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CN108616332B - Multi-user data transmission method based on random linear network coding - Google Patents

Multi-user data transmission method based on random linear network coding Download PDF

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CN108616332B
CN108616332B CN201810456833.7A CN201810456833A CN108616332B CN 108616332 B CN108616332 B CN 108616332B CN 201810456833 A CN201810456833 A CN 201810456833A CN 108616332 B CN108616332 B CN 108616332B
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CN108616332A (en
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陈超
陆献轩
张俐楠
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Blue Cloud Smart Digital Technology Co ltd
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Zhejiang Gongshang University
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00Arrangements for detecting or preventing errors in the information received
    • H04L1/004Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0076Distributed coding, e.g. network coding, involving channel coding
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L67/00Network arrangements or protocols for supporting network services or applications
    • H04L67/01Protocols
    • H04L67/06Protocols specially adapted for file transfer, e.g. file transfer protocol [FTP]
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W4/00Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/06Selective distribution of broadcast services, e.g. multimedia broadcast multicast service [MBMS]; Services to user groups; One-way selective calling services

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Abstract

本发明公开了一种基于随机线性网络编码的多用户数据传输方法。该方法将网络编码技术用在存储服务器上:服务器先根据所有用户的下载请求,计算出所要需要传输的文件集合;然后利用随机线性网络编码的方法,将这些文件进行编码,随后将编码过的数据发送给用户;当用户收到足够数量的数据包之后,可解码出所有参与编码的原始文件,并从中选取自己感兴趣的文件,丢弃其他的文件;最后,存储服务器通过用户的反馈信息来获知用户是否已成功解码;当收到所有用户的确认信息,则传输结束。本发明的多用户数据传输方法可提高整体的传输效率,增加网络的吞吐量。

Figure 201810456833

The invention discloses a multi-user data transmission method based on random linear network coding. This method uses network coding technology on the storage server: the server first calculates the set of files to be transmitted according to the download requests of all users; then uses the random linear network coding method to encode these files, and then encodes the encoded The data is sent to the user; when the user receives a sufficient number of data packets, all the original files involved in the encoding can be decoded, and the files that he is interested in are selected from them, and other files are discarded; finally, the storage server uses the user's feedback information. Know whether the user has successfully decoded; when the confirmation information from all users is received, the transmission ends. The multi-user data transmission method of the present invention can improve the overall transmission efficiency and increase the throughput of the network.

Figure 201810456833

Description

一种基于随机线性网络编码的多用户数据传输方法A Multi-User Data Transmission Method Based on Random Linear Network Coding

技术领域technical field

本发明属于无线网络通信技术领域,尤其涉及一种基于随机线性网络编码的多用户数据传输方法。The invention belongs to the technical field of wireless network communication, and in particular relates to a multi-user data transmission method based on random linear network coding.

背景技术Background technique

随着社会经济和科学技术的发展,信息化建设的不断推进与深入,无线网络与无线通信数据传输在各个领域的应用越来越广。其中,多播是无线网络中最常用的数据传输方式之一。在无线多播中,由于无线信道极易受到干扰及衰减、衰弱等影响,无线信道有时呈现出较高的信道误码率或丢包率,致使无线链路质量较差,数据包传输容易受损,进而严重影响了传输效率。针对该问题,传统的解决方法之一是采用重传技术,例如自动请求重传(Automatic Repeat Request,ARQ)策略:当某个数据包未被所有用户成功接收时,源节点会不断重传该数据包,直到所有接收节点都成功接收到该数据包为止。因此,重传技术的传输效率其实不高。With the development of social economy and science and technology, and the continuous advancement and deepening of information construction, wireless networks and wireless communication data transmission are more and more widely used in various fields. Among them, multicast is one of the most commonly used data transmission methods in wireless networks. In wireless multicast, because the wireless channel is easily affected by interference, attenuation, weakening, etc., the wireless channel sometimes presents a high channel bit error rate or packet loss rate, resulting in poor wireless link quality and easy packet transmission. loss, which seriously affects the transmission efficiency. To solve this problem, one of the traditional solutions is to use retransmission technology, such as Automatic Repeat Request (ARQ) strategy: when a data packet is not successfully received by all users, the source node will continue to retransmit the data packet. packet until all receiving nodes have successfully received the packet. Therefore, the transmission efficiency of the retransmission technology is actually not high.

