CN107769894A - The joint-detection interpretation method of the mimo system of polarization code coding - Google Patents
The joint-detection interpretation method of the mimo system of polarization code coding Download PDFInfo
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- H—ELECTRICITY
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- H04L1/0045—Arrangements at the receiver end
- H04L1/0047—Decoding adapted to other signal detection operation
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Abstract
The invention discloses a kind of joint-detection interpretation method of the mimo system of polarization code coding, comprise the following steps：(1) K best are detected；(2) polarization code coding and decoding；(3) SDD algorithms；(4) JDD algorithmic systems configure；(5) the JDD algorithms based on detection decoding combined optimization.Beneficial effects of the present invention are：MIMO technology is combined with the polarization code up to shannon capacity, improves power system capacity and data rate；With reference to the coding bound of polarization code, the extension and renewal of Invalid path are avoided, reduces overall computation complexity, while improve system entirety error performance performance；The joint-detection decoding algorithm is applied to the polarization code of any code length and parameter configuration.
Description
Technical field
The present invention relates to wireless communication technology field, especially a kind of joint-detection of the mimo system of polarization code coding is translated
Code method.
Background technology
Mobile communication experienced first generation analogue communication (1G), second generation cellular digital communicates (2G), third generation CDMA is loose
Development course with communication (3G), has had been enter into the application stage of forth generation mobile communication (4G) industrialization at present.Mobile communication
Just develop towards high-speed, high power capacity, spectral efficient and the direction of low-power consumption, constantly meet the growing data of people and
Video requirement.Predicted according to major carrier and authoritative advisory organization：Mobile broadband service flow will increase by 1000 in coming 10 years
Times.Existing 4G technologies still can not meet the needs of following in transmission rate and resource utilization etc., its wireless coverage and
Consumer's Experience also needs further to be improved.Countries in the world are while 4G industrialization work is promoted, the 5th third-generation mobile communication technology
(5G) has become the study hotspot of domestic and international wireless communication field.5G will meet the various of people's work, life and amusement
Change business demand, there is ultra high flux density, super even in central business district, residential areas of denseness, stadium and highway etc.
The scene of height connection number density and ultrahigh-mobility feature, or user provides super clear video, augmented reality and online trip
The ultimate attainment business experiences such as play.
The significant key technology of 5G mobile communication be mainly reflected in ultra high performance Radio Transmission Technology and high density without
Line network technology.Relative to traditional small-scale mimo system, extensive MIMO significantly improves spectrum efficiency, connection reliably
Property and coverage.At the same time, high-performance, efficient channel coding technology are also by as 5G important research side
To.As first channel coding that can reach Shannon capacity, polarization code is the great of information theory and wireless communication field
Break through, cause the extensive concern of academia and industrial quarters.Under the whole new set of applications scene of 5G mobile communication, polarization code by
3GPP is adopted as the up-downgoing short code scheme of 5G eMBB control channels.
In actual applications, in order to improve error performance, mimo system generally with error correction coding such as Turbo code or
LDPC is combined.In transmitting terminal, signal source and channel, the symbol being then modulated in complex value constellation point first are carried out to information bit
Number.In receiving terminal, MIMO detectors are estimated to send symbol first from the signal of reception；Then, symbol of the decoder from estimation
Middle recovery information bit.Although error performance can be effectively improved with reference to error correction coding, but extra decoding module will
The greatly overall implementation complexity of increase receiver.Generally, detect and decode and be often considered as two independent processing
Module.Output information mutual iteration between two standalone modules, so as to improve decoding performance.However, the detection decoding of iteration
System delay will be increased.The mimo system encoded for convolutional code and Turbo code, compared to traditional separation method, joint inspection
Survey interpretation method and significantly reduce implementation complexity and system delay, while improve error performance.Recently, polarization code has been
The up-downgoing short code scheme of 5G eMBB control channels is adopted as by 3GPP.Therefore, the inspection of the mimo system of polarization code coding is studied
Decoding algorithm is surveyed to be significant.
The content of the invention
The technical problems to be solved by the invention are, there is provided a kind of joint-detection of the mimo system of polarization code coding is translated
Code method, improves power system capacity and data rate, suitable for the polarization code of any code length and parameter configuration.
In order to solve the above technical problems, the present invention provides a kind of joint-detection decoding side of the mimo system of polarization code coding
Method, comprise the following steps：
(1) K-best is detected；If in equivalent real value mimo system, transmitting vector is s, channel matrix H, additive white gaussian
Noise is n, received vector y；Quadrature amplitude modulation (QAM) constellation set is Θ,The QR of channel matrix points
Solution is expressed as H=QR, wherein, Q 2Nr×2NtMatrix, R 2Nt×2NtUpper triangular matrix, in K-best detectors,
Estimate vectorIt is expressed as：
Formula (1) regards a 2N astThe tree search problem of layer, each node haveIndividual child nodes；In tree-shaped
In search procedure, part Euclidean distance is defined as path metric value；In each layer of tree, retain KpBar has minimum PED values
Path as survivor path, at i-th layer of tree, the PED of extensions path is expressed as
Its initial value PED0=0, inciRepresent the distance between two survival nodes of adjacent two layers increment；In the every of tree
One layer, retain KpBar has the path of minimum PED values as survivor path；The road with minimum PED values is taken in last layer choosing
Footpath is as outgoing route.
