CN109150384B

CN109150384B - 极化码编码的方法和装置

Info

Publication number: CN109150384B
Application number: CN201710503600.3A
Authority: CN
Inventors: 徐晨; 张公正; 黄凌晨; 张华滋; 陈莹; 李榕
Original assignee: Huawei Technologies Co Ltd
Current assignee: Huawei Technologies Co Ltd
Priority date: 2017-06-27
Filing date: 2017-06-27
Publication date: 2020-11-17
Anticipated expiration: 2037-06-27
Also published as: CN109150384A

Abstract

本申请提供了一种极化码编码的方法，能够提高极化码的译码性能。该方法包括：发送设备获取待编码比特；发送设备采用长度为N的母码序列对待编码比特进行极化编码，得到编码后的序列。

Description

极化码编码的方法和装置

技术领域

本申请涉及信道编码领域，并且更具体地，涉及一种极化码编码的方法和装置。

背景技术

信道编码作为最基本的无线接入技术，在保证数据的可靠性传输方面起到至关重要的作用。在现有的无线通信系统中，一般采用Turbo码、低密度奇偶校验码(Low DensityParity Check，LDPC)和极化(Polar)码进行信道编码。Turbo码不能够支持过低或过高码率的信息传输。而对于中短包传输，Turbo码和LDPC码也由于自身编译码的特点，在有限码长下很难达到理想的性能。在实现方面，Turbo码和LDPC码在编译码实现过程中具有较高的计算复杂度。极化(Polar)码是理论上证明可以取得香农容量，且具有相对简单的编译码复杂度的好码，因而得到了越来越广泛的应用。

但是，随着无线通信系统的快速演进，未来的通信系统(例如，5G)将会出现一些新的特点。例如，最典型的三个通信场景包括增强型移动互联网(Enhance MobileBroadband，eMBB)、海量机器连接通信(Massive Machine Type Communication，mMTC)和高可靠低延迟通信(Ultra Reliable Low Latency Communication，URLLC)。这些通信场景对于极化码的编译码性能提出了更高的要求。

现阶段，极化码在应用过程中的编译码性能还并不理想，需要进一步提高。

发明内容

本申请提供一种极化码编码的方法和装置，能够提高极化码的译码性能。

第一方面，本申请提供一种极化码编码的方法，该方法包括：发送设备获取待编码比特；发送设备采用长度为N的母码序列对待编码比特进行极化编码，得到编码后的序列。

在一种可能的实现方式中，该方法包括：该长度为N的母码序列是根据一个长度为N₀的序列生成的，该长度为N的母码序列是该长度为N₀的序列中的一部分或者全部。

在一种可能的实现方式中，该长度为N₀的序列如序列1至序列16中的任意一个所示。

这里所说的序列1至序列16参见说明书部分。

在一种可能的实现方式中，该长度为N₀的序列中包括按照信道容量或者信道可靠性进行排序的N₀个极化信道的索引。

在一种可能的实现方式中，该方法还包括：发送设备根据初始信道容量和N₀，获取该长度为N₀的序列。

在一种可能的实现方式中，该长度为N₀的序列满足如下特性:所述长度为N₀的序列的对称长度的子序列满足相同的排序。

在一种可能的实现方式中，该方法还包括：发送设备根据M个序列和T个指示序列，确定该长度为N的母码序列，其中，所述M大于或等于2，所述T大于或等于1。

在一种可能的实现方式中，发送设备根据M个序列和T个指示序列，确定该长度为N的母码序列之前，该方法还包括：发送设备存储第一序列和该T个指示序列；发送设备获取M个序列中的第一序列，该M个序列中剩余M-1个序列是根据第一序列生成的；发送设备获取该T个指示序列。

在一种可能的实现方式中，发送设备获所述第一序列，包括：发送设备从第三序列中读取第一序列，第一序列包括的n个索引为第三序列中第(i·n+1)个位置的索引至第(i+1)·n个位置的索引分别减去i·n得到的，i≥0且为整数，第三序列中的索引是按照极化信道的可靠度或者信道容量的大小顺序排列的。

在一种可能的实现方式中，发送设备获取指示序列，包括：发送设备从第四序列中读取第五序列，第五序列包括的M·n个索引为第四序列中第(j·M·n+1)个位置的索引至第(j+1)·M·n个位置的索引，j≥0且为整数，第四序列中的索引是按照各自对应的极化信道的可靠度的大小顺序排列的；发送设备根据第五序列生成指示序列。

第二方面，本申请提供一种极化码编码的方法，该方法包括：发送设备获取第一序列，第一序列包括n个信道的索引，n≥1且为整数；发送设备根据第一序列，确定M-1个第二序列，该所述M-1个第二序列中每个第二序列包括n个信道的索引；发送设备根据指示序列，对第一序列和该M-1个第二序列中的索引进行排序，生成长度为M·n的母码序列，M·n为2的整数次幂。

需要说明的是，这里的M-1个第二序列互不相同。每个第二序列是对第一序列增加不同的偏移量得到的。即，在本申请实施例中，多个第二序列是将第一序列作为基础序列，通过对基础序列增加不同的偏移量得到的偏移序列。这多个第二序列中包括的极化信道的索引互不相同。

在一种可能的实现方式中，发送设备根据第一序列，确定该M-1第二个序列，包括：发送设备对第一序列中的每个索引依次增加偏移量q·n，得到该M-1个第二序列中的第q个第二序列，q为大于或等于1的整数。

在一种可能的实现方式中，指示序列包括M·n个元素，指示序列中的每个元素等于第一数值或第二数值，以及，发送设备根据该指示序列，对第一序列和该M-1个第二序列中的索引进行排序，生成长度为M·n的母码序列，包括：发送设备依次读取指示序列中的M·n个元素；若指示序列中第i个元素等于第一数值，则发送设备从第一序列中读取索引，若指示序列中的第i个元素等于第二数值，则发送设备从该M-1个第二序列中读取索引，i遍历[1,M·n]；发送设备将依次读取的索引构成的序列确定为母码序列。

在一种可能的实现方式中，发送设备获取第一序列，包括：发送设备从第三序列中读取第一序列，第一序列包括的n个信道的索引为第三序列中第(i·n+1)个位置的索引至第(i+1)·n个位置的索引分别减去i·n得到的，i≥0且为整数，第三序列包括的索引的个数大于或等于n，第三序列中的索引是按照各自对应的极化信道的可靠度或者信道容量的大小顺序排列的。

在一种可能的实现方式中，该方法还包括：发送设备从第四序列中读取第五序列，第五序列包括2n个索引，该2n个索引为第四序列中第(j·2n+1)个位置的索引至第(j+1)·2n个位置的索引，j≥0且为整数，第四序列包括的索引的个数大于或等于2n，第四序列中的索引是按照各自对应的极化信道的可靠度的大小顺序排列的；发送设备根据第五序列，生成指示序列。

第三方面，本申请提供一种极化码编码的装置，用于执行第一方面或第一方面的任意可能的实现方式中的方法。具体地，该装置包括执行第一方面或第一方面的任意可能的实现方式中的方法的单元。

第四方面，本申请提供一种极化码编码的装置，用于执行第二方面或第二方面的任意可能的实现方式中的方法。具体地，该装置包括执行第二方面或第二方面的任意可能的实现方式中的方法的单元。

第五方面，本申请提供一种设备，该设备包括一个或多个处理器，一个或多个存储器，一个或多个收发器(每个收发器包括发射机和接收机)。发射机或接收机通过天线收发信号。存储器用于存储计算机程序指令(或者说，代码)。处理器用于执行存储器中存储的指令，当指令被执行时，处理器执行第一方面或第一方面的任意可能的实现方式中的方法。