网络编码是另外一种提高无线多播效率的技术。发送端首先利用网络编码技术将原始数据包进行编码,生成编码后的数据包,然后发送给用户。对于用户来说,只来接收到足够数量的线性独立的编码后的数据包,就可以成功解码出所有的原始数据包。因此,不存在严重影响多播效率的数据包重传问题。Network coding is another technique that improves the efficiency of wireless multicast. The sender first uses the network coding technology to encode the original data packet, generates the encoded data packet, and then sends it to the user. For the user, all the original data packets can be successfully decoded only by receiving a sufficient number of linearly independent encoded data packets. Therefore, there is no packet retransmission problem that seriously affects multicast efficiency.

本发明将网络编码应用于单跳无线网络,主要用来提高数据包的传输效率。有一组移动用户,想要从一个中心存储服务器上下载自己感兴趣的一个或多个文件;不同用户想要下载的文件可能存在重复,例如某些热门资源会被多个用户下载。针对上述特点,本发明将网络编码技术用在存储服务器上:服务器先根据所有用户的下载请求,计算出所要需要传输的文件集合;然后利用随机线性网络编码的方法,将这些文件进行编码,随后将编码过的数据发送给用户;当用户收到足够数量的数据包之后,可解码出所有参与编码的原始文件,并从中选取自己感兴趣的文件,丢弃其他的文件;最后,存储服务器通过用户的反馈信息来获知用户是否已成功解码;当收到所有用户的确认信息,则传输结束。The present invention applies network coding to a single-hop wireless network, and is mainly used to improve the transmission efficiency of data packets. There is a group of mobile users who want to download one or more files they are interested in from a central storage server; the files that different users want to download may be duplicated, for example, some popular resources will be downloaded by multiple users. In view of the above-mentioned characteristics, the present invention uses network coding technology on the storage server: the server first calculates the set of files to be transmitted according to the download requests of all users; Send the encoded data to the user; when the user receives a sufficient number of data packets, all the original files involved in the encoding can be decoded, and the files that they are interested in can be selected from them, and other files are discarded; finally, the storage server can pass the user The feedback information to know whether the user has successfully decoded; when the confirmation information from all users is received, the transmission ends.

发明内容SUMMARY OF THE INVENTION

本发明针对无线网络中的文件传输,提供一种基于随机线性网络编码的多用户数据传输方法。The invention provides a multi-user data transmission method based on random linear network coding for file transmission in wireless network.

本发明的技术方案为:The technical scheme of the present invention is:

一种基于随机线性网络编码的数据传输方法,包括以下处理步骤:A data transmission method based on random linear network coding, comprising the following processing steps:

假设存储服务器有m个数据包,记为Xi,X2,K,Xm;有n个用户,每个用户都要从存储服务器上下载自己想要的一个或者多个数据包;记第i个用户所要下载的数据包集合为Ai,我们有

Figure BDA0001659885440000021
记第i个用户收到的线性独立的数据包的个数为ci,其初始值设为0,即
Figure BDA0001659885440000022
Suppose the storage server has m data packets, denoted as X i , X 2 , K, X m ; there are n users, and each user must download one or more data packets they want from the storage server; denote the first The set of data packets to be downloaded by i users is A i , we have
Figure BDA0001659885440000021
The number of linearly independent data packets received by the i-th user is c i , and its initial value is set to 0, that is,
Figure BDA0001659885440000022

(1)传输准备阶段:(1) Transmission preparation stage:

各个用户与存储服务器之间建立连接,并向存储服务器发起数据包传输请求,告知存储服务器自己所要下载的数据包集合Ai,i∈{1,K,n};服务器收到所有用户发起的下载请求后,计算出所需要传输的所有数据包的集合,记为B,因此我们有B=A1UA2UKUAnEach user establishes a connection with the storage server, and initiates a data packet transmission request to the storage server, informing the storage server of the set of data packets A i ,i∈{1,K,n} to be downloaded; the server receives all user-initiated After downloading the request, calculate the set of all data packets that need to be transmitted, denoted as B, so we have B=A 1 UA 2 UKUA n .

