same as the methods provided above, and are not described herein again.
technical features related to the method, such as transition probability, pre-merging, greedy merging, basic unit of polarization code, error probability, etc., are similar to or correspond to technical features related to the method embodiment of the present invention, and a repeated description thereof is omitted.
The embodiment of the present invention further provides kinds of wireless communication devices, where the wireless device includes the apparatus in the above apparatus embodiments.
The embodiment of the present invention further provides apparatuses for data transmission by using multi-component polarization codes, which, as shown in fig. 8, include a processor 801, a memory 802, a transmitter 803, and a bus 804, wherein the processor 801, the memory 802, and the transmitter 803 are connected via the bus 804 for data transmission, and the memory 802 is used for storing data processed by the processor 801;
the bus 804 may be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, an Extended ISA (EISA) bus, or the like, and is not limited thereto, the bus 804 may be divided into an address bus, a data bus, a control bus, and the like, for ease of illustration, FIG. 8 illustrates only bold lines, but does not illustrate only buses or types of buses, wherein:
memory 802 may comprise high-speed RAM memory and may also comprise non-volatile memory, such as at least disk drives.
The processor 801 may be Central Processing Units (CPUs), or an Application Specific Integrated Circuit (ASIC), or or more ICs configured to implement embodiments of the present invention.
The processor 801 is configured to implement the method for data transmission by using a multi-polarization code in the foregoing embodiments by executing the program code in the memory 802, and specifically includes:
combining a plurality of channels of a basic unit of a multi-element polarization code, wherein the size of an alphabet of the plurality of channels is larger than 2; updating the transition probabilities of the combined channels; obtaining the upper limit of the error probability of the combined channels according to the transition probability;
and a transmitter 803 configured to transmit information bits using K channels with the minimum upper limit of error probability among the combined plurality of channels.
Further , the processor 801 merges multiple channels of the basic unit of the multi-component polarization code, including a pre-merge or a greedy-merge, where a specific implementation flow of the pre-merge and the greedy-merge is the same as the method provided above, and is not described here again.
technical features related to the method, such as transition probability, pre-merging, greedy merging, basic unit of polarization code, error probability, etc., are similar to or correspond to technical features related to the method embodiment of the present invention, and a repeated description thereof is omitted.
Those of ordinary skill in the art will appreciate that the various method steps and elements described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both, and that the steps and components of the embodiments have been described in the foregoing description generally in terms of the function for clarity of explanation of interchangeability of hardware and software.
It is clear to those skilled in the art that, for convenience and brevity of description, the specific working processes of the above-described systems, apparatuses and units may refer to the corresponding processes in the foregoing method embodiments, and are not described herein again.
For example, the above-described embodiments of the apparatus are merely illustrative, e.g., the division of the units into only logical functional divisions, and additional divisions may be made in practice, e.g., multiple units or components may be combined or integrated into another systems, or features may be omitted or not implemented.
The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, that is, may be located in places, or may also be distributed on multiple network units.
In addition, the functional units in the embodiments of the present invention may be integrated into processing units, or each unit may exist alone physically, or two or more units are integrated into units.
Based on the understanding, the technical solution of the present invention is essentially or partially contributing to the prior art, or all or part of the technical solution can be embodied in the form of a software product, which is stored in storage media and includes several instructions for making computer devices (which may be personal computers, servers, or network devices) execute all or part of the steps of the methods described in the embodiments of the present invention.
While the invention has been described with reference to specific embodiments, the invention is not limited thereto, and various equivalent modifications and substitutions can be easily made by those skilled in the art within the technical scope of the invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (22)

1, A method for data transmission using a multi-polarization code, comprising:
combining a plurality of channels of a basic unit of a multi-component polarization code, wherein the size of an alphabet of the plurality of channels is greater than 2;
updating the transition probabilities of the combined channels;
obtaining the upper limit of the error probability of the combined channels according to the transition probability;
and transmitting information bits by using K channels with the minimum upper limit of the error probability in the combined plurality of channels.
2. The method of claim 1,
the combining the plurality of channels of the basic unit of the multi-component polarization code comprises:
and performing pre-combination or greedy combination on a plurality of channels of the elementary units with the multi-polarization.
