CN101179279B - Non-rate code coding/decoding method fit for additive white Gaussian noise channel - Google Patents

本发明公开了一种适合于加性白高斯噪声信道的无速率码编译码方法，包括编码方法和译码方法。其基本技术思想是在LT码的编码器后面再添加一个累加器，以使得二部图中编码节点的度数不再为1，从而解决LT码工作于加性白高斯噪声信道的“差错平台”问题，同时采用了被广泛应用的系统码结构。然后提出了两种易于实现且性能较好的编码器为新增校验节点选择信息节点的方式，一种方式使得信息节点的度数分布近似均匀，一种方式使得信息节点的度数分布在某一速率受限。

The invention discloses a rateless encoding and decoding method suitable for additive white Gaussian noise channel, including an encoding method and a decoding method. The basic technical idea is to add an accumulator after the encoder of the LT code, so that the degree of the coding node in the bipartite graph is no longer 1, so as to solve the "error platform" of the LT code working on the additive white Gaussian noise channel problems, while using the widely used system code structure. Then, two easy-to-implement and better-performance encoders are proposed to select information nodes for new check nodes. One way makes the degree distribution of information nodes approximately uniform, and the other way makes the degree distribution of information nodes in a certain Rate limited.

适合于加性白高斯噪声信道的无速率码编译码方法A Rateless Coding and Decoding Method for Additive White Gaussian Noise Channels

技术领域technical field

本发明涉及无线通信领域，具体涉及一种适合于加性白高斯噪声(AWGN)信道的无速率码编译码方法。The invention relates to the field of wireless communication, in particular to a rateless encoding and decoding method suitable for additive white Gaussian noise (AWGN) channels.

背景技术Background technique

分组码被广泛的用于信道纠错编码。我们通常先估计信道参数，根据这个参数设计一个码率固定为R＝N/K的(N，K)分组码。当估计的信道参数大于实际的信道参数时，虽然可以实现可靠传输，但是造成了传输的浪费，因为此时可以使用更高码率的分组码；当估计的信道参数小于实际的信道参数时，不能实现可靠传输，此时需要更低码率的分组码。因此，在发送端不知道信道准确的状态信息情况下，要保证信息的可靠有效传输，往往需要ARQ。如何自适应的选择合适的码率进行传输，以适应不同的信道参数，无速率码为我们提供了一种解决问题的新思路。Block codes are widely used in channel error correction coding. We usually estimate the channel parameter first, and design a (N, K) block code with a code rate fixed at R=N/K according to this parameter. When the estimated channel parameter is greater than the actual channel parameter, although reliable transmission can be achieved, it causes a waste of transmission, because a block code with a higher code rate can be used at this time; when the estimated channel parameter is smaller than the actual channel parameter, Reliable transmission cannot be achieved, and a block code with a lower code rate is required at this time. Therefore, when the sending end does not know the accurate state information of the channel, ARQ is often required to ensure reliable and effective transmission of information. How to adaptively select the appropriate code rate for transmission to adapt to different channel parameters, the rateless code provides us with a new way to solve the problem.

无速率码与传统固定码率编码方式最大的不同在于它在发送端不设定固定码率，发送端可以以某种方式源源不断的产生编码包并发送出去。接收端则可以接收到这些编码包然后尝试译码。如果译码失败，接收端可以再多接收一些编码包然后继续尝试译码。接收端将一直重复这个过程直到译码成功。这时接收端只需要发送一个非常简单的反馈信号告知发送端译码成功，然后发送端停止发送，这样就完成了整个传输过程。此时，实际传输的码率取决于实际发送的编码包数目，而需要发送的编码包数目取决于当时的信道状况，如何使得实际传输的码率逼近当时的信道容量成为无速率码设计的关键问题。The biggest difference between the rateless code and the traditional fixed code rate encoding method is that it does not set a fixed code rate at the sending end, and the sending end can continuously generate encoded packets in a certain way and send them out. The receiving end can receive these encoded packets and try to decode them. If the decoding fails, the receiver can receive some more encoded packets and continue to try to decode. The receiver will repeat this process until the decoding is successful. At this time, the receiving end only needs to send a very simple feedback signal to inform the sending end that the decoding is successful, and then the sending end stops sending, thus completing the entire transmission process. At this time, the actual code rate of transmission depends on the number of coded packets actually sent, and the number of coded packets to be sent depends on the channel conditions at that time. How to make the actual code rate of transmission close to the channel capacity at that time becomes the key to the design of rateless codes question.