(2)传输阶段:(2) Transmission stage:

在传输阶段的每个时隙里,存储服务器和用户按照如下步骤进行数据包的传输与接收:In each time slot in the transmission phase, the storage server and the user transmit and receive data packets according to the following steps:

(2.1)存储服务器用随机线性网络编码的方法生成一个编码后的数据包Y,该数据包是集合B中所有数据包的随机线性组合,即

Figure BDA0001659885440000031
其中|B|表示集合B中的元素的个数,a1,K,a|B|为编码系数,在每次编码的时候从编码域Fq={0,1,K,q-1}中随机选取,q表示编码域的大小,为事先确定好的整数。进入步骤(2.2)。(2.1) The storage server uses the random linear network coding method to generate an encoded data packet Y, which is a random linear combination of all the data packets in the set B, namely
Figure BDA0001659885440000031
where |B| represents the number of elements in the set B, a 1 , K, a |B| are the coding coefficients, from the coding field F q ={0,1,K,q-1} in each coding It is randomly selected from , and q represents the size of the coding field, which is an integer determined in advance. Proceed to step (2.2).

(2.2)存储服务器将生成的编码后的数据包通过无线信道广播给所有的用户。进入步骤(2.3)。(2.2) The storage server broadcasts the generated encoded data packet to all users through a wireless channel. Proceed to step (2.3).

(2.3)在接收端,若第i个用户在当前时隙里成功接收到了存储服务器广播的数据包,则该用户判断该数据包是否与自己缓存中的其他数据包线性独立。若是,则将该数据包加入缓存,同时将ci的值增加1,即ci=ci+1,进入步骤(2.4);反之则丢弃该数据包,进入步骤(2.6)。(2.3) At the receiving end, if the i-th user successfully receives the data packet broadcast by the storage server in the current time slot, the user determines whether the data packet is linearly independent from other data packets in its own cache. If so, add the data packet to the cache, and at the same time increase the value of c i by 1, that is, c i = ci +1, and enter step (2.4); otherwise, discard the data packet and enter step (2.6).

(2.4)若ci=|B|,则表示第i个用户已经收到了足够数量的线性独立的编码后的数据包,因此可用高斯消元法将集合B中所有的原始数据包解码出来。由于

Figure BDA0001659885440000032
用户可从集合B中找出所有自己所要下载的数据包,并丢弃那些自己不需要的数据包,进入步骤(2.5)。反之,则返回步骤(2.1)。(2.4) If c i = |B|, it means that the i-th user has received a sufficient number of linearly independent encoded data packets, so Gaussian elimination method can be used to decode all the original data packets in set B. because
Figure BDA0001659885440000032
The user can find all the data packets that he wants to download from the set B, and discard those data packets that he does not need, and go to step (2.5). Otherwise, go back to step (2.1).

(2.5)第i个用户发送一个ACK确认信息给存储服务器告知存储服务器自己已经解码出自己所要下载的数据包。之后该用户进入静默状态,丢弃在随后的时隙里收到的其他数据包,进入步骤(2.6)。(2.5) The i-th user sends an ACK confirmation message to the storage server to inform the storage server that it has decoded the data packet to be downloaded. After that, the user enters a silent state, discards other data packets received in the subsequent time slot, and proceeds to step (2.6).

(2.6)存储服务器判断是否已从所有的用户那里都收到了ACK确认信息。若是,则传输阶段结束,反之则返回步骤(2.1)。(2.6) The storage server determines whether ACK confirmation information has been received from all users. If so, the transmission phase ends, otherwise, return to step (2.1).

本发明具有以下特点:The present invention has the following characteristics:

本发明存储服务器不是单纯地将原始数据包广播给用户,而是利用不同用户想要下载的文件存在重复性这一特点,采用了随机线性网络编码的方法,将所有需要发送的数据包先汇总后编码,然后发送给用户。采用这种方法,虽然每个用户需要接收的数据包个数比之前变得更多,但是存储节点不需要对丢失的数据包进行重传,因此可提高整体的传输效率,增加网络的吞吐量。The storage server of the present invention does not simply broadcast the original data packets to the users, but utilizes the characteristic of the repetition of the files that different users want to download, adopts the method of random linear network coding, and collects all the data packets to be sent first. post-encoded and then sent to the user. Using this method, although the number of data packets that each user needs to receive becomes more than before, the storage node does not need to retransmit the lost data packets, so the overall transmission efficiency can be improved and the network throughput can be increased. .