(2) polarization code coding and decoding；ForPolarization code, N, K,WithRespectively represent code length,
Information bit length, information bit set and freeze bit value, it is assumed that decoder input isOutput
ForGNAnd BNRepresent that generator matrix and bit inverted sequence reset the coding of permutation matrix, then polarization code respectively
It is represented by：
Wherein,RepresentKronecker product；
Similar to K-best algorithms, the SCL decodings of polarization code and the searching algorithm of breadth-first, on full binary tree by
Layer extends and selects optimal path；In SCL decodings, using following log-likelihood form as path metric value：
Wherein, max is obtained by Jacobi logarithmic approximations：
(3) SDD algorithms；The SDD methods of the mimo system of polarization code coding are by two K-best detectors separated and pole
Change code decoder cascade to realize；All path candidate of leaf node layer is combined by K-best detectors, and calculates reception
Vectorial y LLP, it is assumed that symbol skIth bit be designated asThen y LLP is calculated as follows：
Wherein,Represent set of the ith bit as b all symbols, b ∈ { 0,1 }, σ2For noise n variance, SCL is translated
LLP is carried out the SCL based on LL as input and decoded by code device, you can recovers original information bit, referred to as based on SCL decodings
SDD algorithms；
(4) JDD algorithmic systems configure；In SDD algorithms, each channel is realized and carries out individually handling the hair estimated
Directive amount, however, JDD algorithms need to combine several channels, carry out Combined Treatment；It is assumed that n channel is considered simultaneously, for
I channel, transmitting vector is si, channel matrix Hi, AWGN ni, received vector yi, channel matrix HiQR decompose and pre-
Processing is as follows：
Then the joint of the received vector of n channel represents that z is represented by：
Z=Rs+n, (8)
I.e.：
In transmitting terminal, K information bit is encoded to obtain N number of coded-bit output, for each code word, channel reality
Now count n=N/ (NtMc), the search number of plies of tree is by 2NtIncrease as 2NtN, the 1st layer of 2N for representing matrix R of search treetN rows, search
Set 2NtN-layer represents matrix R the 1st row；
(5) the JDD algorithms based on detection-decoding combined optimization；For (N, K) polarization code, based on column vector x and row vector
xTRepresentation, formula (3) is rewritten as：
Wherein,ThenOnly to include the upper triangular matrix of 0,1 element；
Collective formula (1) and (10) can obtain：
Wherein, map { * } represents mapping of the bit sequence in GF (2) to real value transmitting symbol；Representative pair
Information bit vector inverted sequence resets obtained new vector；The constraints of optimization problem isFor the GF (2) of K dimensions
Space；Due toIt is upper triangular matrix with R, therefore in detection or decoding, current symbol is only dependent upon what is previously translated
Symbol.For one use 16-QAM, channel realize number for 12 × 2MIMO systems,It is with R：
Within the system, detection and decoding can be carried out simultaneously, the connection of detection-decoding of the mimo system of polarization code coding
Combinatorial optimization problem can represent the mathematical expression of an accepted way of doing sth (11), that is, seek intermediate variable urevOptimization problem；By traditional K-best
The optimization expression (1) of algorithm, joint corresponding to JDD algorithms can be obtained and optimize expression：
Wherein, mod (x, 2) represents Modulo-two operation；The joint optimization problem of detection decoding can still regard a 2nN astLayer tree
Breadth-first search problem；When the code length N increases of polarization code, with increase, the number of plies for detecting decoding tree also increases n therewith
Add；The increase according to code length N is needed, the appropriate candidate's chained list length K for increasing search procedurep。
Breadth-first search problem is specially in JDD algorithms based on detection-decoding combined optimization：2NtThe tree-like of layer is searched
Suo Wenti, each node haveIndividual child nodes；In each layer of tree, retain KpBar has the path conduct of minimum PED values
Survivor path, therefore obtained after each layer of extensionIndividual node；In the JDD algorithms based on detection-decoding combined optimization, root
Expanding node number can be reduced according to the distribution of polarization code information bit；Each node can use Mc/ 2 bits represent, if wherein
Freeze position as m, then information bit has Mc/ 2-m, expanding node number can be fromIt is reduced toIndividual, JDD is calculated
Breadth-first search speed is obviously improved in method.
Beneficial effects of the present invention are：MIMO technology is combined with the polarization code up to shannon capacity, improved
Power system capacity and data rate；With reference to the coding bound of polarization code, the extension and renewal of Invalid path are avoided, reduces entirety
Computation complexity, while improve system entirety error performance performance；The joint-detection decoding algorithm is applied to any code length
With the polarization code of parameter configuration.
Brief description of the drawings
Fig. 1 is mimo system configuration schematic diagram in JDD algorithms of the invention.
Fig. 2 is the tree search schematic diagram optimized based on detection-decoding joint of the present invention.
Fig. 3 is performance comparison schematic diagrames of 4 × 4MIMO systems SDD with combined optimization JDD algorithms of the present invention.
SDD and JDD algorithms performance comparison are illustrated when Fig. 4 is 4 × 4MIMO system difference Path extension numbers of the present invention
Figure.
Embodiment
As shown in figure 1, a kind of joint-detection interpretation method of the mimo system of polarization code coding, comprises the following steps：
1.K-best detection algorithms
If in equivalent real value mimo system, transmitting vector be s, channel matrix H, additive white Gaussian noise n, receive to
Measure as y.Quadrature amplitude modulation (QAM) constellation set is Θ,The QR exploded representations of channel matrix are H=QR.