第六方面，本申请提供一种设备，该设备包括一个或多个处理器，一个或多个存储器，一个或多个收发器(每个收发器包括发射机和接收机)。发射机或接收机通过天线收发信号。存储器用于存储计算机程序指令(或者说，代码)。处理器用于执行存储器中存储的指令，当指令被执行时，处理器执行第二方面或第二方面的任意可能的实现方式中的方法。

第七方面，本申请提供一种计算机可读存储介质，该计算机可读存储介质中存储有指令，当其在计算机上运行时，使得计算机执行上述第一方面或第一方面的任意可能的实现方式中的方法。

第八方面，本申请提供一种计算机可读存储介质，该计算机可读存储介质中存储有指令，当其在计算机上运行时，使得计算机执行上述第二方面或第二方面的任意可能的实现方式中的方法。

第九方面，本申请提供一种芯片(或者说，芯片系统)，包括存储器和处理器，存储器用于存储计算机程序，处理器用于从存储器中调用并运行该计算机程序，使得安装有该芯片的通信设备执行上述第一方面和第二方面及其任一种可能的实现方式中的方法。

应理解这里的通信设备可以为第一方面和第二方面的发送设备。

第十方面，本申请提供一种编码装置，该编码装置具有实现上述第一方面和第一方面的任一种可能的设计中发送设备行为的功能。所述功能可以通过硬件实现，也可以通过硬件执行相应的软件实现。所述硬件或软件包括一个或多个与上述功能相对应的模块。

在一个可能的设计中，当所述功能的部分或全部通过硬件实现时，所述编码装置包括：输入接口电路，用于获取待编码比特；逻辑电路，用于执行上述第一方面和第二方面的及其任意一种可能的设计中发送设备的行为；输出接口电路，用于输出极化编码后的序列。

可选的，所述编码装置可以是芯片或者集成电路。

在一个可能的设计中，当所述功能的部分或全部通过软件实现时，所述编码装置包括：存储器，用于存储程序；处理器，用于执行所述存储器存储的所述程序，当所述程序被执行时，所述编码装置可以实现如上述第一方面和第二方面及其任意一种可能的设计中所述的方法。

可选的，上述存储器可以是物理上独立的单元，也可以与处理器集成在一起。

在一个可能的设计中，当所述功能的部分或全部通过软件实现时，所述编码装置包括处理器。用于存储程序的存储器位于所述编码装置之外，处理器通过电路/电线与存储器连接，用于读取并执行所述存储器中存储的程序。

根据本申请实施例提供的极化编码的方法，确定得到的母码序列具有嵌套特性和对称性，能够降低存储和译码实现的复杂度。

附图说明

图1为本申请实施例所适用的无线通信系统。

图2是采用无线技术进行通信的基本流程图。

图3为本申请实施例提供的极化码编译码的示意性交互图。

图4为信道极化过程的示意图。

图5为本申请实施例提供的极化码编码的装置300的示意性框图。

图6为本申请实施例提供的设备500的示意性结构图。

图7为本申请实施例提供的设备600的示意图。

图8为处理装置的内部结构示意图。

具体实施方式

下面将结合附图，对本申请中的技术方案进行描述。

图1为本申请实施例所适用的无线通信系统。该无线通信系统中可以包括至少一个网络设备，该网络设备与一个或多个终端进行通信。该网络设备可以是基站，也可以是基站与基站控制器集成后的设备，还可以是具有类似通信功能的其它设备。

本申请实施例中所涉及到的终端可以包括各种具有无线通信功能的手持设备、车载设备、可穿戴设备、计算设备或连接到无线调制解调器的其它处理设备。终端可以是移动台(Mobile Station，MS)、用户单元(subscriber unit)、蜂窝电话(cellular phone)、智能电话(smart phone)、无线数据卡、个人数字助理(Personal Digital Assistant，PDA)电脑、平板型电脑、无线调制解调器(modem)、手持设备(handset)、膝上型电脑(laptopcomputer)、机器类型通信(Machine Type Communication，MTC)终端等。

图1中的网络设备与终端之间采用无线技术进行通信。当网络设备发送信号时，其为发送端，当网络设备接收信号时，其为接收端。终端也是一样的，当终端发送信号时，其为发送端，当终端接收信号时，其为接收端。

图2是采用无线技术进行通信的基本流程图。发送端的信源依次经过信源编码、信道编码、速率匹配和调制后在信道上发出，接收端收到信号后依次经过解调、解速率匹配、信道解码和信源解码后获得信宿。

本申请实施例提及的无线通信系统包括但不限于：窄带物联网系统(NarrowBand-Internet of Things,NB-IoT)、全球移动通信系统(Global System for MobileCommunications,GSM)、增强型数据速率GSM演进系统(Enhanced Data rate for GSMEvolution,EDGE)、宽带码分多址系统(Wideband Code Division Multiple Access,WCDMA)、码分多址2000系统(Code Division Multiple Access，CDMA2000)、时分同步码分多址系统(Time Division-Synchronization Code Division Multiple Access,TD-SCDMA)，长期演进系统(Long Term Evolution，LTE)、下一代5G移动通信系统的三大应用场景eMBB、URLLC和eMTC或者将来出现的新的通信系统。

信道编解码是无线通信领域的核心技术之一，其性能的改进将直接提升网络覆盖及用户传输速率。目前，极化码是可理论证明达到香农极限，并且具有可实用的线性复杂度编译码能力的信道编码技术。极化码构造的核心是通过“信道极化”的处理，在编码侧，采用编码的方法使各个子信道呈现出不同的可靠性，当码长持续增加时，一部分信道将趋向于容量接近于1的无噪信道，另一部分信道趋向于容量接近于0的全噪信道，选择在容量接近于1的信道上直接传输信息以逼近信道容量。

Polar码的编码策略正是应用了这种现象的特性，利用无噪信道传输用户有用的信息，全噪信道传输约定的信息或者不传信息。Polar码也是一种线性块码，其编码矩阵(也称为生成矩阵)为F_N，编码过程为

其中，

是一个二进制的行矢量，长度为N(即,码长),且N＝2ⁿ，n为正整数。F_N是一个N×N的矩阵，且

定义为log2^N个矩阵F₂的克罗内克(Kronecker)乘积，

以上各式中涉及的加法、乘法操作均为二进制伽罗华域上的加法、乘法操作。

Polar码的编码过程中，

中的一部分比特用来携带信息，称为信息比特集合。这些比特的索引的集合记作A。另外的一部分比特设置为接收端和发送端预先约定的固定值，称之为固定比特集合或冻结比特(frozen bits)集合，其索引的集合用A的补集A^c表示。Polar码的编码过程相当于

这里，F_N(A)是F_N中由集合A中的索引对应的行得到的子矩阵。F_N(A^C)是F_N中由集合A^C中的索引对应的行得到的子矩阵。u_A为

中的信息比特集合，数量为K。

为

中的固定比特集合，其数量为(N-K)，是已知比特。这些固定比特通常被设置为0，但是只要接收端和发送端预先约定，固定比特可以被任意设置。从而，Polar码的编码输出可简化为

这里的u_A为

中的信息比特集合，u_A为长度K的行矢量，即|A|＝K,符号| |表示集合中元素的个数，K为信息块大小，F_N(A)是矩阵F_N中由集合A中的索引对应的那些行得到的子矩阵，F_N(A)是一个N×N的矩阵。

