CN110380815A - A kind of code construction method of polarization code under non degenerate compound channel - Google Patents
A kind of code construction method of polarization code under non degenerate compound channel Download PDFInfo
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- CN110380815A CN110380815A CN201910452395.1A CN201910452395A CN110380815A CN 110380815 A CN110380815 A CN 110380815A CN 201910452395 A CN201910452395 A CN 201910452395A CN 110380815 A CN110380815 A CN 110380815A
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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
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L1/00—Arrangements for detecting or preventing errors in the information received
- H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
- H04L1/0045—Arrangements at the receiver end
- H04L1/0047—Decoding adapted to other signal detection operation
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L1/00—Arrangements for detecting or preventing errors in the information received
- H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
- H04L1/0056—Systems characterized by the type of code used
- H04L1/0057—Block codes
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L1/00—Arrangements for detecting or preventing errors in the information received
- H04L1/12—Arrangements for detecting or preventing errors in the information received by using return channel
- H04L1/16—Arrangements for detecting or preventing errors in the information received by using return channel in which the return channel carries supervisory signals, e.g. repetition request signals
- H04L1/18—Automatic repetition systems, e.g. Van Duuren systems
- H04L1/1812—Hybrid protocols; Hybrid automatic repeat request [HARQ]
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L1/00—Arrangements for detecting or preventing errors in the information received
- H04L1/12—Arrangements for detecting or preventing errors in the information received by using return channel
- H04L1/16—Arrangements for detecting or preventing errors in the information received by using return channel in which the return channel carries supervisory signals, e.g. repetition request signals
- H04L1/18—Automatic repetition systems, e.g. Van Duuren systems
- H04L1/1829—Arrangements specially adapted for the receiver end
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Abstract
The present invention relates to a kind of code construction methods of polarization code under non degenerate compound channel.Existing method no longer sets up non degenerate compound channel, the nesting property of polarization code, can not freeze re-transmission policy using increment and carry out the reachable information transmission of channel capacity.The method of the present invention determines the form of aggregate channel and polarisation channel first, determines recurrence Construction according to transmission code rate, then determine the code construction of generic polarization code, as transmission code rate r > 1/2, change the channel for participating in recursive transformation every time, and introduce additional channel displacement, in all RnPlacement information bit in polarisation channel is placed on residual polarization channel and freezes bit, obtains sending code word.The method of the present invention determines the code construction of generic polarization code according to transmission code rate, ensure that nesting property of the generic polarization code under non degenerate channel.The method of the present invention combination increment freezes re-transmission policy, and the transmission under non degenerate compound channel can be made theoretically to reach channel capacity.
Description
Technical field
The invention belongs to fields of communication technology, and the code construction method specifically in channel coding is related to a kind of non degenerate
The code construction method of polarization code under compound channel.
Background technique
Polarization code is the reachable channel coding method of a kind of channel capacity.In upcoming 5th third-generation mobile communication,
Polarization code is selected as enhancing field mobile broadband (Enhanced Mobile BroadBand, eMBB) by international wireless standard mechanism
The encoding scheme of uplink downlink control channel under scape.The deterministic code construction of polarization code, therefore deposited under time varying channel
Bring error-correcting performance degenerate problem is mismatched in channel status and code construction.In order to solve this problem, it is intended that be based on
The communication system of polarization code can be adaptively adjusted code construction according to actual channel state, and hybrid automatic repeat-request
A kind of common technology of (Hybrid Automatic Repeat reQuest, HARQ) as link circuit self-adapting, agrees with ours
Demand.
For non degenerate compound channel, the nesting property of polarization code is no longer set up, and can not be freezed using increment
(Incremental Freezing, IF) HARQ carries out the reachable information transmission of channel capacity.Pass through the volume to generic polarization code
Code construction adjusts, and changes the channel for participating in recursive transformation every time, and introduces additional channel displacement, can make generic polarization
Code has nesting property under non degenerate channel.In conjunction with IF HARQ strategy, the transmission under non degenerate compound channel theoretically can
Enough reach channel capacity.
Summary of the invention
In view of the deficiencies of the prior art, it is an object of the present invention to provide a kind of codings of polarization code under non degenerate compound channel
Building method.The method of the present invention has nesting property under non degenerate channel, so as to combine IF HARQ strategy, non degenerate
Transmission under compound channel can theoretically reach channel capacity.
Specific steps of the method for the invention are:
Step (1) determines the form of aggregate channel and polarisation channel:
The given memoryless symmetric channel C:{ 0,1 of two binary } → Y and V:{ 0,1 } → Z, Y and Z be respectively channel C and V
Output collection；It is as follows to define aggregate channel (C, V):
Wherein,That is u0And u1, it is the input of aggregate channel (C, V), x0And y0Respectively channel C's outputs and inputs, x1
And z1Respectively channel V's outputs and inputs,For polarization code core generator matrix, andIndicate letter
The input of road C and channel V.According to chain rule, the mutual information of aggregate channel (C, V) is split, polarisation channel is obtained:
WhereinIndicate xor operation.