Wherein, Q 2Nr×2NtMatrix, R 2Nt×2NtUpper triangular matrix.In K-best detectors, estimate vectorCan table
It is shown as：
Formula (1) can regard a 2N astThe tree search problem of layer, each node haveIndividual child nodes.Setting
In type search procedure, part Euclidean distance (PED) is defined as path metric value.In each layer of tree, retain KpBar has most
The path of small PED values is as survivor path.At i-th layer of tree, the PED of extensions path is represented by
Its initial value PED0=0, inciRepresent the distance between two survival nodes of adjacent two layers increment.In the every of tree
One layer, retain KpBar has the path of minimum PED values as survivor path；The road with minimum PED values is taken in last layer choosing
Footpath is as outgoing route.
2. polarization code encodes and decoding
ForPolarization code, N, K,WithCode length, information bit length, information bit are represented respectively
Set and freeze bit value.It is assumed that decoder input isExport and beGNWith
BNRepresent that generator matrix and bit inverted sequence reset permutation matrix respectively.Then the coding of polarization code is represented by：
Wherein,RepresentKronecker product.
Similar to K-best algorithms, the SCL decodings of polarization code and the searching algorithm of breadth-first, on full binary tree by
Layer extends and selects optimal path.In SCL decodings, using following log-likelihood (LL) form as path metric value：
Wherein, max is obtained by Jacobi logarithmic approximations：
3.SDD algorithms
In MIMO detections, compared to hard decision, the error performance of soft-decision is obviously improved.Therefore, in Error Correction of Coding
(ECC) in the receiver design of system, frequently with soft technology for adjudication.The SDD methods of the mimo system of polarization code coding are by two
The K-best detectors of separation and polarization code decoder cascade are realized.K-best detectors are by all candidate road of leaf node floor
Footpath is combined, and calculates received vector y LLP.It is assumed that symbol skIth bit be designated asThen y LLP is calculated as follows：
Wherein,Represent set of the ith bit as b all symbols, b ∈ { 0,1 }, σ2For noise n variance.SCL is translated
LLP is carried out the SCL based on LL as input and decoded by code device, you can recovers original information bit, referred to as based on SCL decodings
SDD algorithms.
4.JDD algorithmic systems configure
In SDD algorithms, each channel is realized and carries out individually handling the transmitting estimated vector.However, JDD algorithms
Need to combine several channels, carry out Combined Treatment.It is assumed that n channel is considered simultaneously.For i-th of channel, transmitting vector is
si, channel matrix Hi, AWGN ni, received vector yi.Channel matrix HiQR decompose and pretreatment it is as follows：
Then the joint of the received vector of n channel represents that z is represented by：
Z=Rs+n, (8)
I.e.：
In transmitting terminal, K information bit is encoded to obtain N number of coded-bit output.It is real for each code word, channel
Now count n=N/ (NtMc), detailed system configuration is as shown in Figure 1.Therefore, the search number of plies of tree is by 2NtIncrease as 2Ntn.Need
It is noted that the 1st layer of 2N for representing matrix R of search treetN rows, search tree 2NtN-layer represents matrix R the 1st row.
5. the JDD algorithms based on detection-decoding combined optimization
For (N, K) polarization code, based on column vector x and row vector xTRepresentation, formula (3) is rewritable to be：
Wherein,ThenOnly to include the upper triangular matrix of 0,1 element.
Collective formula (1) and (10) can obtain：
Wherein, map { * } represent bit sequence in GF (2) to real value launch symbol (modulation constellation points it is in the same direction or orthogonal
Component) mapping；The new vector that representative resets to obtain to information bit vector inverted sequence；The constraint bar of optimization problem
Part isFor GF (2) space of K dimensions.Due toIt is upper triangular matrix with R, therefore in detection or decoding, when
Preceding symbol is only dependent upon the symbol previously translated.For one use 16-QAM, channel realize number for 12 × 2MIMO systems
System,It is with R：
Therefore, within the system, detection and decoding can be carried out simultaneously, the detection-translate of the mimo system of polarization code coding
The joint optimization problem of code can represent the mathematical expression of an accepted way of doing sth (11), that is, seek intermediate variable urevOptimization problem.By tradition
The optimization expression (1) of K-best algorithms, joint corresponding to JDD algorithms can be obtained and optimize expression：
Wherein, mod (x, 2) represents Modulo-two operation.Now, can still be regarded as by detecting the joint optimization problem of decoding by one
2nNtThe breadth-first search problem of layer tree.When the code length N increases of polarization code, n detects the number of plies of decoding tree with increase
Increase therewith.At this time, it may be necessary to retain enough path candidates, the influence of error propagation could be reduced, obtains desired detection
Performance.Therefore, it is necessary to according to code length N increase, the appropriate candidate's chained list length K for increasing search procedurep。
From formula (13), the tree-shaped search of the JDD algorithms optimized based on detection-decoding joint and K-best algorithms
It is similar.Only difference is that：The region of search of JDD algorithms is GF (2), it is necessary to by GF (2) domain when enumerating each symbol
Interior product accumulation computing, is then mapped to transmitting symbol space, similar to a polarization code pre-encode operation.Therefore, only
By increasing this similar pre-encode operation, you can obtain binary sequence by a tree search processBy bit
After inverted sequence is reset, you can obtainCompletely without the decoding problem for considering polarization code, greatly reduce and receive machine testing decoding
Overall complexity.