Polar码的构造过程即集合A的选取过程，它决定了Polar码的性能。Polar码的构造过程通常是，根据母码码长N确定共存在N个极化信道，这N个极化信道分别对应编码矩阵的N个行。计算极化信道的可靠度，将可靠度较高的前K个极化信道的序号(或者说，索引)作为集合A的元素，剩余(N-K)个极化信道对应的序号作为固定比特序号集合A^C的元素。集合A决定了信息比特的位置，集合A^C决定了固定比特的位置。

本申请实施例提供的极化码编码的方法主要涉及极化编码时母码序列的确定。下面对本申请实施例提供的极化码编码的方法进行说明。

本申请实施例中出现的编号“第一”、“第二”等仅仅为了区分不同的对象。例如，为了区分不同的序列，不应对本申请实施例的保护范围构成限定。

参见图3，图3为本申请实施例提供的极化码编码的方法100的示意性交互图。

110、发送设备获取待编码比特。

120、发送设备采用长度为N的母码序列对待编码比特进行极化编码，得到编码后的序列。

应理解，发送设备根据长度为N的母码序列，确定信息比特索引集合，再根据信息比特索引集合对待编码比特进行极化编码，得到编码后的序列。

假定信息比特的长度为K，则发送设备可以从母码序列包括索引中选取可靠度或信道容量最高的K个索引构成信息比特索引集合。或者，发送设备也可以采用现有技术中的其它方式确定信息比特索引集合，这里不作赘述。

需要说明的是，信道的索引也即信道的序号，因此，在本申请实施例中，信息比特索引集合也可以称作信息比特序号集合。

这里，长度为N的母码序列，即是说母码序列中包括N个索引(或者说，序号)，这N个索引与N个极化信道一一对应，每个索引用于标识自己所对应的极化信道。

另外，可以选用错误概率、信道容量或极化权重等参数作为衡量极化信道可靠性的参数，或者，也可以选用能够衡量极化信道的可靠度的其它参数，本申请实施例对此不作特别限定。

下面对本申请实施例中的母码序列的生成过程进行详细说明。

在本申请实施例中，假定进行极化编码时所需的母码序列的长度为N，则该长度为N的母码序列可以是根据一个长度为N₀的序列生成的，其中，该长度为N的母码序列可以为该长度为N₀的序列的一部分或全部。

其中，若长度为N的母码序列是长度为N₀的序列的一部分，即，该长度为N的母码序列可以该长度为N₀的序列中读取。若长度为N的母码序列是长度为N₀的序列的全部，则长度为N的母码序列即为该长度为N₀的序列。其中，N和N₀均为正整数。

在本申请实施例中，长度为N₀的序列可以如下面的序列1所示。

序列1

[1,2,3,5,9,17,33,65,129,4,6,257,7,10,11,18,13,19,513,34,21,35,25,66,37,67,41,8,130,69,49,131,12,73,258,133,14,81,259,20,15,137,97,22,261,514,145,23,36,26,515,265,161,38,27,517,273,39,29,68,42,193,521,43,70,289,50,16,45,71,132,529,51,74,321,75,53,134,24,545,82,77,57,135,385,260,83,138,28,98,577,85,139,40,262,30,99,146,141,89,31,263,147,101,641,516,44,266,162,149,105,46,72,267,518,163,52,47,274,769,153,269,113,194,519,165,76,54,275,522,195,55,290,78,169,58,277,136,523,84,79,291,197,59,530,281,177,525,32,61,322,86,140,293,201,531,87,100,323,90,546,142,297,209,264,533,91,102,48,148,143,386,325,547,103,93,305,537,225,106,150,387,578,268,329,549,56,151,107,164,154,114,389,579,270,80,109,337,553,520,155,166,115,276,271,60,642,581,393,167,157,196,117,561,353,170,88,62,278,643,524,585,121,401,63,171,198,279,292,178,282,92,144,770,645,173,199,526,593,179,202,417,104,283,294,94,532,527,771,649,203,181,295,285,95,324,152,210,298,609,108,449,534,205,185,773,211,299,657,326,535,548,156,110,306,226,272,538,213,301,327,116,168,111,777,388,158,307,330,227,673,539,550,217,159,64,118,331,309,390,229,172,551,785,541,280,580,119,338,554,122,333,705,313,391,174,233,200,339,394,555,123,582,180,175,284,801,354,562,241,528,96,341,395,125,296,557,583,204,182,286,644,355,402,563,586,397,345,183,287,833,206,186,403,357,300,587,565,646,212,207,112,536,187,418,594,405,302,361,328,589,569,647,160,189,214,897,772,419,308,303,595,650,540,409,215,369,228,610,120,450,218,332,421,310,597,651,552,774,542,219,230,176,611,658,311,451,334,314,425,653,601,392,543,124,775,231,221,340,335,659,613,556,453,315,234,778,126,433,674,288,317,342,184,235,396,661,127,558,617,584,779,457,242,343,356,208,675,564,559,786,237,346,398,665,781,625,243,465,188,706,347,358,304,588,404,677,566,399,787,245,359,349,216,567,190,707,802,481,590,362,406,570,681,789,648,249,191,596,591,312,407,363,803,709,420,571,220,410,370,793,689,336,544,365,573,834,598,652,232,411,805,422,713,371,222,316,599,612,423,835,413,452,602,223,654,373,809,426,344,776,318,721,128,236,603,614,560,660,655,898,377,837,319,427,454,615,605,817,434,238,737,348,400,618,662,899,429,455,780,841,244,239,435,458,360,568,663,619,676,350,666,626,901,782,592,459,437,192,246,351,621,849,408,667,678,466,627,788,783,364,572,247,461,441,905,250,679,669,708,467,629,865,682,600,574,412,366,790,251,482,633,469,913,575,683,372,367,710,424,791,804,224,414,253,690,483,794,604,656,685,711,473,415,320,374,691,714,929,616,795,806,485,606,428,375,240,715,693,807,797,607,836,378,664,430,489,722,456,810,620,961,717,697,379,436,431,723,811,838,497,668,622,352,381,818,738,248,784,460,438,725,813,839,680,628,623,900,670,819,842,739,439,462,729,442,671,576,630,252,843,821,902,741,468,684,463,368,792,443,631,850,634,845,254,825,903,686,416,745,712,445,470,851,906,635,255,692,687,796,471,484,866,753,376,608,474,853,907,637,808,716,694,798,867,914,475,486,432,695,909,857,799,718,380,698,915,487,869,477,812,724,719,490,624,699,930,382,917,814,873,840,440,672,491,701,383,726,931,820,815,498,464,921,727,881,740,493,632,962,730,844,499,933,822,444,731,742,688,823,963,501,846,826,937,472,446,904,636,256,743,733,852,847,505,965,827,447,746,638,945,476,800,829,854,696,747,908,639,969,488,478,754,855,868,720,749,858,910,479,755,977,700,384,859,816,870,492,916,911,757,871,861,728,702,993,494,874,918,761,703,500,495,824,919,875,932,732,922,882,848,877,448,502,744,923,934,883,734,828,503,935,925,964,735,506,885,938,856,830,640,748,507,889,831,939,966,480,946,750,509,860,912,941,967,756,751,947,970,872,862,971,949,704,758,863,920,496,978,876,759,973,953,762,979,924,878,763,994,981,884,504,879,936,736,926,765,995,985,927,832,886,508,997,940,887,752,890,942,1001,510,968,891,948,943,511,1009,864,893,760,972,950,951,974,954,764,980,975,880,955,766,928,957,982,767,983,996,888,986,987,998,944,892,999,989,512,1002,894,952,1003,895,1010,976,1005,1011,956,1013,984,958,768,1017,959,988,1000,990,991,896,1004,1006,1012,1007,960,1014,1015,1018,1019,992,1021,1008,1016,1020,1022,1023,1024]。

