TWI823126B - 5g adaptive contention access system with shared wireless channels for multiple traffic categories and method thereof - Google Patents

Abstract

A 5G adaptive contention access system with shared wireless channels for multiple traffic classes and a method thereof are provided. Low modulo(namely mod) is assigned to higher flow type of 5G flow data transmission. High modulo is assigned to lower flow type of 5G flow data transmission. Request data rates of different types of flows are predicted. Numbers of random access subframe of port physical layer frame is decided dynamically. Ranges of random access preambles of random access subframes are decided according to each of flow type adaptively and upper and lower of contention ranges are decided according to each of flow type adaptively. Consequently, several important objectives can be achieved certainly in 5G, including: first: minimizing random access (RA) collision probability and contention delay, maximizing reward and net-profit, minimizing the E2E delay and maximizing reliability of SFC for higher types of flows (e.g., Emergency, uRLLC); second: maximizing data rate for Lower types of flow (e.g., eMBB, mMTC), etc.

Description

5G adaptive contention access system and method for sharing wireless channels with multiple traffic types

A 5G communication system and a method thereof, in particular, a method that adaptively determines the random access pre-signal required for the random access contention range of a conflict domain and the upper and lower limits of the contention range for each type of traffic. A 5G adaptive contention access system and method where traffic types share wireless channels.

5G has many new mechanisms and functions that have been proposed and defined, including Virtualizing Network Function (VNF), Software Defined Network (SDN), Service Function Chaining (SFC), Network Slicing (NS), Mobile Edge Computing (MEC), Traffic Steering...etc.

Because 5G has the above mechanisms and functions, 5G can achieve the following functions: forward data packets according to decentralized routing to centralized software-defined network traffic for sending data flow data, and improve the connection between physical machines/virtual machines and the network. Distributive elasticity…etc.

In 5G new wireless transmission, preamble signals are based on competitive random methods. Although 3GPP provides several preamble signal types, due to the large and different traffic corresponding to the E2E service quality/relevance The key performance index has no collision value range distinction and lacks a dynamic backoff mechanism for conflict competition, resulting in a serious increase in the probability of collision. Therefore, high-priority traffic with high collision probability will definitely reduce the overall 5G access latency, outstanding traffic data transmission, net profit, throughput, etc.

In summary, it can be seen that there has long been a problem in the previous technology that the high contention conflict rate of high-priority traffic during existing 5G data transmission leads to the overall 5G access delay. Therefore, it is necessary to propose improved technical means to solve this problem. .

In view of the problem in the prior art that the high contention conflict rate of high-priority traffic during existing 5G data transmission causes overall 5G access delay, the present invention discloses a 5G adaptive contention access system and method for multiple traffic types to share wireless channels. Among them: the 5G adaptive contention access system for multiple traffic types sharing wireless channels disclosed in the present invention is suitable for mobile terminal devices of 5G communication, and includes: allocation module, prediction analysis module, dynamic adjustment module and adaptive calculation Mods.

The allocation module allocates low modulo to high traffic types when transmitting 5G traffic data, and allocates high modulo to low traffic types when transmitting 5G traffic data; the predictive analysis module predicts each traffic type. The request data rate; the dynamic adjustment module dynamically determines the number of random access (Random Access, RA) subframes (subframes) of the physical layer (Port Physical Layer, PHY) frame; and the adaptive calculation module The required random access preamble range in the random access subframe and the upper and lower limits of the contention range for each traffic type are adaptively determined based on each traffic type.

The 5G adaptive contention access method for multiple traffic types sharing wireless channels disclosed by the present invention is suitable for mobile terminal devices for 5G communications. It includes the following steps: first, allocate a low modulo to 5G traffic data transmission. High traffic types; then, assign high modulus to low traffic types during 5G traffic data transmission: then, predict the requested data rate of each traffic type; then, dynamically determine the physical layer (Port Physical Layer, PHY) frame ( frame; finally, the required random access preamble range in the random access subframe is adaptively determined according to each traffic type As well as the upper and lower limits of the competition range for each traffic type.

The system and method disclosed by the present invention are as above. The difference between the system and the previous technology is that the low modulus is assigned to the high traffic type when 5G traffic data is transmitted, and the high modulus is assigned to the low traffic type when 5G traffic data is transmitted. Predict the requested data rate of each traffic type, dynamically determine the number of random access sub-frames in the physical layer frame, and adaptively determine the required random access preamble range in the random access sub-frame based on each traffic type. As well as the upper and lower limits of the competition range for each traffic type.