By taking 16-QAMMIMO systems as an example, the tree search optimized based on detection-decoding joint is described in detail in Fig. 2.
Wherein, path candidate chained list length Kp=4；Small circle represents bit node, and great circle represents symbol node.In each node layer
During extension, it is required for carrying out extra pretreatment operation：Modulo-two operation and bit-symbol mapping in GF (2).In each layer,
According to the information bit set of polarization codeTwo bits (two nodes in figure in elliptic curve) are enumerated, one shares 4 kinds of feelings
Condition：(freezing bit, freeze bit), (freezing bit, information bit), (information bit, freezing bit) and (information bit, letter
Cease bit), corresponding expanding node number is respectively：1,2,2 and 4.The corresponding 4 kinds of precodings behaviour of these four situations
Make, produce different extension child node numbers, respectively with four kinds of grid, right inclined stripe, left inclined stripe and round dot backgrounds in figure
Distinguish and represent., it is necessary to which the child node number of extension is from 4K when two bits of current layer are (freezing bit, freeze bit)pSubtract
It is K lessp；, it is necessary to extend when two bits of current layer are (freezing bit, information bit) or (information bit, freezing bit)
Child node number from 4KpIt is reduced to 2Kp.In these three cases, the calculating of path metric value and sequence complexity are shown
Writing reduces.Therefore, JDD algorithms based on detection-decoding combined optimization are according to the coding bound of polarization codeAvoid
The extension of Invalid path, greatly reduce the complexity of path metric value renewal and sequence.
If path candidate list and corresponding PED lists are respectively P=[0,0 ..., 0], PED=[0,0 ..., 0]
The operating procedure of the present invention is as follows：
1) initialization path list and its PED lists：P0=[0,0 ..., 0], PED0=[0,0 ..., 0].
2) active path extends：At i-th layer, to last layer path listIn
Each paths, the coding bound based on polarization codeM is extended respectivelyc/ 2 bits.Then, carry out Modulo-two operation and
Bit-symbol map operation, the path list updatedAs active path.According to formula
(2) the measurement value list updatedWherein m possibility value is
3) path candidate list is selected：To the measurement value list PED of renewalnewAscending order arrangement is carried out, obtains PEDsort.Protect
Stay PEDsortIn the corresponding K paths of preceding K PED values as path candidate list Pi。
4) detection terminates to judge：If i=2NtN, export the path candidate list P of leaf layer2Ntn, it isBy bit
Inverted sequence resets to obtainOtherwise, return to step 3).
In order to verify the applicability of the JDD algorithms based on detection-decoding combined optimization, for 16-QAM modulating systems, adopt
Configured with following polarization code：N=256, K=128.Now the number of channel is n=16；K-best is detected and the candidate chains of SCL decodings
Table length is set to Kp=64 and L=4.FER (FER) performance of algorithms of different is as shown in Figure 3.From the figure 3, it may be seen that it is based on
The FER performance of the JDD algorithms of combined optimization is always better than the SDD algorithms based on SCL soft decodings.FER=10-4When, it is based on
The JDD algorithms SNR of combined optimization improves 2.5dB or so.
Fig. 4 compares different KpWhen FER performances, wherein N=128, K=64.For Kp=8, JDD are in low SNR regions ratio
SDD performances are good, but steeper in high SNR regions, SDD curve descending slope.Main reasons is that SDD is translated by soft-decision
Code, and JDD can be regarded as a kind of hard decision.Due to being decomposed in detection using RVD, such as shown in (12), such as first
Individual symbol, odd-numbered line and even number line in R are independent, therefore are translating s2Nt-1With s2NtIt is independent.So if it is desired to lifting
Performance is, it is necessary to expand Kp.As seen from Figure 4, FER performances are with KpIncrease have great lifting.Work as FER=10-4When,
JDD(Kp=64) performance is than JDD (Kp=16) 6dB is improved.And KpPerformance boost of the increase for SDD it is little because
SDD is soft-decision.
The JDD algorithms based on detection-decoding combined optimization that the SSD algorithms and this chapter of detection-decoding cascade propose
Computation complexity essentially consists in Path extension and selection and the additional behaviour related to polarization code decoding in tree-shaped search procedure
Make.During tree search, it would be desirable to carry out the number of path of PED renewals and sequence as Path extension and the complexity chosen.
For the JDD algorithms based on detection-decoding combined optimization, the modular two multiplication before every layer of symbol point spread is subject to and bit-symbol reflects
The added complexity related as polarization code decoding of complexity caused by penetrating.
The computation complexity such as table 1 for the JDD algorithms based on detection-decoding combined optimization that SDD algorithms and this chapter are proposed
It is shown.Compared to cascade SDD algorithms, the Path extension and selection complexity of the JDD algorithm tree search of combined optimization reduce K/N
× 100%.SDD algorithms are cascaded to decode, it is necessary to which substantial amounts of arithmetical operation, its corresponding computation complexity are using SCLIt is introduced into larger decoding delay simultaneously.However, the JDD algorithms based on combined optimization in pre-encode operation only
Need perform complexity beBinary arithmetic operation.Its binary system arithmetic section can by efficient hardware structure,
Reach higher system throughput.Therefore, compared to cascade SDD algorithms, this chapter propose based on detection-decoding combined optimization
JDD algorithms greatly reduce the overall computation complexity of detection-decoder, and higher system throughput can be achieved.