Luby提出了为二进制除删信道(BEC)设计的无速率码，称为LT码(见“LTCodes”，Proceedings of the 43rd Annual IEEE Symposium on Foundation ofComputer Science)。在发送端不知道信道除删率时，LT码能提供可靠的传输并且能够逼近信道容量。但是LT码并不适合于AWGN信道。LT码的编码器首先选择若干数据包，然后将它们的校验和作为编码包发送出去。LT码的发送端能够通过上述方式源源不断的产生编码包并发送出去。LT码的二部图如图1所示。图中有两类节点，圆圈表示变量节点(variable node)，方框表示校验节点(checknode)。而变量节点又分为两类，左边为信息节点(information node)代表数据包，右边为编码节点(parity node)代表编码包。与每一个校验节点相连的各节点的校验和为0。若从二部图的观点来看LT码，它的编码节点的度数恒定为1。由于这部分变量节点的消息永远不会更新，始终是接收到的初始值，它们的错误概率由信道状况决定而不会随着迭代次数的增加而趋向于0，从而形成一个固定的错误注入影响迭代译码过程，这会严重影响基于二部图的译码算法(例如：置信传播(Blief Propagation(BP))译码算法)的性能从而导致“差错平台”(Error Floor)的产生。Ravi Palanki等的文章“Rateless Codes on noisy channels”中的仿真结果清楚的说明了这一点。Shokrollahi也为BEC设计了无速率码，称为Raptor码(见“Raptor Codes”，IEEE Transactions on Information Theory，Vol.52，No.6，June2006)。虽然它能够解决LT码工作于AWGN信道时的“差错平台”问题，但它将LT码作为内码与低密度奇偶校验(low-density parity-check，LDPC)码级联，编译码的复杂度均提高。另外，实际应用中系统码被广泛采用，因为信道条件很好时不需要译码，可以降低译码消耗，LT码没有系统码的选项，而Raptor码的系统码选项又将进一步提高编译码复杂度。Luby proposed rateless codes designed for binary delete channels (BEC), called LT codes (see "LTCodes", Proceedings of the 43rd Annual IEEE Symposium on Foundation of Computer Science). When the channel erasure rate is not known at the sender, LT codes can provide reliable transmission and can approach the channel capacity. But LT codes are not suitable for AWGN channels. The encoder of the LT code first selects several data packets, and then sends their checksums as encoded packets. The sending end of the LT code can continuously generate coded packets and send them out through the above method. The bipartite graph of the LT code is shown in Figure 1. There are two types of nodes in the figure, circles represent variable nodes, and squares represent check nodes. The variable nodes are divided into two types, the information node on the left represents the data packet, and the parity node on the right represents the encoding packet. The checksum of each node connected to each check node is 0. If we look at LT codes from the point of view of a bipartite graph, the degree of its coded nodes is always 1. Since the messages of these variable nodes are never updated and are always the initial values received, their error probabilities are determined by the channel conditions and will not tend to 0 as the number of iterations increases, thus forming a fixed error injection effect Iterative decoding process, which will seriously affect the performance of bipartite graph-based decoding algorithms (such as: belief propagation (Blief Propagation (BP)) decoding algorithm) and lead to the generation of "error floor". This is clearly illustrated by the simulation results in the article "Rateless Codes on noisy channels" by Ravi Palanki et al. Shokrollahi also designed a rateless code for BEC, called Raptor code (see "Raptor Codes", IEEE Transactions on Information Theory, Vol.52, No.6, June2006). Although it can solve the "error floor" problem when the LT code works in the AWGN channel, it uses the LT code as the inner code and the low-density parity-check (low-density parity-check, LDPC) code cascaded, complicating the encoding and decoding process. degree increased. In addition, systematic codes are widely used in practical applications, because decoding is not required when channel conditions are good, which can reduce decoding consumption. LT codes do not have systematic code options, and Raptor codes have systematic code options that will further increase the complexity of encoding and decoding. Spend.

发明内容Contents of the invention

本发明的目的是提供一种适合于AWGN信道的无速率码编译码方法，我们把这种适合于AWGN信道的无速率码简称为SAR(Systematic AccumulateRateless)码。The purpose of the present invention is to provide a kind of rateless code encoding and decoding method suitable for AWGN channel, we abbreviate this rateless code suitable for AWGN channel as SAR (Systematic AccumulateRateless) code.

适合于AWGN信道的无速率码编译码方法包括编码方法和译码方法。编码方法如下，考虑编码发送端要发送m个数据包，每个数据包内由若干数据比特组成，每个数据包内部包括一个循环冗余校验码用于译码器判断译码是否成功。d₀，d₁，...，d_j...，d_m-1分别表示每一个数据包，下标j为数据包的编号。t_i表示编码包，其中i为编码包的编号。编码发送端首先将m个数据包发送出去形成系统码的信息比特部分，然后按如下步骤产生编码包t_i：The rateless encoding and decoding methods suitable for AWGN channels include encoding methods and decoding methods. The encoding method is as follows. Considering that the encoding sender needs to send m data packets, each data packet is composed of several data bits, and each data packet includes a cyclic redundancy check code for the decoder to judge whether the decoding is successful. d ₀ , d ₁ , . . _. , d _j . t _i represents an encoded packet, where i is the number of an encoded packet. The coding sender first sends m data packets to form the information bit part of the system code, and then generates the coding packet t _i as follows:

1)首先按使信息节点度数近似均匀分布的信息节点选择方式或者是使在某个码率处信息节点度数分布受限的信息节点选择方式产生m维二元域向量{G_ji}，m维二元域向量{G_ji}中为“1”的元素的个数为a_i；1) Firstly, an m-dimensional binary field vector {G _ji } is generated according to the information node selection method that makes the information node degree approximately uniformly distributed or the information node selection method that restricts the information node degree distribution at a certain code rate, and the m-dimensional The number of "1" elements in the binary field vector {G _ji } is a _i ;

2)m维二元域向量{G_ji}中的元素G_ji的取值为“0”或者“1”，元素G_ji为“1”，则它对应的编号为j的数据包将被选中，将这些被选中的数据包按比特作模2加后得到和值s_i，可以表示为：2) The value of the element G _ji in the m-dimensional binary domain vector {G _ji } is "0" or "1", and the element G _ji is "1", then its corresponding data packet numbered j will be selected , add these selected data packets by modulo 2 to get the sum value s _i , which can be expressed as:

sthe s ii == ΣΣ jj == 00 mm -- 11 dd jj GG jithe ji ,, ii == 0,1,20,1,2 .. .. ..

3)由累加器将s_i与上一个编码包t_i-1按比特作模2和得到新的编码包t_i，表示为下式：3) The accumulator performs modulo 2 sum of si and the last coded packet t _i-1 to obtain a new coded packet _{t i ,} expressed as the following formula:

                     t_i＝t_i-1+s_i，其中t_-1＝0t _i =t _i-1 +s _i , where t _-1 =0

发送端根据以上规则源源不断的产生编码包直到接收端告知它停止发送。The sending end continuously generates encoded packets according to the above rules until the receiving end tells it to stop sending.