The important goals achieved by the present invention in 5G are as follows: minimizing the random access conflict probability and contention conflicts of traffic types, maximizing connection rewards and performance of different traffic types, minimizing E2E delay and maximizing SFC for higher types Traffic reliability, maximizing the data rate of low traffic types (such as: eMBB, mMTC...etc.), etc.

Through the above technical means, the present invention can achieve the technical effects of increasing the probability of 5G access competition for higher-priority traffic, minimizing the probability of conflict, and reducing 5G access delay.

10: Mobile terminal device

11: Assign modules

12: Predictive analysis module

13:Dynamic adjustment module

14:Adaptive computing module

21: Delayed data

22:Simulated data

Step 101: Assign low modulus to high traffic types during 5G traffic data transmission

Step 102: Assign high modulus to low traffic type during 5G traffic data transmission

Step 103: Predict the requested data rate for each traffic type

Step 104: Dynamically determine the number of random access sub-frames of the physical layer frame

Step 105: Adaptively determine the required random access preamble range in the random access subframe and the upper and lower limits of the contention range for each traffic type based on each traffic type.

Figure 1 is a system block diagram of a 5G adaptive contention access system for multiple traffic types sharing wireless channels according to the present invention.

Figure 2 shows the average access delay data under different types of single frequency network modules for 5G adaptive contention access of multiple traffic types sharing wireless channels according to the present invention.

Figure 3 shows a simulation data diagram of the success rate under different competition times for 5G adaptive contention access of multiple traffic types sharing wireless channels according to the present invention.

Figure 4 shows a method flow chart of the 5G adaptive contention access method for multiple traffic types sharing wireless channels according to the present invention.

The embodiments of the present invention will be described in detail below with reference to the drawings and examples, so that the implementation process of how to apply technical means to solve technical problems and achieve technical effects of the present invention can be fully understood and implemented accordingly.

The following will first describe the 5G adaptive contention access system for multi-traffic types sharing wireless channels disclosed in the present invention, and please refer to "Figure 1". "Figure 1" illustrates the multi-traffic types sharing wireless channels of the present invention. System block diagram of the 5G adaptive contention access system.

The 5G adaptive contention access system for multiple traffic types sharing wireless channels disclosed by the present invention is suitable for mobile terminal devices 10 of 5G communications. It includes: an allocation module 11, a prediction analysis module 12, a dynamic adjustment module 13 and an automatic Adapt to Compute Module 14.

In terms of delay, reliability, loss, data rate, etc., various services with different Quality of Service (QoS)/Key Performance Indicator (KPI) Various applications require limited physical layer (Port Physical Layer, PHY) in the Random Access (RA) subframe (subframe) of 5G New Radio (NR) before traffic data transmission. ) preamble competes. Although additional random access is extended from Long Term Evolution-Advanced (LTE-A), a huge amount of traffic data packets pass through the 5G UpLink entity. The layer random access channel (PHY Random Access Channel, PRACH) will increase the probability of contention conflicts and the obvious delay of random access. 5G new wireless transmission is based on different types of single frequency network (Single Frequency Network, SFN) modulus. )'s mobile terminal device (User Equipment, UE) specifies different physical layer random access channel configuration indexes, thereby requiring an efficient random access contention mechanism for random access collisions and contention delays.

)分配給低流量類型的切片，例如：eMBB以及mMTC…等，反之亦然，在此僅為舉例說明之，並不以侷限本發明的應用範疇。 In order to increase the access probability of high-traffic types, the allocation module 11 allocates modulo x =1 to the slicing of high-traffic types, such as: eMERGENCY and uRLLC, etc. This is only an example. , and does not limit the scope of application of the present invention, and then adaptively determine other larger modulus x values (

) is allocated to low-traffic types of slices, such as eMBB and mMTC, etc., and vice versa. This is only an example and does not limit the application scope of the present invention.