附图说明Description of drawings

图1为本发明的网络示意图。FIG. 1 is a schematic diagram of a network of the present invention.

图2为本发明数据传输方法的流程图。FIG. 2 is a flow chart of the data transmission method of the present invention.

具体实施方式Detailed ways

为了进一步说明本发明,下面给出一个优选实施范例。此范例仅对本发明的原理性说明,不代表本发明的任何限制。In order to further illustrate the present invention, a preferred embodiment is given below. This example only illustrates the principle of the present invention and does not represent any limitation of the present invention.

假设有一个存储服务器,一共有10个不同的文件。假设每个文件只包含一个数据包,因此服务器上共有10个原始数据包,记为X1,X2,K,X10。现有3个用户,想要下载的数据包集合分别为A1={X1,X2,X3},A2={X3,X4,X5,X6},A3={X2,X3,X6,X7}。用户收到的线性独立的数据包的个数,其初始值为0,即c1=c2=c3=0。设编码域的大小为q=16,因此编码域为F16={0,1,K,15}。Suppose there is a storage server with a total of 10 different files. It is assumed that each file contains only one data packet, so there are 10 original data packets on the server, denoted as X 1 , X 2 , K, X 10 . There are currently 3 users, and the sets of data packages to be downloaded are A 1 ={X 1 ,X 2 ,X 3 },A 2 ={X 3 ,X 4 ,X 5 ,X 6 },A 3 ={ X 2 , X 3 , X 6 , X 7 }. The number of linearly independent data packets received by the user, and its initial value is 0, that is, c 1 =c 2 =c 3 =0. Let the size of the coding field be q=16, so the coding field is F 16 ={0,1,K,15}.

3个用户先与服务器建立连接,向服务器发送下载请求,并告知服务器自己想要下载的数据包集合A1,A2,A3。服务器收到所有的用户下载请求后,计算出所需要传输的所有数据包的集合,即B=A1UA2UA3={X1,X2,X3,X4,X5,X6,X7}。The three users first establish a connection with the server, send a download request to the server, and inform the server of the data packet sets A 1 , A 2 , and A 3 that they want to download. After the server receives all user download requests, it calculates the set of all data packets to be transmitted, that is, B=A 1 UA 2 UA 3 ={X 1 ,X 2 ,X 3 ,X 4 ,X 5 ,X 6 , X 7 }.

在传输阶段的第1个时隙,服务器用随机线性网络编码的方法生成第1个编码后的数据包,记为

Figure BDA0001659885440000041
其中编码系数a1,a2,K,a7从编码域F16={0,1,K,15}中随机选取。服务器将编码后的数据包Y1广播给3个用户。假设第1,2个用户成功接收到了数据包Y1,而第3个用户因为噪声的影响没有成功接收。由于用户1和用户2的缓存中没有任何数据包,所以用户1和用户2将Y1放入自己的缓存中,并更新用户收到的线性独立的数据包的个数c1和c2,即c1=c2=1。由于c1,c2,c3的值都小于|B|=7,因此3个用户都不需要发送ACK确认信息给服务器。In the first time slot of the transmission phase, the server uses the random linear network coding method to generate the first encoded data packet, denoted as
Figure BDA0001659885440000041
The coding coefficients a 1 , a 2 , K, a 7 are randomly selected from the coding field F 16 ={0,1,K,15}. The server broadcasts the encoded packet Y 1 to 3 users. It is assumed that the 1st and 2nd users successfully receive the data packet Y 1 , while the 3rd user fails to receive it due to the influence of noise. Since user 1 and user 2 do not have any data packets in their caches, user 1 and user 2 put Y 1 into their own caches, and update the numbers c 1 and c 2 of linearly independent data packets received by users, That is, c 1 =c 2 =1. Since the values of c 1 , c 2 , and c 3 are all less than |B|=7, the three users do not need to send ACK confirmation information to the server.