译码方法包括如下步骤：The decoding method comprises the following steps:

首先接收数据包，m个数据包接收完成后开始译码：First receive data packets, and start decoding after m data packets are received:

1)译码器利用各个包内的循环冗余校验码判断m个数据包是否都正确，如果都正确，转入步骤5)；否则转入步骤2)；1) the decoder utilizes the cyclic redundancy check code in each packet to judge whether m data packets are all correct, if all correct, proceed to step 5); otherwise proceed to step 2);

2)译码器接收若干编码包；2) The decoder receives several encoded packets;

3)由于接收端知道每个编码包t_i对应的m维二元域向量{G_ji}，所以译码器可以准确的在接收端重构该码的二部图；3) Since the receiving end knows the m-dimensional binary field vector {G _ji } corresponding to each encoded packet t _i , the decoder can accurately reconstruct the bipartite graph of the code at the receiving end;

4)在步骤3)中重构的二部图上运行译码算法，这个译码算法是BP算法或改进的BP算法，然后再次转入操作步骤1)；4) Run the decoding algorithm on the bipartite graph reconstructed in step 3), this decoding algorithm is a BP algorithm or an improved BP algorithm, and then turn to operation step 1) again;

5)译码结束，接收端通过反馈信道告知发送端停止发送。5) After the decoding is completed, the receiving end notifies the sending end to stop sending through the feedback channel.

所述的使信息节点度数近似均匀分布的信息节点选择方式：为新增校验节点C_i选择a个信息节点的步骤如下，其中i为0时从步骤2)开始：The information node selection method that makes the degree of information nodes approximately uniformly distributed: the steps for selecting a information nodes for the newly added check node C _i are as follows, wherein when i is 0, start from step 2):

1)新增校验节点C_i与上一个编码节点P_i-1相连，从而与原有的m个信息节点I₀，I₁，...，I_m-1，(i-1)个编码节点P₀，P₁，...，P_i-1，(i-1)个校验节点C₀，C₁，...，C_i-1构成的二部图相连，需要更新C_i到各个信息节点的距离；1) The new check node C _i is connected to the previous encoding node P _i-1 , so as to be connected to the original m information nodes I ₀ , I ₁ ,..., I _m-1 , (i-1) Coding nodes P ₀ , P ₁ ,...,P _i-1 , (i-1) check nodes C ₀ , C ₁ ,...,C _i-1 are connected in a bipartite graph, and C needs to be updated The distance from _i to each information node;

2)为新增校验节点C_i选择一个离它距离最大的信息节点与之相连，由于二部图拓扑变化，需要更新新增校验节点C_i到各个信息节点的距离，重复步骤2)直到a个信息节点选择完成；2) For the new check node C _i, select an information node with the largest distance from it to connect to it. Due to the topology change of the bipartite graph, it is necessary to update the distance between the new check node C _i and each information node, and repeat step 2) Until a information node is selected;

3)新增校验节点C_i与新增编码节点P_i相连，形成了一张由m个信息节点I₀，I₁，...，I_m-1，i个编码节点P₀，P₁，...，P_i，i个校验节点C₀，C₁，...，C_i构成的新的二部图。3) The newly added check node C _i is connected to the newly added coding node P _i , forming a sheet consisting of m information nodes I ₀ , I ₁ ,..., I _m-1 , and i coding nodes P ₀ , P ₁ ,...,P _i , a new bipartite graph composed of i check nodes C ₀ , C ₁ ,...,C _i .

步骤2)中选择信息节点时，当距离最远的信息节点不止一个时我们将选择度数最小的一个，若此时度数最小的信息节点仍不止一个时，我们将随机选择其中一个。When selecting information nodes in step 2), when there is more than one information node with the farthest distance, we will choose the one with the smallest degree. If there are still more than one information nodes with the smallest degree at this time, we will randomly select one of them.

所述的使在某个码率处信息节点度数分布受限的信息节点选择方式：如果期望信息节点度数分布在码率为R时达到分布λ(x)，编码发送端将预先运用PEG(Progressive Edge-Growth)算法(见“Regular and Irregular Progressive Edge-GrowthTanner Graphs”’，IEEE Transactions On Information Theory，Vol.51，No.1，January2005)生成一张码率为R、信息节点度数分布为λ(x)的二部图，然后为新增校验节点C_i选择信息节点的方法如下：The information node selection method that limits the degree distribution of information nodes at a certain code rate: if the degree distribution of information nodes is expected to reach the distribution λ(x) when the code rate is R, the encoding sender will use PEG (Progressive Edge-Growth) algorithm (see "Regular and Irregular Progressive Edge-Growth Tanner Graphs"', IEEE Transactions On Information Theory, Vol.51, No.1, January 2005) generates a code rate R, information node degree distribution is λ( The bipartite graph of x), and then the method for selecting the information node for the new check node C _i is as follows:

1)当码率大于等于R时，编码器按照预先生成的二部图的连接关系为新增校验节点C_i选择a_i个信息节点；1) When the code rate is greater than or equal to R, the encoder selects a _i information nodes for the new check node C _i according to the connection relationship of the pre-generated bipartite graph;

2)当码率小于R时，编码器将使用使得信息节点度数近似均匀分布的信息节点选择方式为新增校验节点C_i选择a个信息节点。2) When the code rate is less than R, the encoder will use an information node selection method that makes the degree of information nodes approximately uniformly distributed to select a information nodes for the newly added check node C _i .