3. The method of claim 2,
the pre-combining of the plurality of channels of the multi-polarized elementary units comprises:
and combining the plurality of channels according to the posterior probability distance between two letters of the plurality of channels.
4. The method of claim 3, wherein the combining the plurality of channels according to a posterior probability distance between two letters of the plurality of channels comprises:
and when the posterior probability distance between the two letters is smaller than a preset confidence parameter, combining the channels corresponding to the two letters, and adding the channel transfer probabilities corresponding to the two combined letters.
5. The method according to claim 3 or 4,
the posterior probability distance is obtained according to the following method:
channels W, y of input alphabet size q and output alphabet size M1、y2For two letter indices, then y is received1、y2The probabilities of (c) are respectively:
Figure FDA0002225653750000011
Figure FDA0002225653750000012
will receive y1、y2The probabilities of (A) and (B) are respectively classified into and 1/2, the results after classification into are as follows:
Figure FDA0002225653750000013
Figure FDA0002225653750000014
when y is calculated1、y2Capacity difference at merging:
Figure FDA0002225653750000015
the capacity difference is then: 1+ sigma/q, wherein sigma is a noise variance;
then y is1、y2The posterior probability distance between them is:
APPdistance(y1,y2)＝1+σ/q。
6. the method of claim 5,
the combination of the plurality of channels is realized by the following processes:
for two letters y1、y2Merging, wherein u is 1,2, …, q, for every u:
W(y1|u)＝W(y1|u)+W(y2|u)
W(y2|u)＝W(yM|u)
wherein, after the above operation is completed for all u, the value of M is reduced by 1; and by analogy, combining any plurality of channels by combining two letter classes.
7. The method of claim 2,
the greedy merging of the plurality of channels of the multi-polarized elementary units comprises:
and combining the plurality of channels according to the combination distance between two letters of the plurality of channels.
8. The method of claim 7,
the combining the plurality of channels according to the combining distance between two letters of the plurality of channels comprises:
when the combination distance between two letters is smaller than the optimal limit, combining the pre-combined channels corresponding to the two letters, and so on until the size of the output alphabet is smaller than or equal to the preset reliability parameter, wherein the initial value of the optimal limit is 0, and then the combination distance between the two letters with the minimum combination distance of times is included.
9. The method according to claim 7 or 8,
the merging distance is obtained according to the following method:
channels W, y of input alphabet size q and output alphabet size M1、y2For two letter indices, then y is received1、y2The probabilities of (c) are respectively:
Figure FDA0002225653750000021
Figure FDA0002225653750000022
calculating an entropy difference:
Figure FDA0002225653750000023
then y is1、y2The merging distance between them is:
Figure FDA0002225653750000024
a method of data transmission using a multi-polarization code, characterized in that the method has all the features of the method of any of claims 1 to 9, and,
the addition operation under 16QAM of the multi-polarization code that can cause channel polarization is defined as follows:
wherein the content of the first and second substances,
Figure FDA0002225653750000031
the expression "3" indicates that,
Figure FDA0002225653750000032
represents-1.
Figure FDA0002225653750000033
11, an apparatus for data transmission using a multi-polarization code, comprising:
a merging unit, configured to merge multiple channels of a basic unit of a multi-component polarization code, where the size of an alphabet of the multiple channels is greater than 2;
an updating unit, configured to update transition probabilities of the combined multiple channels;
a processing unit, configured to obtain an upper limit of the error probability of the combined multiple channels according to the transition probability;
and a transmission unit, configured to transmit information bits using the K channels with the minimum upper limit of the error probability in the combined multiple channels.
12. The apparatus of claim 11,
the merging unit includes: a pre-merge unit or a greedy-merge unit;
the pre-combining unit is used for pre-combining a plurality of channels of the basic unit with multi-polarization;
the greedy merging unit is used for performing pre-greedy merging on a plurality of channels of the multi-polarization basic unit.
13. The apparatus of claim 12,
the pre-merging unit is used for: and combining the plurality of channels according to the posterior probability distance between two letters of the plurality of channels.
14. The apparatus of claim 13,
said combining the plurality of channels according to a posterior probability distance between two letters of the plurality of channels comprises:
and when the posterior probability distance between the two letters is smaller than a preset confidence parameter, combining the channels corresponding to the two letters, and adding the channel transfer probabilities corresponding to the two combined letters.