)以及動態調整模組13是動態決定實體層訊框T+1所需要的隨機存取子訊框數量(

)，除此之外，如果隨機存取的子訊框 數量超過門檻值時，則可以將快取檔案置換機制(Least recently used，LRU)隨機存取子訊框分配給行動終端裝置。 Next, the predictive analysis module 12 predicts the requested data rate (

) and the dynamic adjustment module 13 dynamically determines the number of random access subframes required for the physical layer frame T +1 (

), in addition, if the number of random access sub-frames exceeds the threshold, the cache file replacement mechanism (Least recently used, LRU) random access sub-frame can be allocated to the mobile terminal device.

Specifically, the required number of random access subframes is 3, the configured index is q =23, the available random access subframes are 2, 5, and 8 respectively, and the subframes of the cache file replacement mechanism One of them will be configured.

The adaptive calculation module 14 adaptively determines the random access preamble required in the random access subframe (i.e., the contention random access range of the collision domain) and the contention range of each traffic type for each traffic type. Upper and lower limits.

)，為了區分不同流量類型的衝突域，將前置訊號配置索引進行劃分，即基於模數x以及子訊框數量的k流量類型從q映入k類型，其中x

{1,2,4,8,16}，子訊框

{1,2,3,5,10}，使得在每個實體層訊框中引起不同的競爭。 First, the classified random access configuration index, single frequency network modulus x and dynamically determine the number of random access subframes (

), in order to distinguish the collision domains of different traffic types, the pre-signal configuration index is divided, that is, the k traffic type based on the modulus x and the number of subframes is mapped from q to k type, where x

{1,2,4,8,16}, subframe

{1,2,3,5,10}, causing different contentions in each physical layer frame.

In order to improve Random Access Opportunity (RAO) and utilization, the resources of the physical layer random access channel can be dynamically adjusted based on demand or periodically by using different physical layer random access channel configuration indexes. Based on the proposed scheme for distinguishing contention domains, the physical layer random access channel configuration index for different types of traffic with different service classification TCIDs is therefore dynamically determined by the serving base station (Generation Node B, gNB). Then, the serving base station sends the latest physical layer random access channel configuration index of different types of traffic to the mobile terminal device through a System Information Block (SIB) message.

{5,10}配置索引 q分配給eMERGENCY，其中q

{25,26,27}，使eMERGENCY可以與任何單一頻率網路進行競爭。 For the highest type of traffic (e.g. eMERGENCY) to maximize access probability and minimize contention delay, modulus x =1 and

{5,10} configuration index q is assigned to eMERGENCY, where q

{25,26,27}, allowing eMERGENCY to compete with any single frequency network.

{1,2,3}配置索引q分配給uRLLC，其中q

{16,…,24}。 For higher types of traffic (for example: uRLLC), in order to increase access probability and reduce contention delay, modulus x =1 and

{1,2,3} configuration index q is assigned to uRLLC, where q

{16,…,24}.

{1}，分配給這些低流量類型，其中x

{2,4,8,16}。也就是說，對於較低類型的流量(例如：eMBB或Gaming…等)，將帶有模數x

{2,4}以及

{1}配置索引q分配給較低類型的流量，其中q

{8,…,15}，對於最低類型的流量(例如：mMTC)，將帶有模數x

{8,16}以及

{1}配置索引q分配給最低類型的流量，其中q

{0,…,7}。 On the contrary, for lower (e.g. eMBB or Gaming...etc.) and lowest (i.e. mMTC) type traffic, we will have other configuration index q with larger value x and a minimum number of random access subframes

{1}, assigned to these low traffic types, where x

{2,4,8,16}. That is, for lower types of traffic (eg: eMBB or Gaming... etc.), there will be a modulus x

{2,4} and

{1} Configure index q to be assigned to lower type traffic, where q

{8,…,15}, for the lowest type of traffic (eg: mMTC), will be with modulus x

{8,16} and

{1} Configure index q to be assigned to the lowest type of traffic, where q

{0,…,7}.

Please refer to "Figure 2". "Figure 2" shows the average access delay data under different types of single frequency network modules for 5G adaptive contention access of multiple traffic types sharing wireless channels according to the present invention.

，延時數據21請參考「第2圖」所示，在此不再進行贅述。 Based on dynamic contention probabilities using different configuration indexes q and different numbers of random access subframes, the access delays of different types of single-frequency networks modulus x under different numbers of mobile terminal devices are evaluated. All access delays vary with Increased with the increase in the number of mobile terminal devices. The type of single-frequency network modulus x = 1 produces the smallest access delay because random access preambles are allowed to be connected on any given single-frequency network. On the contrary, the type of single-frequency network modulus x =16 leads to the longest access delay, because the contention probability drops to

, please refer to "Figure 2" for the delay data 21, and will not be described again here.