本发明的基本技术思想是在LT码的编码器后面再添加一个累加器，以使得二部图中编码节点的度数不再为1，从而解决LT码工作于AWGN信道的“差错平台”问题，同时采用了被广泛应用的系统码结构。The basic technical idea of the present invention is to add an accumulator again behind the encoder of the LT code, so that the degree of the coding node in the bipartite graph is no longer 1, thereby solving the "error platform" problem of the LT code working on the AWGN channel, At the same time, the widely used systematic code structure is adopted.

附图说明Description of drawings

图1是LT码的二部图；Fig. 1 is the bipartite graph of LT code;

图2是SAR码的编码示意图；Fig. 2 is the coding schematic diagram of SAR code;

图3是SAR码的译码流程图；Fig. 3 is the decoding flowchart of SAR code;

图4是SAR码的二部图；Figure 4 is a bipartite graph of the SAR code;

图5是LT码和信息节点度数近似均匀分布的SAR码在各速率点上的误比特率对比图，信噪比SNR(E_s/N₀)＝-1.9dB；Fig. 5 is a bit error rate comparison diagram of LT codes and SAR codes with approximately uniform distribution of information node degrees at each rate point, signal-to-noise ratio SNR (E _s /N ₀ )=-1.9dB;

图6是LT码和信息节点度数近似均匀分布的SAR码在各信噪比下的误比特率对比图，码率R＝0.5；Fig. 6 is a bit error rate comparison diagram of LT codes and SAR codes with approximately uniform distribution of information node degrees at various signal-to-noise ratios, code rate R=0.5;

图7是LT码和在R＝0.5处信息节点度数分布受限的SAR码在各速率点上的误比特率对比图，信噪比SNR(E_s/N₀)＝-1.9dB。Fig. 7 is a comparison diagram of the bit error rate at each rate point between the LT code and the SAR code with restricted information node degree distribution at R=0.5, and the signal-to-noise ratio SNR (E _s /N ₀ )=-1.9dB.

具体实施方式Detailed ways

适合于AWGN信道的无速率码编译码方法，包括编码方法和译码方法。其特征在于编码方法如下，考虑编码发送端要发送10000个数据包，每个数据包内由若干数据比特组成，每个数据包内部包括一个循环冗余校验码，这个循环冗余校验码采用CRC32，用于译码器判断译码是否成功。d₀，d₁，...，d_j...，d_m-1分别表示每一个数据包，下标j为数据包的编号。t_i表示编码包，其中i为编码包的编号。编码发送端首先将10000个数据包发送出去形成系统码的信息比特部分，然后按如下步骤产生编码包t_i：A rateless coding and decoding method suitable for AWGN channels, including a coding method and a decoding method. It is characterized in that the encoding method is as follows. Considering that the encoding sender needs to send 10,000 data packets, each data packet is composed of several data bits, and each data packet includes a cyclic redundancy check code, the cyclic redundancy check code CRC32 is used for the decoder to judge whether the decoding is successful. d ₀ , d ₁ , . . _. , d _j . t _i represents an encoded packet, where i is the number of an encoded packet. The encoding sender first sends 10,000 data packets to form the information bit part of the system code, and then generates the encoding packet t _i as follows:

1)首先按使信息节点度数近似均匀分布的信息节点选择方式或者是使在某个码率处信息节点度数分布受限的信息节点选择方式产生10000维二元域向量{G_ji}，10000维二元域向量{G_ji}中为“1”的元素的个数为a_i；1) Firstly, a 10,000-dimensional binary field vector {G _ji } is generated according to the information node selection method that makes the information node degree approximately uniformly distributed or the information node selection method that restricts the information node degree distribution at a certain code rate, and the 10,000-dimensional The number of "1" elements in the binary domain vector {G _ji } is a _i ;

2)10000维二元域向量{G_ji}中的元素G_ji的取值为“0”或者“1”，元素G_ji为“1”，则它对应的编号为j的数据包将被选中，将这些被选中的数据包按比特作模2加后得到和值s_i，可以表示为：2) The value of the element G _ji in the 10000-dimensional binary domain vector {G _ji } is "0" or "1", and the element G _ji is "1", then its corresponding data packet numbered j will be selected , add these selected data packets by modulo 2 to get the sum value s _i , which can be expressed as:

sthe s ii == ΣΣ jj == 00 mm -- 11 dd jj GG jithe ji ,, ii == 0,1,20,1,2 .. .. ..

3)由累加器将s_i与上一个编码包t_i-1按比特作模2和得到新的编码包t_i，表示为下式：3) The accumulator performs modulo 2 sum of si and the last coded packet t _i-1 to obtain a new coded packet _{t i ,} expressed as the following formula:

                    t_i＝t_i-1+s_i，其中t_-1＝0t _i =t _i-1 +s _i , where t _-1 =0

发送端根据以上规则源源不断的产生编码包直到接收端告知它停止发送。The sending end continuously generates encoded packets according to the above rules until the receiving end tells it to stop sending.

译码方法包括如下步骤：The decoding method comprises the following steps:

首先接收数据包，10000个数据包接收完成后开始译码：First receive data packets, and start decoding after receiving 10,000 data packets:

1)译码器利用各个包内的循环冗余校验码判断10000个数据包是否都正确，如果都正确，转入步骤5)；否则转入步骤2)；1) the decoder utilizes the cyclic redundancy check code in each packet to judge whether the 10,000 data packets are all correct, if all correct, proceed to step 5); otherwise proceed to step 2);

2)译码器接收500编码包；2) The decoder receives 500 encoded packets;

3)由于接收端知道每个编码包t_i对应的10000维二元域向量{G_ji}，所以译码器可以准确的在接收端重构该码的二部图；3) Since the receiving end knows the 10,000-dimensional binary field vector {G _ji } corresponding to each encoded packet t _i , the decoder can accurately reconstruct the bipartite graph of the code at the receiving end;

4)在步骤3)中重构的二部图上运行译码算法，这个译码算法是BP算法或改进的BP算法，然后再次转入操作步骤1)；4) Run the decoding algorithm on the bipartite graph reconstructed in step 3), this decoding algorithm is a BP algorithm or an improved BP algorithm, and then turn to operation step 1) again;

5)译码结束，接收端通过反馈信道告知发送端停止发送。5) After the decoding is completed, the receiving end notifies the sending end to stop sending through the feedback channel.