序列1的长度为1024，若极化编码时所需的母码长度N＝1024，则发送设备将序列1作为母码序列。若极化编码时所需的母码长度N小于1024，则发送设备从序列1中依次读取小于或等于N的索引，读取的索引构成的序列即为母码序列。

例如，如果所需母码长度为16，发送设备从序列1中顺序读取小于或等于16的索引，读取的索引组成的序列即为长度为16的母码序列。

类似的，长度为N₀的序列中包括N₀个索引，该N₀个索引与N₀个极化信道一一对应，该N₀个索引是按照该N₀个极化信道的信道容量或可靠度进行排序的。

上述序列1仅是作为本申请实施例中长度为N₀的序列的一个示例。本申请实施例对N₀的具体取值不作限定，N₀应该为2的整数次幂。例如，N₀可以等于32、256、512等。

下面详细说明发送设备如何生成长度为N₀的序列。

发送设备根据初始信道容量和N₀，生成长度为N₀的序列。

在本申请实施例中，发送设备可以将码率R作为初始信道容量。

为了说明极化信道的信道容量的计算方法，先对信道的极化过程进行说明。

参见图4，图4为信道极化过程的示意图。图4中所示是一个2×2的信道极化过程。可以认为，极化之后信道W+的可靠度大于信道W-的可靠度。信道容量I表示信道W能发生可靠通信的最高码率，可以视作衡量信道可靠度的一种参量。

在加性高斯白噪声(Additive White Gaussian Noise，AWGN)信道中，信道容量的传递计算过程表示如下：

I(W-)＝2I(W)-I(W+) (2)

其中，J和J^-1互为逆函数。

在上式(4)中，I^*＝0.6363，a_σ,1＝1.09542，b_σ,1＝0.214217，c_σ,1＝2.33727，a_σ,2＝0.706692，b_σ,2＝0.386013，c_σ,2＝-1.75017。

对于长度为N₀的polar码极化过程而言，将码率R作为初始信道容量。在进行log₂N₀次极化后，产生的各子信道的信道容量可以通过以上公式计算得到，信道容量的上限为1，下限为0。其中，码率R对应上数公式中的信道容量I。

为了便于说明，这里定义一个序列#A。序列#A中不包括任何元素。也或者说，序列#A中的元素构成的集合为空集。

具体过程如下：

(1)发送设备获取初始信道容量。

(2)发送设备计算log₂N次极化后，各个子信道的信道容量。

这里，可以根据上面的公式(4)计算各个子信道的信道容量。

(3)发送设备确定某个子信道的信道容量大于预设的信道容量阈值且该子信道的索引不属于序列#A时，将该子信道的序号加入序列#A的头部。否则根据一定的步长增加信道容量，并返回执行步骤(2)。

(4)发送设备确定母码序列中的元素数量等于N₀时，得到该长度为N₀的序列。

其中，码率的初始值可以设置为0，步长可以设置为0.001。信道容量阈值可以设为0.999。信道容量的最大值等于1。

需要说明的是，在生成长度为N₀的序列的过程中，若存在多个子信道的信道容量均大于预设的信道容量阈值，且不属于序列#A时，发送设备可以按照这些子信道的索引从大到小或从小到大的顺序进行排序，并加入序列#A。

或者，发送设备也可以按照这些子信道的码重从大到小或从小到大的顺序进行排序，并加入序列#A。

或者,发送设备也可以回退到上一个输入信道容量,并减半增加步长,返回执行步骤(2)。

可以理解的是，随着信道容量大于信道容量阈值的极化信道的索引不断加入到序列#A中，序列#A中包括的索引的数量不断增加。直至序列#A中的索引的数量达到N₀时，此时的序列#A即为长度等于N₀的序列。

上述序列#1是以N₀＝1024，生成的长度为1024的序列。当N₀的取值为其它数值，例如，32、64、512等时，即可按照上述的方法生成相应长度的序列。

本申请实施例中所说的长度为N₀的序列具有嵌套特性和对称性。

嵌套特性，是指从该长度为N₀的序列中读取信息比特长度为K的信息比特索引集合，是读取长度为K+1的信息比特索引集合的子集。

对称性，是指长度为N₀的序列的对称长度的子序列中的索引具有相同的排序。

具体地，对称性可以表示为如下的表达式(5)：

Seq(i·seg+1≤Seq≤(i+1)·seg)＝Seq(j·seg+1≤Seq≤(j+1)·seg)-(j-i)·seg (5)

其中，上述表达式(5)中，seg＝32,16,8,4,2,1,i≤(1024/seg)-1且为整数，j≤(1024/seg)-1且为整数，且i<j。

例如，序列1中，当i＝0，seg＝32时，子序列A为

[1,2,3,5,9,17,4,6,7,10,11,18,13,19,21,25,8,12,14,20,15,22,23,26,27,29,16,24,28,30,31,32]

当j＝3，seg＝32时，子序列B为

[97,98,99,101,105,113,100,102,103,106,107,114,109,115,117,121,104,108,110,116,111,118,119,122,123,125,112,120,124,126,127,128]

子序列A与子序列B每个对应元素之间差值为3×32＝96。

需要说明的是，上述序列#1具有32位的对称性。在本申请实施例中，生成序列#1之后，可以对序列#1进一步进行调整，使其依然具有嵌套特性，同时，使得调整后的序列(以下记作序列2)具有512位的对称性。即，

Seq(i·seg+1≤Seq≤(i+1)·seg)＝Seq(j·seg+1≤Seq≤(j+1)·seg)-(j-i)·seg，其中，seg＝512,256,128,64,32,16,8,4,2,1。