{5,10}進行分配以及為uRLLC設置x=1以及

{1,2,3}進行分配。對於這兩種情況(即k=1 or 2)，用於競爭前置訊號的隨機存取子訊框

，是根據實體層訊框T+1,

處的預測所需類型k競爭確定，即可由下列公式確定：

In addition, in order to minimize the probability of collision, dynamically available random access subframes are added to high-type traffic (such as eMERGENCY and uRLLC...etc.) for higher types of traffic (ie. eMERGENCY and uRLLC...etc.), that is Set x =1 for eMERGENCY and

{5,10} for allocation and setting x = 1 for uRLLC and

{1,2,3} is assigned. For both cases (i.e. k =1 or 2), the random access sub-frame used to compete for the preamble signal

, based on the physical layer frame T +1,

The type k required for prediction at is competitively determined and can be determined by the following formula:

分配最佳擬合

，即當

越大時

也會越大，反之亦然。具體而言，假設uRLLC(例如：k=2)在實體層訊框T+1的預測競爭次數為

，則將選擇產生最小值的值n，如下公式所示：

或

Among them, F ^total is the total number of preamble signals in a random access subframe, which can be the prediction request

Assign best fit

, that is, when

When it is bigger

will also be larger and vice versa. Specifically, assuming that uRLLC (for example: k =2), the predicted number of competitions in physical layer frame T +1 is

, then the value n that produces the minimum value will be selected, as shown in the following formula:

or

>1，則採用最近最少使用(Least Recently Used，LRU)機制來選擇最優配置索引q。例如，假設

對於uRLLC已決定並且具有使用累積計數的配置索引q

{22,23,24}，決定最優配置索 引即{

}，即實體層訊框T+1的子訊框

集為子訊框2、5、8。 if

>1, then the least recently used (Least Recently Used, LRU) mechanism is used to select the optimal configuration index q . For example, suppose

For uRLLC has been decided and has configuration index q using cumulative count

{22,23,24}, determine the optimal configuration index, which is {

}, that is, the sub-frame of the physical layer frame T +1

The sets are subframes 2, 5, and 8.

1，對於eMBB以及mMTC方塊…等，單一頻率網路模數

,x

{2,4}為根據預測所需的實體層訊框T+1,

的類型k競爭確定，如下列公式所示：

On the contrary, for lower types of traffic (such as: eMBB, Gaming and mMTC... etc.), although the number of random access sub-frames in the physical layer frame is set to 1, that is

1. For eMBB and mMTC blocks... etc., single frequency network module

, x

{2,4} is the physical layer frame T +1 required according to prediction,

The type k competition is determined as shown in the following formula:

分配最佳擬合

，因此，當

越小時，

會越大。例如，假設mMTC(k=4)在實體層訊框T+1的預測競爭次數為

，則

將選擇產生最大值16，如下列公式所示：

或

Request for prediction

Assign best fit

, therefore, when

The smaller the time, the

will be bigger. For example, assume that the predicted number of competitions for mMTC ( k =4) in physical layer frame T +1 is

, then

The selection yields a maximum value of 16, as shown in the following formula:

or

，

將選擇產生最大值8，如下列公式所示：

或

For another example, when

,

The selection will produce a maximum value of 8, as shown in the following formula:

or

子訊框t中可用隨機存取前置訊號的成功競爭機率

，如下列公式所示：

Analyze the entity layer frame T ,

Probability of successful competition for available random access preamble in subframe t

, as shown in the following formula:

In addition, from the perspective of the mobile terminal device, as shown in the following formula:

Please refer to "Figure 3". "Figure 3" illustrates a simulation data diagram of the success rate under different competition times for 5G adaptive contention access of multiple traffic types sharing wireless channels according to the present invention.

The success probabilities of analysis and simulation were evaluated separately. The success probabilities of analysis and simulation under different competition times were very close. In addition, the probability of success in analysis and simulation increases logarithmically to the highest point, and then decreases exponentially to zero. Please refer to "Figure 3" for the simulation data 22, which will not be described again here.