当发现接收到的编码包不足以正确译码时，接收端需要再接收500个编码包。当接收端收到m个数据包和n个编码包时，对应的码率为：When it is found that the received encoded packets are not enough for correct decoding, the receiving end needs to receive another 500 encoded packets. When the receiving end receives m data packets and n encoded packets, the corresponding code rate is:

RR == mm mm ++ nno

为了表示方便，我们用码率的倒数R^-1来刻画码率的变化。每次多接收Δn个编码包后，码率变化为ΔR^-1：For the convenience of expression, we use the reciprocal R ^-1 of the code rate to describe the change of the code rate. After receiving Δn more encoded packets each time, the code rate changes to ΔR ^-1 :

ΔΔ RR -- 11 == ΔnΔ n mm

此处Δn为500，所以ΔR^-1为0.05。表1给出了接收端收到的编码包数目从7500到10000对应的各个码率。Here, Δn is 500, so ΔR ^-1 is 0.05. Table 1 shows the code rates corresponding to the number of encoded packets received by the receiving end from 7500 to 10000.

  nn   75007500   80008000   85008500   90009000   95009500   1000010000   R^-1 R ^-1   1.751.75   1.801.80   1.851.85   1.901.90   1.951.95   2.002.00

                             表1 Table 1

根据以上对编码和译码的描述，SAR码的二部图如图4所示。图中有两类节点，圆圈表示变量节点(variable node)，方框表示校验节点(check node)。而变量节点又分为两类，左边为信息节点(information node)，右边为编码节点(paritynode)。信息节点一共有m个，分别表示为I₀，I₁，...，I_j，...，I_m-1，与数据包d₀，d₁，...，d_j，...，d_m-1一一对应。编码节点分别表示为P₀，P₁，...，P_i，...，与编码包t₀，t₁，...，t_i，...一一对应。校验节点分别表示为C₀，C₁，...，C_i，...。与一个校验节点相连的各节点的校验和为0。SAR码的二部图与一般的二部图最大区别在于它是可以不断扩大的。每产生一个新的编码包t_i，图中就会增加一个新的编码节点P_i和一个新的校验节点C_i，所以随着编码包的增多，这张图会越来越大。其中新增校验节点C_i与编码节点的连接关系是固定的，除了第一个校验节点C₀只与P₀相连外，C_i总是与上一个编码节点P_i-1及新增的编码节点P_i相连。According to the above description of encoding and decoding, the bipartite graph of SAR code is shown in Figure 4. There are two types of nodes in the figure, circles represent variable nodes, and squares represent check nodes. The variable nodes are divided into two types, the left is the information node (information node), and the right is the code node (paritynode). There are a total of m information nodes, represented as I ₀ , I ₁ , ..., I _j , ..., I _m-1 , and data packets d ₀ , d ₁ , ..., d _j , .. ., d _m-1 one-to-one correspondence. The encoding nodes are _denoted as P ₀ , P ₁ , _{. .} . , P _i , . Check nodes are denoted as C ₀ , C ₁ , . . . , C _i , . . . respectively. The checksum of each node connected to a check node is 0. The biggest difference between the bipartite graph of the SAR code and the general bipartite graph is that it can be continuously expanded. Every time a new encoding packet t _i is generated, a new encoding node P _i and a new check node C _i will be added in the graph, so as the number of encoding packets increases, the graph will become larger and larger. Among them, the connection relationship between the new check node C _i and the coding node is fixed, except that the first check node C ₀ is only connected to P ₀ , and C _i is always connected to the previous coding node P _i-1 and the newly added The coding nodes P _i are connected.

二部图中，连接到某个节点的边的总数称为这个节点的度数。我们定义信息节点的度数分布为：In a bipartite graph, the total number of edges connected to a node is called the degree of the node. We define the degree distribution of information nodes as:

λλ (( xx )) == ΣΣ ii λλ ii xx ii -- 11

λ_i表示在所有连接校验节点和信息节点所有边中，与度数为i的信息节点相连的边所占的比例。λ _i represents the proportion of edges connected to information nodes with degree i among all edges connecting check nodes and information nodes.

从图2的编码器示意图可以看出，SAR码设计的关键问题就是如何产生{G_ji}的问题，也就是如何选择产生编码包t_i的a_i个数据包的问题。从图论的观点看，发送端产生一个编码包t_i，对应的二部图中增加一个校验节点C_i和编码节点P_i，新增的校验节点C_i有a_i条边与信息节点相连，那么，选择产生t_i的数据包的问题本质上就是为新增的信息节点C_i选择a_i个信息节点的问题，而不同的选择方式将使得信息节点在每个码率处的度数分布不同，也就使得SAR码的性能不同。本发明提出了两种易于实现，性能较好的信息节点选择方式。It can be seen from the schematic diagram of the encoder in Figure 2 that the key issue in SAR code design is how to generate {G _ji }, that is, how to select the a _i data packets that generate the encoded packet t _i . From the point of view of graph theory, the sender generates an encoded packet t _i , and a check node C _i and an encoding node P _i are added to the corresponding bipartite graph. The newly added check node C _i has a _i edge and information The nodes are connected, then, the problem of selecting the data packet that generates t _i is essentially the problem of selecting a _i information nodes for the newly added information node C _i , and different selection methods will make the information nodes at each code rate Different degree distributions lead to different performances of SAR codes. The invention proposes two easy-to-implement and better-performance information node selection methods.