下面给出序列2。

序列2

[1,2,3,5,9,17,33,65,129,4,6,257,7,10,11,18,13,19,513,34,21,35,25,66,37,67,41,8,130,69,49,131,12,73,258,133,14,81,20,15,259,137,97,22,261,514,145,23,36,26,515,265,161,27,38,517,39,273,29,68,42,193,521,43,70,289,50,16,45,71,132,529,51,74,321,75,53,134,24,545,82,77,57,135,385,260,83,138,28,98,577,85,139,40,262,30,99,146,141,89,31,263,147,101,641,516,44,266,162,149,46,105,72,267,518,163,52,47,274,769,153,269,113,194,519,76,165,54,275,522,55,195,290,78,58,169,277,136,523,84,79,291,197,59,530,281,177,525,32,61,322,86,140,293,201,531,87,100,323,90,546,142,297,264,209,533,91,102,48,148,143,386,325,547,103,93,305,537,225,106,150,387,578,268,329,549,56,151,107,164,154,114,389,579,270,80,109,337,553,520,155,166,115,276,271,60,642,581,393,167,157,196,117,561,353,170,88,62,278,643,524,585,121,401,63,171,198,279,292,178,282,92,144,770,645,173,199,526,593,179,202,417,104,283,294,94,532,527,771,649,203,181,295,285,95,324,152,210,298,609,108,449,534,205,185,773,211,299,657,326,535,548,156,110,306,226,272,538,213,301,327,116,111,168,777,388,158,307,330,227,673,539,550,217,159,64,118,331,309,390,229,172,551,785,541,280,580,119,338,554,122,333,705,313,391,174,233,200,339,394,555,123,582,180,175,284,801,354,562,241,528,96,341,395,125,296,557,583,204,182,286,644,355,402,563,586,183,397,345,287,833,206,186,403,357,300,587,565,646,212,207,112,536,187,418,594,405,302,361,328,589,569,647,160,189,214,897,772,419,308,303,595,650,540,409,215,369,228,610,120,450,218,332,421,310,597,651,552,774,542,219,230,176,611,658,311,451,334,314,425,653,601,392,543,124,775,231,221,340,335,659,613,556,453,315,234,778,126,433,674,288,317,342,184,235,396,661,127,558,617,584,779,457,242,343,356,208,675,564,559,786,237,346,398,665,781,625,243,465,188,706,347,358,304,588,404,677,566,399,787,245,359,349,216,567,190,707,802,481,590,362,406,570,681,789,648,249,191,596,591,312,407,363,803,709,420,571,220,410,370,793,689,336,544,365,573,834,598,652,232,411,805,422,713,371,222,316,599,612,423,835,413,452,602,223,654,373,809,426,344,776,318,721,128,236,603,614,560,660,655,898,377,837,319,427,454,615,605,817,434,238,737,348,400,618,662,899,429,455,780,841,244,239,435,458,360,568,663,619,676,350,666,626,901,782,592,459,437,192,246,351,621,849,408,667,678,466,627,788,783,364,572,247,461,441,905,250,679,669,708,467,629,865,682,600,574,412,366,790,251,482,633,469,913,575,683,372,367,710,424,791,804,224,414,253,690,483,794,604,656,685,711,473,415,320,374,691,714,929,616,795,806,485,606,428,375,240,715,693,807,797,607,836,378,664,430,489,722,456,810,620,961,717,697,379,436,431,723,811,838,497,668,622,352,381,818,738,248,784,460,438,725,813,839,628,623,680,900,670,819,842,739,439,462,729,442,671,576,630,252,843,821,902,741,468,684,463,368,792,443,631,850,634,845,254,825,903,686,416,745,712,445,470,851,906,635,255,692,687,796,471,484,866,753,376,608,474,853,907,637,808,716,694,798,867,914,475,486,432,695,909,857,799,718,380,698,915,487,869,477,812,724,719,490,624,699,930,382,917,814,873,840,440,672,491,701,383,726,931,820,815,498,464,921,727,881,740,493,632,962,730,844,499,933,822,444,731,742,688,823,963,501,846,826,937,472,446,904,636,256,743,733,852,847,505,965,827,447,746,638,945,476,800,829,854,696,747,908,639,969,488,478,754,855,868,720,749,858,910,479,755,977,700,384,859,870,816,492,916,911,757,871,861,728,702,993,494,874,918,761,703,500,495,824,919,875,932,732,922,882,848,877,448,502,744,923,934,883,734,828,503,935,925,964,735,506,885,938,856,830,640,748,507,889,831,939,966,480,946,750,509,860,912,941,967,756,751,947,970,872,862,971,949,704,758,863,920,496,978,876,759,973,953,762,979,924,878,763,994,981,884,504,879,936,736,926,765,995,985,927,832,886,508,997,940,887,752,890,942,1001,510,968,891,948,943,511,1009,864,893,760,972,950,951,974,954,764,980,975,880,955,766,928,957,982,767,983,996,888,986,987,998,944,892,999,989,512,1002,894,952,1003,895,1010,976,1005,1011,956,1013,984,958,768,1017,959,988,1000,990,991,896,1004,1006,1012,1007,960,1014,1015,1018,1019,992,1021,1008,1016,1020,1022,1023,1024]

以上对本申请实施例中生成长度为N₀的序列的过程作了详细说明。可以理解的是，在得到长度为N₀的序列之后，发送设备可以对该长度为N₀的序列进行存储。这样，在进行极化编码时，根据所需的母码序列的长度，从所述长度为N₀的序列中读取相应长度的序列作为所述母码序列。

应理解，长度为N₀的序列实际上就是一个母码序列，因此，N₀的取值也应为2的整数次幂。我们可以将该长度为N₀的序列视作系统所能支持的最大母码序列。任意长度的母码序列都可以从该最大母码序列中读取得到。

因此，在本申请示例中确定母码序列包括两种方式，以下分别记作方式1和方式2。

方式1

从长度为N₀的序列中读取。

其中，N₀大于或等于N。

上文对方式1已经作了详细说明，这里不再赘述。

方式2

根据M个序列和T个指示序列，确定所述长度为N的母码序列。

其中，所述M大于或等于2，所述T大于或等于1。

该M个序列中的每个序列中包括相同个数的极化信道的索引。或者说，该M个序列是的长度是相等的。

该T个指示序列的长度可能是不相等的。每个指示序列中包括的元素的可能数值也因M的不同取值而不同。

例如，M＝2，T＝1。发送设备根据长度为8的一个序列，确定长度为16的母码序列，则指示序列的个数(即，T的取值)可以等于1。发送设备根据该长度为8的序列(记作序列#1)，通过给序列#1中的每个索引增加偏移量8，得到另一个长度为8的序列(记作序列#2)。这种情况下，指示序列中包括16个元素，每个元素的取值等于第一数值或第二数值。

发送设备依次读取指示序列中的元素。若指示序列中的第i个元素的取值等于第一数值，则发送设备从序列#1中读取极化信道的索引。若指示序列中的第i个元素的取值等于第二数值，则发送设备从序列#2中读取极化信道的索引。i遍历[1,16]中的取值。最后，发送设备将依次读取的索引构成的序列确定为母码序列。

又例如，M＝4，T＝1。发送设备根据长度为8的4个序列，确定长度为32的母码序列。指示序列的个数(即，T的取值)可以等于1。

为了便于说明，以下将该4个长度为8的序列分别记作序列#3、序列#4、序列#5和序列#6。将该指示序列记作指示序列#1。

其中，序列#4是对序列#3增加一个偏移量得到的。序列#5是对序列#3增加两个偏移量得到的。序列#6是对序列#3增加三个偏移量得到的。这里的偏移量为该4个序列的长度，即偏移量等于8。

应理解，这里的序列#3可以看作第一序列，序列#4、序列#5和序列#6均为第二序列。在本申请实施例中，多个第二序列是将第一序列作为基础序列，通过对基础序列增加不同的偏移量得到的。这多个第二序列中包括的索引互不相同。

此时，指示序列#1中包括32个元素，这32个元素有4种取值。例如，0、1、2、3。

发送设备依次读取指示序列中的元素，若指示序列中的第i个元素等于0，则发送设备从序列#3中读取极化信道的索引。若指示序列中的第i个元素等于1，则发送设备从序列#4中读取极化信道的索引。若指示序列中的第i个元素等于2，则发送设备从序列#5中读取极化信道的索引。若指示序列中的第i个元素等于3，则发送设备从序列#6中读取极化信道的索引。

i遍历[1,32]中的取值。最后，发送设备将依次读取的索引构成的序列确定为母码序列。

再例如，当短序列长度为8，需要确定长度为32的母码序列。M＝2，T＝2。先给序列#1增加偏移量8，得到序列#2，序列#1与序列#2结合16个元素的指示序列#3可以获得16长的母码序列#4；对16长的序列#4增加偏移量16，得到序列#5，序列#4和序列#5结合32个元素的指示序列#6可以获得32长的母码序列。T＝2，分别为序列#3和序列#6。

指示序列中的元素可以采用二进制或其它进制，本申请实施例对此不作特别限定。

下面以M＝2，T＝1进行举例说明。

(1)发送设备获取一个长度为n的基础序列(以下记作序列#7)。

(2)发送设备对序列#1进行扩展，得到长度为2n的偏移序列(以下记作序列#8)。

具体地，对序列#7中包括的n个极化信道的索引增加偏移量n，得到的序列即为偏移序列。

假定序列#7＝[1,2,3,5,4,6,7,8]，则n＝8。

对序列#7中的每个元素增加偏移量n，得到序列#8，即序列#8＝序列#7+8＝[9,10,11,13,12,14,15,16]