Step (2) determines recurrence Construction according to transmission code rate r=g/ (g+b), to g+b in each layer of recursive structure
Independent channel executes combination and splits, and obtains the high polarisation channel of g reliability, the low polarisation channel of b reliability:
It enablesIndicate the low polarisation channel of the reliability that n-th layer recursive transformation obtains, 1≤i≤b；
It enablesIndicate the high polarisation channel of the reliability that n-th layer recursive transformation obtains, 1≤j≤g；
Indicate bottom transmission channel；
Due to code rate difference, recursive transformation structure is different, carries out different disposal in two kinds of situation:
(i) g≤b, the i.e. situation of code rate r≤1/2:
Define the intermediate polarisation channel in recursive transformation structure:
The index of t expression intermediate channels；
As g=1, haveWith
As g > 1, intermediate polarisation channel is defined:
The index of s expression intermediate channels；
Then haveWith
(ii) g > b, i.e. 1/2 situation of code rate r >:
Define the intermediate polarisation channel in recursive transformation structure:
As b=1, haveWith
As b > 1, intermediate polarisation channel is defined:
Then have
Step (3) determines the code construction of generic polarization code, enables WnAfter indicating n-th layer channel conversion, all polarization
The aggregate channel that channel is constituted:
In the 1st layer of channel conversion structure, a independent bottom transmission channel W of K (b+g) points are K group, the g+ in each group
B channel executes channel combination according to the recursive structure in step (2) and splits, and obtains the independent polarisation channel of K groupCollectively form W1；
In the 2nd layer of channel conversion structure, in order to guarantee that serially offsetting decoding (Successive Cancellation, SC) calculates
The feasibility of method, using chain structure, i.e. (i, i+1 ..., i+b+g-1) groupIn
It selects channel to execute channel combination and split according to the recursive structure of step (2), obtains the independent polarisation channel of K-b-g+1 groupCollectively form W2；
With W2Recurrence, g+b independent channel W are participated in as primary channel mapped structuren-1Middle selectionIt executes channel combination and splits, generate the independent polarisation channel of K-b-g+1 group
Step (4) is in order to guarantee nesting property of the generic polarization code under non degenerate channel, as transmission code rate r > 1/2
When, change the channel for participating in recursive transformation every time, and introduce additional channel displacement.In n-th layer channel recursive transformation structure,
To participate in polarized channel change isAnd pass through permutation matrixChange its input sequence, wherein ItFor the unit matrix of t × t, finally executes channel combination and split.
After step (5) recurrence, in all RnPlacement information bit in polarisation channel is put on residual polarization channel
It sets and freezes bit, obtain sending code word.Information bit channel RnThe position of appearance be it is fixed, it is unrelated with bottom transmission channel,
Therefore have the characteristics of " general ", while ensure that the nesting property of polarization code in step (4).
The nesting property of polarization code is only set up in degenerate channel, is closed without the subset between information bit channel set
System can not carry out the reachable information transmission of channel capacity using IF HARQ strategy under non degenerate compound channel.There is presently no
Transmission strategy based on polarization code under a kind of degeneration compound channel, which proposes a kind of settling mode, so that non-move back
The transmission changed under compound channel can theoretically reach channel capacity.Generic polarization code uses a kind of different from conventional polar
The recurrence code construction of code, the index position of information bit channel be it is fixed, it is unrelated with bottom transmission channel, therefore have
The characteristics of " general ", however it does not have nesting property still under non degenerate channel.The method of the present invention is started with from generic polarization code,
The code construction of generic polarization code is adjusted, changes the channel for participating in recursive transformation every time, and introduce additional channel and set
It changes, generic polarization code is made to have nesting property under non degenerate channel, so as to utilize IF HARQ scheme, so that non degenerate
Transmission under compound channel can theoretically reach channel capacity.
Detailed description of the invention
Fig. 1 is the generic polarization code recurrence Construction of code rate r=1/4；
Fig. 2 is the generic polarization code recurrence Construction of code rate r=3/4；
Fig. 3 is the 1st, 2 layer of generic polarization code of the channel conversion structure of code rate r=1/4, K=4；
Fig. 4 is the channel conversion structure of the generic polarization code kth layer of code rate r=1/4；
Fig. 5 is the 1st, 2 layer of generic polarization code of the channel conversion structure of code rate r=3/4, K=4；
Fig. 6 is the channel conversion structure of the generic polarization code kth layer of code rate r=3/4.
Specific embodiment
A specific embodiment of the invention is described with reference to the drawings.
Step (1) determines recurrence Construction according to transmission code rate r=g/ (g+b), to g+b in each layer of recursive structure
Independent channel executes combination and splits, and obtains the high polarisation channel of g reliability, the low polarisation channel of b reliability.For code
Rate r=1/4, the polarized recursive structure of available each layer of upper signal channel have if being currently at kth time recurrence:
Its generic polarization code recurrence Construction is as shown in Figure 1.
For code rate r=3/4, the polarized recursive structure of available each layer of upper signal channel,
Its generic polarization code recurrence Construction is as shown in Figure 2.