所述的使信息节点度数近似均匀分布的信息节点选择方式：此方式中采用的a_i为常数a，此处a取为“4”。这种方式将使得信息节点的度数分布在各个码率处近似均匀，所以我们将这种方式称为使信息节点度数分布近似均匀的信息节点选择方式，将采用这种方式的SAR码称为信息节点度数近似均匀分布的SAR码。The information node selection method that makes the degree of information nodes approximately evenly distributed: a _i used in this method is a constant a, where a is taken as "4". This method will make the degree distribution of information nodes approximately uniform at each code rate, so we call this method an information node selection method that makes the degree distribution of information nodes approximately uniform, and the SAR code using this method is called information SAR codes with approximately uniform distribution of node degrees.

此处需要说明的是：二部图中一个节点经过一些边与另一个节点相连，这些边形成一条路径，路径中边的数目为该路径的长度；连接两个节点最短路径的长度为这两个节点的距离，如果两个节点之间没有路径，则它们的距离为无穷大。如前所述，SAR码的译码过程中采用的译码算法都是基于二部图的，二部图中圈的长度将直接影响译码算法的性能，圈的长度越大译码性能越好，所以使得生成的SAR码的二部图中的圈尽量的长是为新增校验节点选择与之相连的信息节点的基本原则，这就要求我们在选择信息节点时永远选择距离该校验节点最远的。What needs to be explained here is: a node in the bipartite graph is connected to another node through some edges, and these edges form a path, and the number of edges in the path is the length of the path; the length of the shortest path connecting two nodes is the two The distance between two nodes is infinite if there is no path between them. As mentioned above, the decoding algorithms used in the decoding process of SAR codes are all based on bipartite graphs. The length of the circle in the bipartite graph will directly affect the performance of the decoding algorithm. The larger the length of the circle, the better the decoding performance. Ok, so making the circle in the bipartite graph of the generated SAR code as long as possible is the basic principle of selecting the information node connected to it for the new check node, which requires us to always choose the distance from the school when selecting the information node. The farthest from the test point.

作为无速率码，SAR码的发送端必须能够源源不断的发送编码包，在每产生一个编码包t_i时，二部图中增加一个校验节点C_i，发送端需要为新增的校验节点C_i选择与之相连的4个信息节点。为新增校验节点C_i选择4个信息节点的步骤如下，其中i为0时从步骤2)开始：As a rateless code, the sender of the SAR code must be able to continuously send encoded packets. When each encoded packet t _i is generated, a check node C _i is added in the bipartite graph, and the sender needs to check the newly added Node C _i selects 4 information nodes connected to it. The steps for selecting 4 information nodes for the new check node C _i are as follows, where i is 0 and starts from step 2):

1)新增校验节点C_i与上一个编码节点P_i-1相连，从而与原有的10000个信息节点I₀，I₁，...，I₉₉₉₉，(i-1)个编码节点P₀，P₁，...，P_i-1，(i-1)个校验节点C₀，C₁，...，C_i-1构成的二部图相连，需要更新C_i到各个信息节点的距离；1) The new check node C _i is connected to the previous encoding node P _i-1 , so as to be connected to the original 10000 information nodes I ₀ , I ₁ ,..., I ₉₉₉₉ , (i-1) encoding nodes P ₀ , P ₁ ,..., P _i-1 , (i-1) check nodes C ₀ , C ₁ ,..., C _i-1 are connected in a bipartite graph, and C _i needs to be updated to The distance of each information node;

2)为新增校验节点C_i选择一个离它距离最大的信息节点与之相连，由于二部图拓扑变化，需要更新新增校验节点C_i到各个信息节点的距离，重复步骤2)直到4个信息节点选择完成；2) For the new check node C _i, select an information node with the largest distance from it to connect to it. Due to the topology change of the bipartite graph, it is necessary to update the distance between the new check node C _i and each information node, and repeat step 2) Until the selection of 4 information nodes is completed;

3)新增校验节点C_i与新增编码节点P_i相连，形成了一张由10000个信息节点I₀，I₁，...，I₉₉₉₉，i个编码节点P₀，P₁，...，P_i，i个校验节点C₀，C₁，...，C_i构成的新的二部图。3) The newly added check node C _i is connected to the newly added coding node P _i , forming a sheet consisting of 10000 information nodes I ₀ , I ₁ ,..., I ₉₉₉₉ , i coding nodes P ₀ , P ₁ , ..., P _i , a new bipartite graph composed of i check nodes C ₀ , C ₁ , ..., C _i .

经过以上3步，生成了新的二部图，校验节点和编码节点都比原二部图增加一个，边也相应增加了。同时为新增校验节点选择好了4个信息节点。After the above 3 steps, a new bipartite graph is generated, the check node and the encoding node are increased by one compared with the original bipartite graph, and the edges are also increased accordingly. At the same time, four information nodes have been selected for the new check node.

在步骤2)中选择信息节点时，当距离最远的信息节点不止一个时我们将选择度数最小的一个，若此时度数最小的信息节点仍不止一个时，我们将随机选择其中一个。我们总是优先选择度数最小的信息节点，这会使得信息节点的度数分布趋向均匀。When selecting information nodes in step 2), when there is more than one information node with the farthest distance, we will choose the one with the smallest degree. If there are still more than one information nodes with the smallest degree at this time, we will randomly select one of them. We always give priority to the information node with the smallest degree, which will make the degree distribution of information nodes tend to be even.