In order to effectively maximize successful competition or minimize the probability of collision in the limited random access preamble signal of 5G new wireless transmission, an adaptive collision domain mechanism is used to distinguish the collision domains of different types of traffic based on the extended Sigmoid function. The adaptive collision domain mechanism to differentiate between different types of traffic should have separate collision domains to minimize inter-type collisions and different types of traffic with different contention requests should have appropriately separated random access contention ranges of preambles.

For each type of traffic, the required random access preamble within a random access subframe and the lower and upper limits of the contention range are adaptively determined. In order to adaptively distinguish and determine the collision domain, the extended Sigmoid function, the Cumulative Distribution Function (CDF) based on the normal distribution, will be considered, as shown in the following formula:

Among them, erf represents the error function, y represents the influence factor, μ represents the mean or expected value of the distribution, and σ represents the standard deviation.

函數作為期望值決定了Sigmoid函數曲線的均值，參數μ公式如下：

ACB factor of parameter μ

The function as the expected value determines the mean value of the Sigmoid function curve. The parameter μ formula is as follows:

，因此參數σ公式如下：

The ACB factor function as the parameter σ of the standard deviation affects the width of the Sigmoid function curve. We extend the Sigmoid function with parameter b , where the probability

, so the parameter σ formula is as follows:

f _id

53增加函數，但是，較低值的σ急劇增加ACB(y,u,σ)函數。 Higher values of σ lie smoothly at 0

f _id

53 increases the function, however, lower values of σ sharply increase the ACB ( y,u,σ ) function.

，所以

為了高效傳輸應該增加。參數如下列公式：

The ACB factor function of parameter y is the influencing factor of the Sigmoid function. The most critical factor in random access is the probability of competition success.

,so

should be increased for efficient transmission. The parameters are as follows:

x

4曲線確定。 Among them, the range of y can be based on the Sigmoid function-3

x

4 curve is determined.

，根據下列公式製定權重：

Dynamically determine the pre-signal for each type of traffic on mobile end devices

, the weight is determined according to the following formula:

]表示k類型流量的預期平均ACB因子。 Among them, F ^total is the competitive pre-signal of 54 very competitive sub-frames, E [

] represents the expected average ACB factor for type k traffic.

You can get the upper limit and lower limit of each k type of traffic on the mobile terminal device. When k =1, it is as follows:

When k ≠1 it is as follows:

表示最低類型(k=K)的下限值。 in,

Represents the lower bound value of the lowest type ( k = K ).

]，如下所示：

Assume that the average access type restriction factor E of mobile terminal device k type traffic [

],As follows:

以及

as well as

Then, the pre-signal range can be determined by the following formula:

以及

as well as

Finally, the upper and lower limits of all types can be determined by the following formula: When k =1,

以及

When k ≠1, as follows:

as well as

以及

as well as

以及

as well as

)以及前置訊號競爭範圍(

) Finally, based on demand and periodic calculation to determine, the serving base station sends the latest information to the mobile terminal device through the System Information Block (SIB) message, using the traffic type ID and the first index of the preamble signal set (

) and the pre-signal competition range (

)

Based on the use of different configuration indexes and different numbers of random access subframes with dynamic contention probabilities and adaptive differentiation of collision domains within random access subframes, the access contention probability of higher types of flows can be increased and minimized Probability of conflict.

Next, the operation method of the present invention will be described below, and please refer to "Figure 1" and "Figure 4" at the same time. "Figure 4" illustrates the 5G adaptive contention storage of multiple traffic types sharing wireless channels of the present invention. Method flow chart of the method.

First, assign a low modulus to the high traffic type when transmitting 5G traffic data (step 101); then, assign a high modulus to the low traffic type when transmitting 5G traffic data (step 102): Next, predict each type of traffic The requested data rate of the type (step 103); then, dynamically determine the number of random access subframes of the physical layer frame (step 104); finally, adaptively determine the required number of random access subframes according to each traffic type. The random access preamble range and the upper and lower bounds of the contention range for each traffic type (step 105).

To sum up, it can be seen that the difference between the present invention and the prior art is that the low modulus is assigned to the high traffic type when 5G traffic data is transmitted, and the high modulus is assigned to the low traffic type when 5G traffic data is transmitted. It is predicted that each The requested data rate of a traffic type dynamically determines the number of random access subframes of the physical layer frame, and adaptively determines the required random access preamble signal range and each random access subframe according to each traffic type. The upper and lower limits of the contention range for a traffic type.