Table 1：SDD is cascaded compared with the complexity of the JDD algorithms of detection-decoding combined optimization
* the computation complexity in GF (2) domain is wanted to compare with existing polarization code decoder, and main contributions of the invention are：From
The angle of combined optimization is set out, and based on mathematical derivation, proposes to be applied to the JDD algorithms of various parameters configuration polarization code.With reference to pole
Change the coding bound of code, by pre-encode operation, only extremely efficient path, reduce route searching model in traditional K-best detections
Enclose.So as to reduce the complexity of Path extension and renewal, while improve the error performance of system.Calculated compared to cascade SDD
Method, the overall complexity of combined optimization JDD algorithms reduce more than K/N × 100%.Therefore, the present invention is applied to low complex degree
Designed with the mimo system receiver of high-throughput.
The present invention is in joint-detection decoding (JDD) algorithm of proposition, it is necessary to consider that several channels are realized simultaneously.For
The mimo system of polarization code coding, it is assumed that the path that can produce effective polarization code is active path.Examined in traditional K-best
In survey, each layer is required for extendingPaths.With reference to polarization code coding bound, these paths are simultaneously not all effective.
In JDD algorithms, optimized based on detection-decoding joint, by using pre-encode operation, the road of each floor only extremely efficient
Footpath, so as to reduce Path extension and update complexity.Original information bits can be recovered by a tree search process.
Although the present invention is illustrated and described with regard to preferred embodiment, it is understood by those skilled in the art that
Without departing from scope defined by the claims of the present invention, variations and modifications can be carried out to the present invention.
Claims (7)
1. a kind of joint-detection interpretation method of the mimo system of polarization code coding, it is characterised in that comprise the following steps：
(1) K-best is detected；
(2) polarization code coding and decoding；
(3) SDD algorithms；
(4) JDD algorithmic systems configure；
(5) the JDD algorithms based on detection-decoding combined optimization.
2. the joint-detection interpretation method of the mimo system of polarization code coding as claimed in claim 1, it is characterised in that step
(1) in, K-best detections are specially：If in equivalent real value mimo system, transmitting vector is s, channel matrix H, additive Gaussian
White noise is n, received vector y；Quadrature amplitude modulation qam constellation collection is combined into Θ,The QR of channel matrix points
Solution is expressed as H=QR, wherein, Q 2Nr×2NtMatrix, R 2Nt×2NtUpper triangular matrix, in K-best detectors,
Estimate vectorIt is expressed as：
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Formula (1) regards a 2N astThe tree search problem of layer, each node haveIndividual child nodes；Searched in tree-shaped
Cheng Zhong, part Euclidean distance is defined as path metric value；In each layer of tree, retain KpBar has the path of minimum PED values
As survivor path, at i-th layer of tree, the PED of extensions path is expressed as
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<mi>i</mi>
</msub>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>l</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>N</mi>
<mi>t</mi>
</msub>
<mo>-</mo>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</munderover>
<mo>|</mo>
<mo>|</mo>
<msub>
<mi>z</mi>
<mi>l</mi>
</msub>
<mo>-</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mi>l</mi>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>N</mi>
<mi>t</mi>
</msub>
</mrow>
</munderover>
<msub>
<mi>r</mi>
<mrow>
<mi>l</mi>
<mi>j</mi>
</mrow>
</msub>
<msub>
<mi>s</mi>
<mi>j</mi>
</msub>
<mo>|</mo>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>l</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>N</mi>
<mi>t</mi>
</msub>
<mo>-</mo>
<mi>i</mi>
</mrow>
</munderover>
<mo>|</mo>
<mo>|</mo>
<msub>
<mi>z</mi>
<mi>l</mi>
</msub>
<mo>-</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mi>l</mi>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>N</mi>
<mi>t</mi>
</msub>
</mrow>
</munderover>
<msub>
<mi>r</mi>
<mrow>
<mi>l</mi>
<mi>j</mi>
</mrow>
</msub>
<msub>
<mi>s</mi>
<mi>j</mi>
</msub>
<mo>|</mo>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
<mo>+</mo>
<mo>|</mo>
<mo>|</mo>
<msub>
<mi>z</mi>
<mrow>
<mn>2</mn>
<msub>
<mi>N</mi>
<mi>t</mi>
</msub>
<mo>-</mo>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>2</mn>
<msub>
<mi>N</mi>
<mi>t</mi>
</msub>
<mo>-</mo>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>N</mi>
<mi>t</mi>
</msub>
</mrow>
</munderover>
<msub>
<mi>r</mi>
<mrow>
<mn>2</mn>
<msub>
<mi>N</mi>
<mi>t</mi>
</msub>
<mo>+</mo>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
<mi>j</mi>
</mrow>
</msub>
<msub>
<mi>x</mi>
<mi>s</mi>
</msub>
<mo>|</mo>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>=</mo>
<msub>
<mi>PED</mi>
<mrow>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>inc</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</mrow>
Its initial value PED0=0, inciRepresent the distance between two survival nodes of adjacent two layers increment；In each layer of tree,
Retain KpBar has the path of minimum PED values as survivor path；The path conduct with minimum PED values is taken in last layer choosing
Outgoing route.