Step (2) determines the code construction of generic polarization code, enables K=4.For code rate r=1/4, become in the 1st layer of channel
It changes in structure, 16 independent transmission channel W points are that each channel executes combination according to recursive structure and splits in 4 groups, each group, life
At 4 groups of polarisation channelsForm W1；In the 2nd layer of channel conversion structure, using chain structure, i.e., i-th,
I+1, i+2, i+3 groupIt is middle to select channel to execute combination and split according to recursive structure, form W2.Then
With W2Recurrence is participated in as primary channel mapped structure.Its 1st, 2 layer channel conversion structure as shown in figure 3, kth layer channel
Mapped structure is as shown in Figure 4.
It for code rate r=3/4, needs to change the channel for participating in recursive transformation every time, and introduces additional channel displacement.?
In kth layer channel recursive transformation structure, will participate in polarized channel change isPass through displacement later
MatrixChange its input sequence, finally execute channel combination and splits.Its 1st, 2 layer channel conversion structure
As shown in figure 5, the channel conversion structure of kth layer is as shown in Figure 6.
Compare Fig. 3 and Fig. 5, Fig. 4 and Fig. 6, it is possible to find the nesting property of polarization code is set up.
In all R after step (3) recurrencenPlacement information bit in polarisation channel is placed on residual polarization channel
Freeze bit, transmission code word can be obtained.
The above-mentioned description to embodiment is for that can understand and apply the invention convenient for those skilled in the art.
Person skilled in the art obviously easily can make various modifications to above-described embodiment, and described herein general
Principle is applied in other embodiments without having to go through creative labor.Therefore, the present invention is not limited to the above embodiments, ability
Field technique personnel announcement according to the present invention, the improvement made for the present invention and modification all should be in protection scope of the present invention
Within.
Claims (1)
1. a kind of code construction method of polarization code under non degenerate compound channel, it is characterised in that this method comprises the concrete steps that:
Step (1) determines the form of aggregate channel and polarisation channel:
The given memoryless symmetric channel C:{ 0,1 of two binary } → Y and V:{ 0,1 → Z, Y and Z be respectively channel C and V output
Collection；It is as follows to define aggregate channel (C, V):
Wherein,That is u0And u1, it is the input of aggregate channel (C, V), x0And y0Respectively channel C's outputs and inputs, x1And z1
Respectively channel V's outputs and inputs；For polarization code core generator matrix, andIndicate channel C
With the input of channel V；According to chain rule, the mutual information of aggregate channel (C, V) is split, polarisation channel is obtained:
WhereinIndicate exclusive or behaviour
Make；
Step (2) determines recurrence Construction according to transmission code rate r=g/ (g+b), independent to g+b in each layer of recursive structure
Channel executes combination and splits, and obtains the high polarisation channel of g reliability, the low polarisation channel of b reliability:
It enablesIndicate the low polarisation channel of the reliability that n-th layer recursive transformation obtains, 1≤i≤b；
It enablesIndicate the high polarisation channel of the reliability that n-th layer recursive transformation obtains, 1≤j≤g；
Indicate bottom transmission channel；
Different disposal is carried out in two kinds of situation:
(i) g≤b, the i.e. situation of code rate r≤1/2:
Define the intermediate polarisation channel in recursive transformation structure:1≤t≤b-g；In t expression
Between channel index；
As g=1, have1≤i≤b, and
As g > 1, intermediate polarisation channel is defined:
1≤s≤g-1；The index of s expression intermediate channels；
Then haveWith
(ii) g > b, i.e. 1/2 situation of code rate r >:
Define the intermediate polarisation channel in recursive transformation structure:b+1≤t≤g；
As b=1, haveG >=j >=1, and
As b > 1, intermediate polarisation channel is defined:
Then haveWith
Step (3) determines the code construction of generic polarization code, enables WnAfter indicating n-th layer channel conversion, all polarisation channels
The aggregate channel of composition:
In the 1st layer of channel conversion structure, a independent bottom transmission channel W of K (b+g) points are K group, g+b in each group
Channel executes channel combination according to the recursive structure in step (2) and splits, and obtains the independent polarisation channel of K groupCollectively form W1；
In the 2nd layer of channel conversion structure, using chain structure, i.e. (i, i+1 ..., i+b+g-1) groupIt is middle to select channel to execute channel combination and split according to the recursive structure of step (2),
Obtain the independent polarisation channel of K-b-g+1 groupCollectively form W2；
With W2Recurrence, g+b independent channel W are participated in as primary channel mapped structuren-1Middle selectionIt executes channel combination and splits, generate the independent polarisation channel of K-b-g+1 group
Step (4) changes the channel for participating in recursive transformation every time as transmission code rate r > 1/2, and introduces additional channel and set
It changes；
In n-th layer channel recursive transformation structure, will participate in polarized channel change is
Pass through permutation matrixChange its input sequence, wherein ItFor the unit matrix of t × t, channel group is finally executed
It closes and splits；
After step (5) recurrence, in all RnPlacement information bit in polarisation channel is placed on residual polarization channel and is freezed
Bit obtains sending code word.
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