15. The apparatus of claim 13 or 14,
the posterior probability distance is obtained according to the following method:
channels W, y of input alphabet size q and output alphabet size M1、y2For two letter indices, then y is received1、y2The probabilities of (c) are respectively:
Figure FDA0002225653750000041
Figure FDA0002225653750000042
will receive y1、y2The probabilities of (A) and (B) are respectively classified into and 1/2, the results after classification into are as follows:
Figure FDA0002225653750000043
when y is calculated1、y2Capacity difference at merging:
the capacity difference is then: 1+ sigma/q, wherein sigma is a noise variance;
then y is1、y2The posterior probability distance between them is:
APPdistance(y1,y2)＝1+σ/q。
16. the apparatus of claim 15,
the combination of the plurality of channels is realized by the following processes:
for two letters y1、y2Merging, wherein u is 1,2, …, q, for every u:
W(y1|u)＝W(y1|u)+W(y2|u)
W(y2|u)＝W(yM|u)
wherein, after the above operation is completed for all u, the value of M is reduced by 1; and by analogy, combining any plurality of channels by combining two letter classes.
17. The apparatus of claim 12,
the greedy merge unit to: and combining the plurality of channels according to the combination distance between two letters of the plurality of channels.
18. The apparatus of claim 17,
the combining the plurality of channels according to the combining distance between two letters of the plurality of channels comprises:
when the combination distance between two letters is smaller than the optimal limit, combining the pre-combined channels corresponding to the two letters, and so on until the size of the output alphabet is smaller than or equal to the preset reliability parameter, wherein the initial value of the optimal limit is 0, and then the combination distance between the two letters with the minimum combination distance of times is included.
19. The apparatus of claim 17 or 18,
the merging distance is obtained according to the following method:
channels W, y of input alphabet size q and output alphabet size M1、y2For two letter indices, then y is received1、y2The probabilities of (c) are respectively:
Figure FDA0002225653750000051
Figure FDA0002225653750000052
calculating an entropy difference:
Figure FDA0002225653750000053
then y is1、y2The merging distance between them is:
Figure FDA0002225653750000054
a wireless communication device of , comprising the apparatus of any of claims 11-19, wherein is configured.
21, computer-readable storage medium, wherein said computer-readable storage medium stores a computer program, wherein said computer program, when executed by hardware, is capable of implementing the method of any of claims 1-10 .
22, , the wireless communication device comprising a processor and a memory,
the memory stores a computer program, wherein the computer program is capable of implementing the method of any of claims 1-10 when executed by the processor.
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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102122966A (en) * 2011-04-15 2011-07-13 北京邮电大学 Channel-polarization-based encoder for staggered structure duplication code, and encoding and decoding methods thereof
CN102164025A (en) * 2011-04-15 2011-08-24 北京邮电大学 Coder based on repeated coding and channel polarization and coding/decoding method thereof
CN103023618A (en) * 2013-01-11 2013-04-03 北京邮电大学 Random code length polar encoding method
CN103281166A (en) * 2013-05-15 2013-09-04 北京邮电大学 Hybrid automatic repeat request transmission method based on polarization code

Family Cites Families (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2012083086A1 (en) * 2010-12-15 2012-06-21 Analog Bits, Inc. Encoder/decoder for balanced transmission of variables over few multi-variable channels
CN103684477B (en) * 2012-09-24 2017-02-01 华为技术有限公司 Generation method and generation device for mixed polar code
US9362956B2 (en) * 2013-01-23 2016-06-07 Samsung Electronics Co., Ltd. Method and system for encoding and decoding data using concatenated polar codes

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102122966A (en) * 2011-04-15 2011-07-13 北京邮电大学 Channel-polarization-based encoder for staggered structure duplication code, and encoding and decoding methods thereof
CN102164025A (en) * 2011-04-15 2011-08-24 北京邮电大学 Coder based on repeated coding and channel polarization and coding/decoding method thereof
CN103023618A (en) * 2013-01-11 2013-04-03 北京邮电大学 Random code length polar encoding method
CN103281166A (en) * 2013-05-15 2013-09-04 北京邮电大学 Hybrid automatic repeat request transmission method based on polarization code

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