3. the joint-detection interpretation method of the mimo system of polarization code coding as claimed in claim 1, it is characterised in that step
(2) in, polarization code coding and decoding are specially：ForPolarization code, N, K,WithRespectively represent code length,
Information bit length, information bit set and freeze bit value, it is assumed that decoder input isOutput
ForGNAnd BNRepresent that generator matrix and bit inverted sequence reset the coding of permutation matrix, then polarization code respectively
It is represented by：
<mrow>
<msubsup>
<mi>x</mi>
<mn>1</mn>
<mi>N</mi>
</msubsup>
<mo>=</mo>
<msubsup>
<mi>u</mi>
<mn>1</mn>
<mi>N</mi>
</msubsup>
<msub>
<mi>G</mi>
<mi>N</mi>
</msub>
<mo>=</mo>
<msubsup>
<mi>u</mi>
<mn>1</mn>
<mi>N</mi>
</msubsup>
<msup>
<mi>F</mi>
<mrow>
<mo>&CircleTimes;</mo>
<msub>
<mi>n</mi>
<mi>s</mi>
</msub>
</mrow>
</msup>
<msub>
<mi>B</mi>
<mi>N</mi>
</msub>
<mo>,</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein,RepresentKronecker product；
Similar to K-best algorithms, the SCL decodings of polarization code and the searching algorithm of breadth-first, successively expand on full binary tree
Open up and select optimal path；In SCL decodings, using following log-likelihood form as path metric value：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>L</mi>
<mi>N</mi>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>y</mi>
<mn>1</mn>
<mi>N</mi>
</msubsup>
<mo>,</mo>
<msubsup>
<mover>
<mi>u</mi>
<mo>^</mo>
</mover>
<mn>1</mn>
<mrow>
<mn>2</mn>
<mi>i</mi>
<mo>-</mo>
<mn>2</mn>
</mrow>
</msubsup>
<mo>|</mo>
<msub>
<mi>u</mi>
<mrow>
<mn>2</mn>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msup>
<mi>max</mi>
<mo>*</mo>
</msup>
<mo>{</mo>
<msubsup>
<mi>L</mi>
<mrow>
<mi>N</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>y</mi>
<mn>1</mn>
<mrow>
<mi>N</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>u</mi>
<mn>1</mn>
<mrow>
<mi>N</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msubsup>
<mo>,</mo>
<msubsup>
<mover>
<mi>u</mi>
<mo>^</mo>
</mover>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mi>o</mi>
</mrow>
<mrow>
<mn>2</mn>
<mi>i</mi>
<mo>-</mo>
<mn>2</mn>
</mrow>
</msubsup>
<mo>&CirclePlus;</mo>
<msubsup>
<mover>
<mi>u</mi>
<mo>^</mo>
</mover>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mi>e</mi>
</mrow>
<mrow>
<mn>2</mn>
<mi>i</mi>
<mo>-</mo>
<mn>2</mn>
</mrow>
</msubsup>
<mo>|</mo>
<msub>
<mi>u</mi>
<mrow>
<mn>2</mn>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msubsup>
<mi>L</mi>
<mrow>
<mi>N</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>y</mi>
<mrow>
<mi>N</mi>
<mo>/</mo>
<mn>2</mn>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</msubsup>
<mo>,</mo>
<msubsup>
<mover>
<mi>u</mi>
<mo>^</mo>
</mover>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mi>e</mi>
</mrow>
<mrow>
<mn>2</mn>
<mi>i</mi>
<mo>-</mo>
<mn>2</mn>
</mrow>
</msubsup>
<mo>|</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
<mo>,</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>L</mi>
<mrow>
<mi>N</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>y</mi>
<mn>1</mn>
<mrow>
<mi>N</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>u</mi>
<mn>1</mn>
<mrow>
<mi>N</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msubsup>
<mo>,</mo>
<msubsup>
<mover>
<mi>u</mi>
<mo>^</mo>
</mover>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mi>o</mi>
</mrow>
<mrow>
<mn>2</mn>
<mi>i</mi>
<mo>-</mo>
<mn>2</mn>
</mrow>
</msubsup>
<mo>&CirclePlus;</mo>
<msubsup>
<mover>
<mi>u</mi>
<mo>^</mo>
</mover>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mi>e</mi>
</mrow>
<mrow>
<mn>2</mn>
<mi>i</mi>
<mo>-</mo>
<mn>2</mn>
</mrow>
</msubsup>
<mo>|</mo>
<msub>
<mover>
<mi>u</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mn>2</mn>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msubsup>
<mi>L</mi>
<mrow>
<mi>N</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>y</mi>
<mrow>
<mi>N</mi>
<mo>/</mo>
<mn>2</mn>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</msubsup>
<mo>,</mo>
<msubsup>
<mover>
<mi>u</mi>
<mo>^</mo>
</mover>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mi>e</mi>
</mrow>
<mrow>
<mn>2</mn>
<mi>i</mi>
<mo>-</mo>
<mn>2</mn>
</mrow>
</msubsup>
<mo>|</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>}</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>L</mi>
<mi>N</mi>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mi>i</mi>
<mo>)</mo>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>y</mi>
<mn>1</mn>