(3)计算长度为2n的极化码对应的2n个极化信道的可靠度，并按照冒泡算法生成长度为2n的母码序列。

I.根据冒泡算法计算当前可靠度最高的极化信道。

II.判断该当前可靠度最高的极化信道的索引是否属于区间[1,n]。

具体地，若当前可靠度最高的极化信道的索引属于区间[1,n]，则在指示序列的头部加1；若当前可靠度最高的极化信道的索引不属于区间[1,n]，则在指示序列的头部加0。直至指示序列中包括2n个元素。

指示序列也具有前文所说的嵌套特性和对称性。

需要说明的是，这里的指示序列在一开始也不包括任何的元素。通过步骤(3)，不断地向指示序列中添加元素，直至该指示序列中的元素个数等于2n。

下面给出一个从码长＝8的基础序列扩展到码长等于16的序列的示例。

序列#7＝[1,2,3,5,4,6,7,8]

序列#8＝序列#7+8＝[9,10,11,13,12,14,15,16]

根据上述生成指示序列的方法，得到的指示序列＝[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]。

发送设备在确定码长为N的母码序列时，恰好是这里描述的生成指示序列的逆过程。发送设备首先获取序列#7。发送设备根据序列#7的长度(即，等于8)，对序列#7中的元素依次增加偏移量n(即，等于8)，就可以确定出序列#8。接下来，发送设备依次读取指示序列中的元素。

继续以上述示例进行说明。指示序列中的第1个元素等于1，则发送设备读取序列#7第1个位置的索引1。指示序列中第2个元素等于1，则发送设备读取序列#7中第2个位置的索引2。以此类推。指示序列中的第5个元素等于0，则发送设备读取序列#2中的第1个位置的索引9。

换句话说，若指示序列中当前位置的元素“1”是该指示序列中的第i个出现的“1”，则发送设备从序列#7中读取第i个位置的索引。若指示序列中当前位置的元素“0”是该指示序列中第j个出现的“0”，则发送设备从序列#8中读取第j个位置的索引。

依次判断指示序列中的每个元素等于数值“1”或等于数值“0”，进而从序列#7或序列#8中读取对应位置的索引。遍历完指示序列中的每个元素，则发送设备依次读取的索引构成一个有序的序列，该有序的序列即为母码序列。

下面给出通过方式2确定得到的母码序列的示例。例如下面给出的序列3至序列8。其中，序列3至序列8中每个序列的长度均为1024。

序列3

[1,2,3,5,9,17,33,65,129,4,6,257,7,10,11,18,13,19,513,34,21,35,25,66,8,67,37,12,130,69,41,131,14,73,258,133,49,81,259,20,15,137,97,22,261,514,145,23,36,26,515,265,161,38,27,517,273,39,29,68,42,193,521,16,70,289,43,50,45,71,132,529,51,74,321,75,24,134,53,545,82,77,28,135,385,260,83,138,57,98,577,85,139,40,262,30,99,146,141,89,31,263,147,72,641,516,44,266,162,149,101,46,76,267,518,163,52,47,274,769,153,269,105,194,519,136,78,54,275,522,195,55,290,113,165,58,277,140,523,84,79,291,197,59,530,281,169,525,32,61,322,86,142,264,201,531,87,100,323,90,546,177,293,209,268,533,102,91,48,148,143,386,325,547,103,93,297,537,225,106,150,387,578,270,329,520,56,151,80,164,154,107,389,579,305,114,109,337,549,524,166,155,115,276,271,60,642,581,393,167,157,196,88,553,353,170,117,62,278,643,526,585,92,401,63,144,198,279,292,171,282,121,178,770,645,173,199,561,593,179,202,417,104,294,283,94,771,532,527,649,203,152,295,285,95,324,181,210,298,609,108,449,534,205,156,773,211,272,657,326,535,548,185,110,299,226,306,538,213,301,327,116,168,111,777,388,158,307,330,227,673,550,539,217,159,64,118,331,280,390,200,172,785,551,541,309,580,119,338,554,122,333,705,284,391,229,174,204,339,394,528,123,582,180,175,313,801,354,555,233,562,96,341,395,125,296,557,583,206,182,286,644,355,402,563,586,397,345,183,287,833,241,186,403,328,300,587,536,646,212,207,112,565,187,418,594,405,357,302,332,589,540,647,160,189,214,897,772,419,308,303,595,650,569,409,215,361,228,610,120,450,218,392,334,310,597,651,552,774,542,230,219,176,611,658,451,311,369,421,314,653,601,396,543,124,775,231,221,340,335,659,584,556,453,315,234,778,126,425,674,288,317,342,184,208,398,661,127,613,558,588,779,457,235,343,356,242,675,564,559,786,237,346,433,665,781,617,243,465,188,706,358,347,304,648,404,590,566,399,787,216,359,349,245,707,190,567,802,481,625,362,406,677,570,789,652,220,191,596,591,312,407,336,803,709,420,571,249,410,363,793,681,370,544,365,573,834,598,654,232,422,776,411,713,371,222,316,599,612,423,835,413,452,602,223,689,344,805,426,373,721,318,780,128,236,614,603,560,660,655,898,348,837,319,400,454,615,605,809,427,238,737,377,434,618,662,899,429,455,782,841,244,239,435,458,360,568,663,592,676,350,666,619,901,817,626,459,408,192,246,351,621,849,437,678,667,466,627,788,783,364,572,247,461,412,905,250,679,669,708,467,600,865,682,629,574,441,366,790,251,482,604,469,913,575,656,372,424,710,367,791,804,224,414,253,683,483,794,633,690,685,711,473,415,320,374,691,714,929,616,806,795,456,606,428,375,240,715,664,807,797,607,836,378,693,485,430,722,460,810,620,961,717,668,379,436,431,723,784,838,489,697,622,352,381,811,738,248,818,462,438,725,813,839,628,680,623,900,670,819,842,739,439,497,729,442,671,576,630,252,843,792,902,712,468,684,463,368,821,443,631,850,634,845,254,796,903,741,416,686,716,445,470,851,906,635,255,692,687,825,471,484,866,745,376,608,474,853,907,637,808,718,694,798,867,914,486,475,432,909,857,695,799,753,380,698,915,487,840,477,812,724,719,490,624,699,930,382,917,869,814,844,440,672,464,701,383,726,931,820,815,491,498,921,727,873,740,493,632,962,730,904,499,846,822,444,742,731,688,963,823,472,881,933,826,501,446,908,636,256,743,733,852,847,476,965,827,447,746,638,937,505,800,829,854,696,720,910,639,969,488,478,747,855,868,754,749,858,945,479,755,977,700,384,870,859,816,492,916,911,728,871,861,757,702,993,494,874,918,732,703,500,495,824,919,848,932,761,922,875,882,877,448,502,744,934,923,883,734,828,503,935,925,964,735,506,856,938,885,830,640,748,507,860,831,912,966,480,939,750,509,889,946,941,967,756,751,947,970,872,862,971,920,704,758,863,949,496,978,876,759,973,924,762,979,953,878,763,994,981,884,504,936,879,736,926,765,995,985,927,832,886,508,968,940,887,752,890,997,942,510,972,891,948,943,511,1001,864,893,760,974,950,951,1009,954,764,980,975,880,955,766,928,957,982,767,983,996,888,986,998,987,944,892,999,989,512,1002,894,952,976,895,1003,1010,1005,1011,956,984,1013,958,768,988,959,1017,1000,990,991,896,1004,1006,1012,1007,960,1014,1015,1018,1019,992,1021,1008,1016,1020,1022,1023,1024]