The important goals achieved by the present invention in 5G are as follows: minimizing the random access conflict probability and contention conflicts of traffic types, maximizing connection rewards and performance of different traffic types, minimizing E2E delay and maximizing SFC for higher types Traffic reliability, maximizing the data rate of low traffic types (such as: eMBB, mMTC...etc.), etc.

This technical means can solve the problem of the previous technology that the high contention conflict rate of high-priority traffic during 5G data transmission leads to the overall 5G access delay, thereby increasing the probability of 5G access competition for higher-priority traffic. , the technical effect of minimizing the probability of conflicts and reducing 5G access delays.

Although the embodiments disclosed in the present invention are as above, the described contents are not used to directly limit the patent protection scope of the present invention. Anyone with ordinary knowledge in the technical field to which the present invention belongs may make slight changes in the form and details of the implementation without departing from the spirit and scope of the disclosure of the present invention. The patent protection scope of the present invention must still be defined by the attached patent application scope.

10: Mobile terminal device

11: Assign module

12: Predictive analysis module

13:Dynamic adjustment module

14:Adaptive computing module

Claims (8)

A 5G adaptive contention access system for multiple traffic types sharing wireless channels, suitable for mobile terminal devices for 5G communications, which includes: an allocation module that allocates low modulo to high traffic types during 5G traffic data transmission , and allocate high modulus to low traffic types when transmitting 5G traffic data; a prediction analysis module to predict the requested data rate of each traffic type; a dynamic adjustment module to dynamically determine the Port Physical Layer (PHY) ) the number of random access (RA) subframes of the frame (frame); and an adaptive calculation module to divide the random access configuration index, allocate a single frequency network module and dynamically determine The number of random access subframes is used to adaptively determine the required random access preamble range in the random access subframe according to each traffic type, as well as the upper and lower limits of the contention range for each traffic type. limit. The 5G adaptive contention access system for multiple traffic types sharing wireless channels as described in request 1, wherein the dynamic adjustment module further includes a cache file replacement mechanism when the number of random access sub-frames exceeds a threshold. (Least recently used, LRU) random access subframes are allocated. The 5G adaptive contention access system for multiple traffic types sharing wireless channels as described in claim 1, wherein the adaptive computing module is further dynamically adjusted according to needs or periodically by using different physical layer random access channel configuration indexes. Physical layer random access channel resources. The 5G adaptive contention access system for multiple traffic types sharing wireless channels as described in request 1, wherein the adaptive calculation module is implemented through an extended Sigmoid function and a cumulative distribution function (Cumulative Distribution Function, CDF) based on normal distribution . A 5G adaptive contention access method for multiple traffic types sharing wireless channels, suitable for mobile terminal devices for 5G communications, which includes the following steps: allocate low modulo to high traffic types during 5G traffic data transmission; Modules are assigned to low traffic types during 5G traffic data transmission; predict the requested data rate of each traffic type; dynamically determine the random access (Random Access, RA) of the physical layer (Port Physical Layer, PHY) frame (frame) The number of subframes; and dividing the random access configuration index, allocating a single frequency network module and dynamically determining the number of random access subframes to adaptively determine the random access subframe according to each traffic type The required random access preamble range and the upper and lower bounds in the contention range for each traffic type. The 5G adaptive contention access method for multiple traffic types sharing wireless channels as described in claim 5, wherein the step of dynamically determining the number of random access subframes of the physical layer frame further includes when the number of random access subframes of the physical layer frame When the number exceeds the threshold, the cache file replacement mechanism (Least recently used, LRU) random access subframe is allocated. The 5G adaptive contention access method for multiple traffic types sharing wireless channels as described in claim 5, wherein the random access preamble signal range required in the random access subframe is adaptively determined according to each traffic type. The step further uses different physical layer random access channel configuration indexes to dynamically adjust physical layer random access channel resources according to needs or periodically. The 5G adaptive contention access method for multiple traffic types sharing wireless channels as described in claim 5, wherein the steps of upper limit value and lower limit value in the contention range of each traffic type are through Extended Sigmoid function and cumulative distribution function (Cumulative Distribution Function, CDF) implementation based on normal distribution.

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