<mi>N</mi>
</msubsup>
<mo>,</mo>
<msubsup>
<mover>
<mi>u</mi>
<mo>^</mo>
</mover>
<mn>1</mn>
<mrow>
<mn>2</mn>
<mi>i</mi>
<mo>-</mo>
<mn>2</mn>
</mrow>
</msubsup>
<mo>|</mo>
<msub>
<mi>u</mi>
<mrow>
<mn>2</mn>
<mi>i</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msubsup>
<mi>L</mi>
<mrow>
<mi>N</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>y</mi>
<mn>1</mn>
<mrow>
<mi>N</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>u</mi>
<mn>1</mn>
<mrow>
<mi>N</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msubsup>
<mo>,</mo>
<msubsup>
<mover>
<mi>u</mi>
<mo>^</mo>
</mover>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mi>o</mi>
</mrow>
<mrow>
<mn>2</mn>
<mi>i</mi>
<mo>-</mo>
<mn>2</mn>
</mrow>
</msubsup>
<mo>&CirclePlus;</mo>
<msubsup>
<mover>
<mi>u</mi>
<mo>^</mo>
</mover>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mi>e</mi>
</mrow>
<mrow>
<mn>2</mn>
<mi>i</mi>
<mo>-</mo>
<mn>2</mn>
</mrow>
</msubsup>
<mo>|</mo>
<msub>
<mi>u</mi>
<mrow>
<mn>2</mn>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>&CirclePlus;</mo>
<msub>
<mi>u</mi>
<mrow>
<mn>2</mn>
<mi>i</mi>
</mrow>
</msub>
<mo>+</mo>
<msubsup>
<mi>L</mi>
<mrow>
<mi>N</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
</msubsup>
<mo>(</mo>
<mrow>
<msubsup>
<mi>y</mi>
<mrow>
<mi>N</mi>
<mo>/</mo>
<mn>2</mn>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</msubsup>
<mo>,</mo>
<msubsup>
<mover>
<mi>u</mi>
<mo>^</mo>
</mover>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mi>e</mi>
</mrow>
<mrow>
<mn>2</mn>
<mi>i</mi>
<mo>-</mo>
<mn>2</mn>
</mrow>
</msubsup>
<mo>|</mo>
<msub>
<mi>u</mi>
<mrow>
<mn>2</mn>
<mi>i</mi>
</mrow>
</msub>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, max is obtained by Jacobi logarithmic approximations：
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mn>1</mn>
</msub>
<mo>,</mo>
<msub>
<mi>x</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>&ap;</mo>
<mi>l</mi>
<mi>n</mi>
<mrow>
<mo>(</mo>
<msup>
<mi>e</mi>
<msub>
<mi>x</mi>
<mn>1</mn>
</msub>
</msup>
<mo>+</mo>
<msup>
<mi>e</mi>
<msub>
<mi>x</mi>
<mn>2</mn>
</msub>
</msup>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
<mo>.</mo>
</mrow>
4. the joint-detection interpretation method of the mimo system of polarization code coding as claimed in claim 1, it is characterised in that step
(3) in, SDD algorithms are specially：The SDD methods of the mimo system of polarization code coding are by two K-best detectors separated and pole
Change code decoder cascade to realize；All path candidate of leaf node layer is combined by K-best detectors, and calculates reception
Vectorial y LLP, it is assumed that symbol skIth bit be designated asThen y LLP is calculated as follows：
Wherein,Represent set of the ith bit as b all symbols, b ∈ { 0,1 }, σ2For noise n variance, SCL decoders
LLP is carried out into the SCL based on LL as input to decode, you can recover original information bit, the referred to as SDD based on SCL decodings
Algorithm.
5. the joint-detection interpretation method of the mimo system of polarization code coding as claimed in claim 1, it is characterised in that step
(4) in, the configuration of JDD algorithmic systems is specially：In SDD algorithms, each channel is realized and carries out what individually processing was estimated
Transmitting vector, however, JDD algorithms need to combine several channels, carry out Combined Treatment；It is assumed that n channel is considered simultaneously, for
I-th of channel, transmitting vector is si, channel matrix Hi, AWGN ni, received vector yi, channel matrix HiQR decompose and
Pretreatment is as follows：
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>H</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<msub>
<mi>Q</mi>
<mi>i</mi>
</msub>
<msub>
<mi>R</mi>
<mi>i</mi>
</msub>
<mo>,</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<msubsup>
<mi>Q</mi>
<mi>i</mi>
<mi>H</mi>
</msubsup>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<mo>.</mo>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>7</mn>
<mo>)</mo>
</mrow>
</mrow>
Then the joint of the received vector of n channel represents that z is represented by：
Z=Rs+n, (8)
I.e.：
In transmitting terminal, K information bit is encoded to obtain N number of coded-bit output, and for each code word, channel realizes number
N=N/ (NtMc), the search number of plies of tree is by 2NtIncrease as 2NtN, the 1st layer of 2N for representing matrix R of search treetN rows, search tree
2NtN-layer represents matrix R the 1st row.