所述的使在某个码率处信息节点度数分布受限的信息节点选择方式：由于这种选择方式只在某一个码率R处限制信息节点的度数分布，所以我们将这种方式称为使在某个码率处信息节点度数分布受限的信息节点选择方式，将采用这种方式的SAR码称为在某个码率处信息节点度数分布受限的SAR码。The information node selection method that limits the degree distribution of information nodes at a certain code rate: since this selection method only limits the degree distribution of information nodes at a certain code rate R, we call this method The information node selection method that restricts the degree distribution of information nodes at a certain code rate, and the SAR code using this method is called a SAR code with restricted degree distribution of information nodes at a certain code rate.

若每个数据包只有一个比特，工作于某个速率的SAR码实际上就是IRA(Irregular Repeat Accumulate)码(见“Irregular Repeat-Accumulate codes，”Proc.2nd Int.Symp.Turbo codes & related topics，Sep.2000)；若数据包内有n个比特，工作于某个速率的SAR码也就是n个并行独立的IRA码。换句话说，SAR码本质上就是速率可变的IRA码。If each data packet has only one bit, the SAR code working at a certain rate is actually an IRA (Irregular Repeat-Accumulate) code (see "Irregular Repeat-Accumulate codes," Proc.2nd Int.Symp.Turbo codes & related topics, Sep.2000); if there are n bits in the data packet, the SAR code working at a certain rate is n parallel independent IRA codes. In other words, SAR codes are essentially rate-variable IRA codes.

AWGN信道的信道参数用σ刻画，它表示信道噪声的标准方差。某个速率的IRA码，给定它的信息节点度数分布表示为λ(x)，则这个码对应一个信道参数门限值σ^*，当信道参数σ小于这个门限，可以保证信息可靠传输；而当信道参数σ大于这个门限，信息则不能可靠传输。在特定速率R下，通常优化λ(x)以使得IRA码门限σ^*尽量的大，也就使得σ^*对应的信道容量尽量的小，进而使得R尽量的逼近信道容量。很多文献中都讨论过λ(x)的优化问题，同时给出了一些逼近信道容量的分布。The channel parameter of the AWGN channel is described by σ, which represents the standard deviation of the channel noise. For an IRA code of a certain rate, given its information node degree distribution expressed as λ(x), this code corresponds to a channel parameter threshold σ ^* , when the channel parameter σ is smaller than this threshold, reliable information transmission can be guaranteed; and When the channel parameter σ is greater than this threshold, information cannot be transmitted reliably. At a specific rate R, λ(x) is usually optimized to make the IRA code threshold σ ^* as large as possible, which means that the channel capacity corresponding to σ ^* is as small as possible, and then makes R as close to the channel capacity as possible. The optimization problem of λ(x) has been discussed in many literatures, and some distributions that approximate the channel capacity are given.

对于IRA码，在各个速率上得到的逼近信道容量的信息节点度数分布是很不同的，所以对于SAR码，随着编码包的增多，码率下降，信息节点的度数分布不断变化，各个码率处都保持信息节点度数分布逼近信道容量是很难的。我们提出一种次优但易于实现的方法，即只保证在某一个特定速率R处，信息节点度数分布达到逼近信道容量的分布，其它速率处信息节点的度数分布与具体的实现方式相关，不作任何限制。这种选择方式只在某一个码率R处限制信息节点的度数分布。For IRA codes, the degree distribution of information nodes approaching the channel capacity obtained at each rate is very different. Therefore, for SAR codes, as the number of coded packets increases, the code rate decreases, and the degree distribution of information nodes changes continuously. Each code rate It is difficult to keep the degree distribution of information nodes close to the channel capacity everywhere. We propose a sub-optimal but easy-to-implement method, which only guarantees that at a certain rate R, the degree distribution of information nodes is close to the distribution of channel capacity, and the degree distribution of information nodes at other rates is related to the specific implementation. any restrictions. This selection method only limits the degree distribution of information nodes at a certain code rate R.

实施中要求信息节点度数分布在码率为0.5时能够达到文献“IrregularRepeat-Accumulate Codes”表3中优化后的分布λ(x)，该分布的各个参数如表2。In the implementation, it is required that the degree distribution of information nodes can reach the optimized distribution λ(x) in Table 3 of the document "IrregularRepeat-Accumulate Codes" when the code rate is 0.5. The parameters of this distribution are shown in Table 2.

  其余参数Other parameters   λ₂ lambda ₂   λ₃ lambda ₃   λ₇ lambda ₇   λ₈ lambda ₈   λ₁₈ lambda ₁₈   λ₂₀ lambda ₂₀   λ₅₅ λ ₅₅   λ₅₈ λ ₅₈   00   0.05771280.0577128   0.1170570.117057   0.21899220.2189922   0.03338440.0333844   0.21472210.2147221   0.07522590.0752259   0.08086760.0808676   0.2020380.202038

                            表2 Table 2

发送端需要根据表2的度数分布利用PEG算法预先生成一张码率为0.5的二部图，图中有10000个信息节点，10000个校验节点，10000编码节点。表3为各个度数的信息节点的个数。The sender needs to use the PEG algorithm to pre-generate a bipartite graph with a code rate of 0.5 according to the degree distribution in Table 2. There are 10,000 information nodes, 10,000 check nodes, and 10,000 encoding nodes in the graph. Table 3 shows the number of information nodes of each degree.

  度数degrees   2 2   33   77   8 8   1818   2020   5555   5858   个数number   23282328   31473147   25232523   337337   962962   303303   119119   281281

                            表3 table 3

由表2知，与每个校验节点相连的信息节点平均个数为8。It is known from Table 2 that the average number of information nodes connected to each check node is 8.