在传输阶段的第2个时隙,服务器生成第2个编码后的数据包

Figure BDA0001659885440000051
其中编码系数a1,a2,K,a7从编码域F16={0,1,K,15}中随机选取。服务器将编码后的数据包Y2广播给3个用户。假设只有第2个用户成功接收到了数据包Y2。由于用户2的缓存已有数据包Y1,所用户2需判断Y2和Y1是否线性独立。若是,则将Y2放入自己的缓存,同时更新c2=2;反之,则丢弃Y2。由于c1,c2,c3的值仍小于|B|=7,因此3个用户都不需要发送ACK确认信息给服务器。In the second slot of the transmission phase, the server generates the second encoded packet
Figure BDA0001659885440000051
The coding coefficients a 1 , a 2 , K, a 7 are randomly selected from the coding field F 16 ={0,1,K,15}. The server broadcasts the encoded packet Y 2 to 3 users. Suppose that only the 2nd user successfully receives the packet Y 2 . Since the cache of user 2 already has data packet Y 1 , user 2 needs to judge whether Y 2 and Y 1 are linearly independent. If so, put Y 2 into its own cache, and update c 2 =2 at the same time; otherwise, discard Y 2 . Since the values of c 1 , c 2 , and c 3 are still smaller than |B|=7, the three users do not need to send ACK confirmation information to the server.

在接下来的时隙里,存储服务器和用户按照以上方法进行数据包的传输与接收。若某个用户收到足够数量的线性独立的数据包的个数,例如c1=7,则用户1可通过高斯消元法解码出集合B中所有数据包,并同时向服务器发送一个ACK确认信息,告知服务器自己已成功解码。若服务器收到了所有3个用户的ACK信息,则整个传输过程结束。In the next time slot, the storage server and the user transmit and receive data packets according to the above method. If a user receives a sufficient number of linearly independent data packets, for example, c 1 =7, then user 1 can decode all data packets in set B through Gaussian elimination, and send an ACK to the server at the same time. message to inform the server that it has successfully decoded. If the server receives the ACK information from all three users, the entire transmission process ends.

本发明基于随机线性网络编码的数据传输方法,属于无线网络通信技术领域;本发明使用编码过的数据包代替原始数据包进行发送,避免了传统传输方法中丢失数据包需要重传的问题,提高了数据的传输效率和网络的吞吐量。The present invention is a data transmission method based on random linear network coding, and belongs to the technical field of wireless network communication; the present invention uses encoded data packets to send instead of original data packets, avoids the problem of retransmission of lost data packets in the traditional transmission method, and improves the The data transmission efficiency and network throughput are improved.

以上对本发明的优选实施范例及原理进行了详细说明,对本领域的普通技术人员而言,依据本发明提供的思想,在具体实施方式上会有改变之处,而这些改变也应视为本发明的保护范围。The preferred embodiments and principles of the present invention have been described in detail above. For those of ordinary skill in the art, according to the ideas provided by the present invention, there will be changes in the specific embodiments, and these changes should also be regarded as the present invention. scope of protection.

Claims (1)