序列4

序列5

[1,2,3,5,9,17,33,65,129,4,6,257,7,10,11,18,13,19,513,34,21,35,25,66,37,67,41,8,130,69,49,131,12,73,258,133,14,81,259,20,15,137,97,22,261,514,145,23,36,26,515,265,161,38,27,517,273,39,29,68,42,193,521,43,70,289,50,16,45,71,132,529,51,74,321,75,53,134,24,545,82,77,57,135,385,260,83,138,28,98,577,85,139,40,262,30,99,146,141,89,31,263,147,101,641,516,44,266,162,149,105,46,72,267,518,163,52,47,274,769,153,269,113,194,519,165,76,54,275,522,195,55,290,78,169,58,277,136,523,84,79,291,197,59,530,281,177,525,32,61,322,86,140,293,201,531,87,100,323,90,546,142,297,209,264,533,102,91,48,148,143,386,325,547,103,93,305,537,225,106,150,387,578,268,329,549,56,151,107,164,154,114,389,579,270,80,109,337,553,520,166,155,115,276,271,60,642,581,393,167,157,196,117,561,353,170,88,62,278,643,524,585,121,401,63,171,198,279,292,178,282,92,144,770,645,173,199,526,593,179,202,417,104,294,283,94,771,532,527,649,203,181,295,285,95,324,152,210,298,609,108,449,534,205,185,773,211,299,657,326,535,548,156,110,306,226,272,538,213,301,327,116,168,111,777,388,158,307,330,227,673,550,539,217,159,64,118,331,309,390,229,172,785,551,541,280,580,119,338,554,122,333,705,313,391,233,174,200,339,394,555,123,582,180,175,284,801,354,562,241,528,96,341,395,125,296,557,583,204,182,286,644,355,402,563,586,397,345,183,287,833,206,186,403,357,300,587,565,646,212,207,112,536,187,418,594,405,361,302,328,589,569,647,160,189,214,897,772,419,308,303,595,650,540,409,215,369,228,610,120,450,218,421,332,310,597,651,552,774,542,230,219,176,611,658,451,311,334,425,314,653,601,392,543,124,775,231,221,340,335,659,613,556,453,315,234,778,126,433,674,288,317,342,184,235,396,661,127,617,558,584,779,457,242,343,356,208,675,564,559,786,237,346,398,665,781,625,243,465,188,706,358,347,304,677,404,588,566,399,787,245,359,349,216,707,190,567,802,481,590,362,406,681,570,789,648,249,191,596,591,312,407,363,803,709,420,571,220,410,370,793,689,336,544,365,573,834,598,652,232,422,805,411,713,371,222,316,599,612,423,835,413,452,602,223,654,373,809,426,344,721,318,776,128,236,614,603,560,660,655,898,377,837,319,427,454,615,605,817,434,238,737,348,400,618,662,899,429,455,780,841,244,239,435,458,360,568,663,619,676,350,666,626,901,782,592,459,437,192,246,351,621,849,408,678,667,466,627,788,783,364,572,247,461,441,905,250,679,669,708,467,629,865,682,600,574,412,366,790,251,482,633,469,913,575,683,372,424,710,367,791,804,224,414,253,690,483,794,604,656,685,711,473,415,320,374,691,714,929,616,806,795,485,606,428,375,240,715,693,807,797,607,836,378,664,489,430,722,456,810,620,961,717,697,379,436,431,723,811,838,497,668,622,352,381,818,738,248,784,460,438,725,813,839,628,680,623,900,670,819,842,739,439,462,729,442,671,576,630,252,843,821,902,741,468,684,463,368,792,443,631,850,634,845,254,825,903,745,416,686,712,445,470,851,906,635,255,692,687,796,471,484,866,753,376,608,474,853,907,637,808,716,694,798,867,914,486,475,432,909,857,695,799,718,380,698,915,487,869,477,812,724,719,490,624,699,930,382,917,873,814,840,440,672,491,701,383,726,931,820,815,498,464,921,727,881,740,493,632,962,730,933,499,844,822,444,742,731,688,963,823,501,846,937,826,472,446,904,636,256,743,733,852,847,505,965,827,447,746,638,945,476,800,829,854,696,747,908,639,969,488,478,754,855,868,720,749,858,910,479,755,977,700,384,870,859,816,492,916,911,757,871,861,728,702,993,494,874,918,761,703,500,495,824,919,875,932,732,922,882,848,877,448,502,744,934,923,883,734,828,503,935,925,964,735,506,885,938,856,830,640,748,507,889,831,939,966,480,946,750,509,860,912,941,967,756,751,947,970,872,862,971,949,704,758,863,920,496,978,876,759,973,953,762,979,924,878,763,994,981,884,504,936,879,736,926,765,995,985,927,832,886,508,997,940,887,752,890,1001,942,510,968,891,948,943,511,1009,864,893,760,972,950,951,974,954,764,980,975,880,955,766,928,957,982,767,983,996,888,986,998,987,944,892,999,989,512,1002,894,952,1003,895,1010,976,1005,1011,956,1013,984,958,768,1017,959,988,1000,990,991,896,1004,1006,1012,1007,960,1014,1015,1018,1019,992,1021,1008,1016,1020,1022,1023,1024]

序列6

[1,2,3,5,9,17,33,65,129,4,6,257,7,10,11,18,13,19,513,34,21,35,25,66,37,67,8,41,130,69,12,131,49,73,258,133,14,81,259,20,15,137,97,22,261,514,145,23,36,26,515,265,161,38,27,517,273,39,29,68,42,193,521,43,70,289,16,50,45,71,132,529,51,74,321,75,24,134,53,545,82,77,57,135,385,260,83,138,28,98,577,85,139,40,262,30,99,146,141,89,31,263,147,101,641,516,44,266,162,149,72,46,105,267,518,163,52,47,274,769,153,269,76,194,519,165,113,54,275,522,195,55,290,78,136,58,277,169,523,84,79,291,197,59,530,281,140,525,32,61,322,86,177,293,201,531,87,100,323,90,546,142,264,209,297,533,102,91,48,148,143,386,325,547,103,93,268,537,225,106,150,387,578,305,329,549,56,151,107,164,154,80,389,579,270,114,109,337,520,553,166,155,115,276,271,60,642,581,393,167,157,196,88,524,353,170,117,62,278,643,561,585,121,401,63,171,198,279,292,144,282,92,178,770,645,173,199,526,593,179,202,417,104,294,283,94,771,532,527,649,203,152,295,285,95,324,181,210,298,609,108,449,534,205,185,773,211,299,657,326,535,548,156,110,272,226,306,538,213,301,327,116,168,111,777,388,158,307,330,227,673,550,539,217,159,64,118,331,280,390,229,172,785,551,541,309,580,119,338,554,122,333,705,313,391,200,174,233,339,394,555,123,582,180,175,284,801,354,528,204,562,96,341,395,125,296,557,583,241,182,286,644,355,402,563,586,397,345,183,287,833,206,186,403,357,300,587,536,646,212,207,112,565,187,418,594,405,328,302,361,589,569,647,160,189,214,897,772,419,308,303,595,650,540,409,215,332,228,610,120,450,218,421,369,310,597,651,552,774,542,230,219,176,611,658,451,311,334,392,314,653,601,425,543,124,775,231,221,340,335,659,613,556,453,315,234,778,126,396,674,288,317,342,184,235,433,661,127,584,558,617,779,457,208,343,356,242,675,564,559,786,237,346,398,665,781,588,243,465,188,706,358,347,304,677,404,625,566,399,787,216,359,349,245,707,190,567,802,481,590,362,406,648,570,789,681,249,191,596,591,312,407,363,803,709,420,571,220,410,336,793,652,370,544,365,573,834,598,689,232,422,805,411,713,371,222,316,599,612,423,835,413,452,602,223,654,344,776,426,373,721,318,809,128,236,614,603,560,660,655,898,377,837,319,427,454,615,605,780,400,238,737,348,434,618,662,899,429,455,817,841,244,239,435,458,360,568,663,619,676,350,666,592,901,782,626,459,408,192,246,351,621,849,437,678,667,466,627,788,783,364,572,247,461,441,905,250,679,669,708,467,600,865,682,629,574,412,366,790,251,482,633,469,913,575,683,372,424,710,367,791,804,224,414,253,656,483,794,604,690,685,711,473,415,320,374,691,714,929,616,806,795,485,606,428,375,240,715,664,807,797,607,836,378,693,456,430,722,489,810,620,961,717,697,379,436,431,723,811,838,460,668,622,352,381,784,738,248,818,497,438,725,813,839,628,680,623,900,670,819,842,739,439,462,729,442,671,576,630,252,843,792,902,741,468,684,463,368,821,443,631,850,634,845,254,825,903,712,416,686,745,445,470,851,906,635,255,692,687,796,471,484,866,716,376,608,474,853,907,637,808,753,694,798,867,914,486,475,432,909,857,695,799,718,380,698,915,487,869,477,812,724,719,490,624,699,930,382,917,840,814,873,440,672,491,701,383,726,931,820,815,464,498,921,727,844,740,493,632,962,730,933,499,881,822,444,742,731,688,963,823,472,846,904,826,501,446,937,636,256,743,733,852,847,505,965,827,447,746,638,908,476,800,829,854,696,747,945,639,969,488,478,720,855,868,754,749,858,910,479,755,977,700,384,870,859,816,492,916,911,728,871,861,757,702,993,494,874,918,761,703,500,495,824,919,875,932,732,922,848,882,877,448,502,744,934,923,883,734,828,503,935,925,964,735,506,856,938,885,830,640,748,507,889,831,939,966,480,912,750,509,860,946,941,967,756,751,947,970,872,862,971,920,704,758,863,949,496,978,876,759,973,953,762,979,924,878,763,994,981,884,504,936,879,736,926,765,995,985,927,832,886,508,997,940,887,752,890,968,942,510,1001,891,948,943,511,972,864,893,760,1009,950,951,974,954,764,980,975,880,955,766,928,957,982,767,983,996,888,986,998,987,944,892,999,989,512,1002,894,952,1003,895,976,1010,1005,1011,956,984,1013,958,768,1017,959,988,1000,990,991,896,1004,1006,1012,1007,960,1014,1015,1018,1019,992,1021,1008,1016,1020,1022,1023,1024]