6. the joint-detection interpretation method of the mimo system of polarization code coding as claimed in claim 1, it is characterised in that step
(5) in, the JDD algorithms based on detection-decoding combined optimization are specially：For (N, K) polarization code, based on column vector x and row to
Measure xTRepresentation, formula (3) is rewritten as：
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<msup>
<mi>x</mi>
<mi>T</mi>
</msup>
<mo>=</mo>
<msup>
<mi>u</mi>
<mi>T</mi>
</msup>
<msub>
<mi>B</mi>
<mi>N</mi>
</msub>
<msup>
<mi>F</mi>
<mrow>
<mo>&CircleTimes;</mo>
<mi>n</mi>
</mrow>
</msup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>&DoubleRightArrow;</mo>
<mi>x</mi>
<mo>=</mo>
<msup>
<mrow>
<mo>(</mo>
<msup>
<mi>F</mi>
<mrow>
<mo>&CircleTimes;</mo>
<mi>n</mi>
</mrow>
</msup>
<mo>)</mo>
</mrow>
<mi>T</mi>
</msup>
<msub>
<mi>B</mi>
<mi>N</mi>
</msub>
<mi>u</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>=</mo>
<msubsup>
<mi>F</mi>
<mi>n</mi>
<mi>T</mi>
</msubsup>
<msubsup>
<mi>B</mi>
<mi>N</mi>
<mi>T</mi>
</msubsup>
<mi>u</mi>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein,ThenOnly to include the upper triangular matrix of 0,1 element；
Collective formula (1) and (10) can obtain：
Wherein, map { * } represents mapping of the bit sequence in GF (2) to real value transmitting symbol；Represent to information ratio
Special vectorial inverted sequence resets obtained new vector；The constraints of optimization problem is For GF (2) space of K dimensions；By
InIt is upper triangular matrix with R, therefore in detection or decoding, current symbol is only dependent upon the symbol previously translated.It is right
Used in one 16-QAM, channel realize number for 12 × 2MIMO systems,It is with R：
<mrow>
<mi>R</mi>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mi>r</mi>
<mn>22</mn>
</msub>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<msub>
<mi>r</mi>
<mn>24</mn>
</msub>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>r</mi>
<mn>23</mn>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<msub>
<mi>r</mi>
<mn>22</mn>
</msub>
</mtd>
<mtd>
<msub>
<mi>r</mi>
<mn>23</mn>
</msub>
</mtd>
<mtd>
<msub>
<mi>r</mi>
<mn>24</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<msub>
<mi>r</mi>
<mn>44</mn>
</msub>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<msub>
<mi>r</mi>
<mn>44</mn>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>,</mo>
<msubsup>
<mi>F</mi>
<mi>n</mi>
<mi>T</mi>
</msubsup>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>.</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
</mrow>
Within the system, detection and decoding can be carried out simultaneously, and the joint of detection-decoding of the mimo system of polarization code coding is most
Optimization problem can represent the mathematical expression of an accepted way of doing sth (11), that is, seek intermediate variable urevOptimization problem；By traditional K-best algorithms
Optimization expression (1), joint corresponding to JDD algorithms can be obtained optimize and represent：
Wherein, mod (x, 2) represents Modulo-two operation；The joint optimization problem of detection decoding can still regard a 2nN astThe width of layer tree
Spend first search problem；When the code length N increases of polarization code, with increase, the number of plies for detecting decoding tree is consequently increased n；Need
Will be according to code length N increase, the appropriate candidate's chained list length K for increasing search procedurep。
7. the joint-detection interpretation method of the mimo system of polarization code coding as claimed in claim 1, it is characterised in that be based on
Breadth-first search problem is specially in the JDD algorithms of detection-decoding combined optimization：2NtThe tree search problem of layer, each
Node hasIndividual child nodes；In each layer of tree, retain KpBar has the path of minimum PED values as survivor path, therefore often
Obtained after one layer of extensionIndividual node；In the JDD algorithms based on detection-decoding combined optimization, according to polarization code information
The distribution of position can reduce expanding node number；Each node can use Mc/ 2 bits represent, if wherein freezing position as m,
Then information bit has Mc/ 2-m, expanding node number can be fromIt is reduced toIt is individual, breadth-first in JDD algorithms
Search speed is obviously improved.
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| CN108390677A (en) * | 2018-03-20 | 2018-08-10 | 山东大学 | A kind of coding and decoding method of polarization code optimization |
| CN109194338A (en) * | 2018-11-07 | 2019-01-11 | 桂林电子科技大学 | A kind of polarization code coding method of the more bit process of mixed node |
| CN109347600A (en) * | 2018-09-26 | 2019-02-15 | 河南科技大学 | A kind of polarization code coding method |
| CN112425078A (en) * | 2019-06-21 | 2021-02-26 | 华为技术有限公司 | Polar code decoding method, device, chip, storage medium and program product |
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN108390677A (en) * | 2018-03-20 | 2018-08-10 | 山东大学 | A kind of coding and decoding method of polarization code optimization |
| CN109347600A (en) * | 2018-09-26 | 2019-02-15 | 河南科技大学 | A kind of polarization code coding method |
| CN109347600B (en) * | 2018-09-26 | 2021-01-05 | 河南科技大学 | Polar code decoding method |
| CN109194338A (en) * | 2018-11-07 | 2019-01-11 | 桂林电子科技大学 | A kind of polarization code coding method of the more bit process of mixed node |
| CN112425078A (en) * | 2019-06-21 | 2021-02-26 | 华为技术有限公司 | Polar code decoding method, device, chip, storage medium and program product |
| CN112425078B (en) * | 2019-06-21 | 2024-04-09 | 华为技术有限公司 | Polarization code decoding method, device, chip, storage medium and program product |
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