1.一种基于随机线性网络编码的多用户数据传输方法,其特征在于,包括以下处理步骤:1. a multi-user data transmission method based on random linear network coding, is characterized in that, comprises the following processing steps: 假设存储服务器有m个数据包,记为Xi,X2,...,Xm;有n个用户,每个用户都要从存储服务器上下载自己想要的一个或者多个数据包;记第i个用户所要下载的数据包集合为Ai
Figure FDA0002612206510000011
记第i个用户收到的线性独立的数据包的个数为ci,其初始值设为0,即
Figure FDA0002612206510000012
Suppose the storage server has m data packets, denoted as X i , X 2 ,..., X m ; there are n users, each user needs to download one or more data packets they want from the storage server; Denote the set of data packets to be downloaded by the i-th user as A i ,
Figure FDA0002612206510000011
The number of linearly independent data packets received by the i-th user is c i , and its initial value is set to 0, that is,
Figure FDA0002612206510000012
(1)传输准备阶段:(1) Transmission preparation stage: 各个用户与存储服务器之间建立连接,并向存储服务器发起数据包传输请求,告知存储服务器自己所要下载的数据包集合Ai,i∈{1,...,n};服务器收到所有用户发起的下载请求后,计算出所需要传输的所有数据包的集合,记为B,B=A1∪A2∪…∪AnEach user establishes a connection with the storage server, and initiates a data packet transmission request to the storage server, informing the storage server of the set of data packets A i ,i∈{1,...,n} to be downloaded by the storage server; the server receives all users After the download request is initiated, calculate the set of all data packets to be transmitted, denoted as B, B=A 1 ∪A 2 ∪...∪A n ; (2)传输阶段:(2) Transmission stage: 在传输阶段的每个时隙里,存储服务器和用户进行数据包的传输与接收;In each time slot in the transmission phase, the storage server and the user transmit and receive data packets; 所述步骤(2)传输阶段的具体步骤为:The concrete steps of the described step (2) transmission stage are: (2.1)存储服务器用随机线性网络编码的方法生成一个编码后的数据包Y,该数据包是集合B中所有数据包的随机线性组合,即
Figure FDA0002612206510000013
其中|B|表示集合B中的元素的个数,a1,...,a|B|为编码系数,在每次编码的时候从编码域Fq={0,1,...,q-1}中随机选取,q表示编码域的大小,为事先确定好的整数;进入步骤(2.2);
(2.1) The storage server uses the random linear network coding method to generate an encoded data packet Y, which is a random linear combination of all the data packets in the set B, namely
Figure FDA0002612206510000013
Where |B| represents the number of elements in the set B, a 1 ,...,a |B| is the coding coefficient, which is obtained from the coding field F q ={0,1,..., q-1} is randomly selected, and q represents the size of the coding field, which is an integer determined in advance; go to step (2.2);
(2.2)存储服务器将生成的编码后的数据包通过无线信道广播给所有的用户,进入步骤(2.3);(2.2) The storage server broadcasts the generated encoded data packet to all users through the wireless channel, and enters step (2.3); (2.3)在接收端,若第i个用户在当前时隙里成功接收到了存储服务器广播的数据包,则该用户判断该数据包是否与自己缓存中的其他数据包线性独立;若是,则将该数据包加入缓存,同时将ci的值增加1,即ci=ci+1,进入步骤(2.4);反之则丢弃该数据包,进入步骤(2.6);(2.3) At the receiving end, if the i-th user successfully receives the data packet broadcast by the storage server in the current time slot, the user determines whether the data packet is linearly independent from other data packets in its own cache; The data packet is added to the cache, and the value of c i is increased by 1 at the same time, that is, c i = ci +1, enter step (2.4); otherwise, discard the data packet and enter step (2.6); (2.4)若ci=|B|,则表示第i个用户已经收到了足够数量的线性独立的编码后的数据包,因此可用高斯消元法将集合B中所有的原始数据包解码出来;由于
Figure FDA0002612206510000021
用户可从集合B中找出所有自己所要下载的数据包,并丢弃那些自己不需要的数据包,进入步骤(2.5);反之,则返回步骤(2.1);
(2.4) If c i =|B|, it means that the i-th user has received a sufficient number of linearly independent encoded data packets, so Gaussian elimination method can be used to decode all the original data packets in set B; because
Figure FDA0002612206510000021
The user can find all the data packets that he wants to download from the set B, and discard those data packets that he does not need, and go to step (2.5); otherwise, go back to step (2.1);
(2.5)第i个用户发送一个ACK确认信息给存储服务器告知存储服务器自己已经解码出自己所要下载的数据包;之后该用户进入静默状态,丢弃在随后的时隙里收到的其他数据包,进入步骤(2.6);(2.5) The i-th user sends an ACK confirmation message to the storage server to inform the storage server that it has decoded the data packet to be downloaded; then the user enters a silent state and discards other data packets received in the subsequent time slot, Enter step (2.6); (2.6)存储服务器判断是否已从所有的用户那里都收到了ACK确认信息;若是,则传输阶段结束,反之则返回步骤(2.1)。(2.6) The storage server judges whether the ACK confirmation information has been received from all users; if so, the transmission phase ends, otherwise, it returns to step (2.1).
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