该方式为新增校验节点C_i选择信息节点的方法如下：In this way, the method of selecting an information node for a new check node C _i is as follows:

1)当码率大于等于0.5时，即在发送的编码包数目小于等于10000个时，编码器按照预先生成的二部图的连接关系为新增校验节点C_i选择a_i个信息节点，a_i取决于生成二部图中的连接关系；1) When the code rate is greater than or equal to 0.5, that is, when the number of encoded packets sent is less than or equal to 10000, the encoder selects a _i information nodes for the new check node C _i according to the connection relationship of the pre-generated bipartite graph, a _i depends on the connection relationship in the generated bipartite graph;

2)当码率小于0.5时，即在发送的编码包数目大于10000个时，编码器将使用使得信息节点度数近似均匀分布的方式为新增校验节点C_i选择a个信息节点，因为预先生成的二部图中与每个校验节点相连的信息节点平均个数为8，所以此处a取8。2) When the code rate is less than 0.5, that is, when the number of encoded packets sent is greater than 10,000, the encoder will select a information node for the newly added check node C _i in a way that makes the degree of the information node approximately uniformly distributed, because in advance The average number of information nodes connected to each check node in the generated bipartite graph is 8, so here a takes 8.

1. non-rate code coding/decoding method that is suitable for additive white gaussian noise channels; Comprise coding method and interpretation method; It is characterized in that coding method is following, consider that the coding transmitting terminal will send m packet, is made up of the plurality of data bit in each packet; Each packet inside comprises that a CRC is used for decoder and judges whether decoding is successful, d ₀, d ₁..., d _j..., d _M-1Represent each packet respectively, subscript j is the numbering of packet, t _iThe presentation code bag, wherein i is the numbering of encoded packets, the coding transmitting terminal at first sends the information bit part that forms systematic code with m packet, produces encoded packets t then as follows _i:

1) at first by making the approximate equally distributed information node selection mode of the information node number of degrees or making the information node selection mode generation m dimension two element field vector { G that distributes limited at certain code check place information node number of degrees _Ji, m dimension two element field vector { G _JiIn for the number of the element of " 1 " be a _i

2) m dimension two element field vector { G _JiIn element G _JiValue be " 0 " perhaps " 1 ", element G _JiBe " 1 " that then its corresponding packet that is numbered j is with selected, the packet that these are selected makes to obtain after mould 2 adds and be worth s by bit _i, can be expressed as:

s i = Σ j = 0 m - 1 d j G ji , i = 0,1,2 . . .

3) by accumulator with s _iWith a last encoded packets t _I-1Make mould 2 and obtain new encoded packets t by bit _i, be expressed as following formula:

t _i=t _I-1+ s _i, t wherein _-1=0

Transmitting terminal produces encoded packets endlessly according to above rule and informs that up to receiving terminal it stops to send;

Interpretation method comprises the steps:

At first receive packet, begin decoding after m packet finishes receiving:

1) decoder utilizes the CRC in each bag to judge that whether m packet be all correct, if all correct, changes step 5) over to; Otherwise change step 2 over to);

2) decoder receives some encoded packets;

3) because receiving terminal is known each encoded packets t _iCorresponding m dimension two element field vector { G _Ji, so decoder can be accurately at the bigraph (bipartite graph) of this sign indicating number of receiving terminal reconstruct;

4) in step 3), move decoding algorithm on the bigraph (bipartite graph) of reconstruct, this decoding algorithm is BP algorithm or improved BP algorithm, and then changes operating procedure 1 over to);

5) decoding finishes, and receiving terminal informs that through feedback channel transmitting terminal stops to send;

The described information node number of degrees that make are similar to equally distributed information node selection mode: be newly-increased check-node C _iSelect the step of a information node following, wherein i began from step b) in 0 o'clock:

A) newly-increased check-node C _iWith a last coding nodes P _I-1Link to each other, thus with original m information node I ₀, I ₁..., I _M-1, (i-1) individual coding nodes P ₀, P ₁..., P _I-1, (i-1) individual check-node C ₀, C ₁..., C _I-1The bigraph (bipartite graph) that constitutes links to each other, and needs to upgrade C _iDistance to each information node;

B) be newly-increased check-node C _iSelect one to be attached thereto apart from information node of maximum, because the bigraph (bipartite graph) change in topology needs to upgrade newly-increased check-node C from its _iTo the distance of each information node, repeat to select to accomplish up to a information node;

C) newly-increased check-node C _iWith newly-increased coding nodes P _iLink to each other, formed one by m information node I ₀, I ₁..., I _M-1, i coding nodes P ₀, P ₁..., P _i, i check-node C ₀, C ₁..., C _iThe new bigraph (bipartite graph) that constitutes;

When selecting information node step 2), we will select minimum one of the number of degrees when more than one of the information node of furthest, if this moment number of degrees minimum still more than one of information node the time, we will select one of them at random;

Described making: if the expectation information node number of degrees reach distribution λ (x) when being distributed in code check for R at the limited information node selection mode of certain code check place information node number of degrees distribution; It is the bigraph (bipartite graph) that R, the information node number of degrees are distributed as λ (x) that the coding transmitting terminal will use the PEG algorithm to generate a code check in advance, is newly-increased check-node C then _iSelect the method for information node following:

D) when code check during more than or equal to R, encoder is newly-increased check-node C according to the annexation of the bigraph (bipartite graph) that generates in advance _iSelect a _iIndividual information node;

E) when code check during less than R, encoder will use and make the approximate equally distributed information node selection mode of the information node number of degrees be newly-increased check-node C _iSelect a information node.