序列7

[1,2,3,5,9,17,33,65,129,4,6,257,7,10,11,18,13,19,513,34,21,35,25,66,37,67,8,41,130,69,49,131,12,73,258,133,14,81,259,20,15,137,97,22,261,514,145,36,23,26,515,265,161,38,27,517,273,39,29,68,42,193,521,43,70,289,16,50,45,71,132,529,51,74,321,75,24,134,53,545,82,77,57,135,385,260,83,138,28,98,577,85,139,40,262,30,99,146,141,89,31,263,147,101,641,516,44,266,162,149,72,46,105,267,518,163,52,47,274,769,153,269,113,194,519,165,76,54,275,522,195,55,290,78,136,58,277,169,523,84,79,291,197,59,530,281,177,525,32,61,322,86,140,293,201,531,100,87,323,90,546,142,264,209,297,533,102,91,48,148,143,386,325,547,103,93,305,537,225,106,150,387,578,268,329,549,56,164,107,151,154,80,389,579,270,114,109,337,520,553,166,155,115,276,271,60,642,581,393,167,157,196,88,561,353,170,117,62,278,643,524,585,121,401,63,171,198,292,279,144,282,92,178,770,645,173,199,526,593,179,202,417,104,294,283,94,771,532,527,649,203,152,295,285,95,324,181,210,298,609,108,449,534,205,185,773,211,299,657,326,548,535,156,110,272,226,306,538,213,301,327,116,168,111,777,388,158,307,330,227,673,550,539,217,159,64,118,331,280,390,229,172,785,551,541,309,580,119,338,554,122,333,705,313,391,200,174,233,339,394,555,123,582,180,175,284,801,354,528,241,562,96,341,395,125,296,557,583,204,182,286,644,355,402,563,586,397,345,183,287,833,206,186,403,357,300,587,536,646,212,207,112,565,187,418,594,405,328,302,361,589,569,647,160,189,214,897,772,419,308,303,595,650,540,409,228,369,215,610,120,450,218,421,332,310,597,651,552,774,542,230,219,176,611,658,451,311,334,392,314,653,601,425,543,124,775,231,221,340,335,659,613,556,453,315,234,778,126,433,674,288,317,342,184,235,396,661,127,584,558,617,779,457,208,356,343,242,675,564,559,786,237,346,398,665,781,625,243,465,188,706,358,347,304,677,404,588,566,399,787,216,359,349,245,707,190,567,802,481,590,362,406,648,570,789,681,249,191,596,591,312,420,363,803,709,407,571,220,410,336,793,689,370,544,365,573,834,598,652,232,422,805,411,713,371,222,316,612,599,423,835,413,452,602,223,654,344,776,426,373,721,318,809,128,236,614,603,560,660,655,898,377,837,319,427,454,615,605,817,400,238,737,348,434,618,662,899,429,455,780,841,244,239,435,458,360,568,676,619,663,350,666,592,901,782,626,459,408,192,246,351,621,849,437,678,667,466,627,788,783,364,572,247,461,441,905,250,679,669,708,467,600,865,682,629,574,412,366,790,251,482,633,469,913,575,683,372,424,710,367,804,791,224,414,253,656,483,794,604,690,685,711,473,415,320,374,691,714,929,616,806,795,485,606,428,375,240,715,664,807,797,607,836,378,693,456,430,722,489,810,620,961,717,697,379,436,431,723,811,838,497,668,622,352,381,784,738,248,818,460,438,725,813,839,628,680,623,900,670,819,842,739,439,462,729,442,671,576,630,252,843,792,902,741,468,684,463,368,821,443,631,850,634,845,254,825,903,712,416,686,745,445,470,851,906,635,255,692,687,796,484,471,866,753,376,608,474,853,907,637,808,716,694,798,867,914,486,475,432,909,857,695,799,718,380,698,915,487,869,477,812,724,719,490,624,699,930,382,917,840,814,873,440,672,491,701,383,726,931,820,815,464,498,921,740,881,727,493,632,962,730,933,499,844,822,444,742,731,688,963,823,472,846,904,826,501,446,937,636,256,743,733,852,847,505,965,827,447,746,638,945,476,800,829,854,696,747,908,639,969,488,478,720,868,855,754,749,858,910,479,755,977,700,384,870,859,816,492,916,911,728,871,861,757,702,993,494,874,918,761,703,500,495,824,932,875,919,732,922,848,882,877,448,502,744,934,923,883,734,828,503,935,925,964,735,506,856,938,885,830,640,748,507,889,831,939,966,480,912,750,509,860,946,941,967,756,751,947,970,872,862,971,920,704,758,863,949,496,978,876,759,973,953,762,979,924,878,763,994,981,884,504,936,879,736,926,765,995,985,927,832,886,508,997,940,887,752,890,968,942,510,1001,891,948,943,511,1009,864,893,760,972,950,951,974,954,764,980,975,880,955,766,928,957,982,767,996,983,888,986,998,987,944,892,999,989,512,1002,894,952,1003,895,976,1010,1005,1011,956,984,1013,958,768,1017,959,988,1000,990,991,896,1004,1006,1012,1007,960,1014,1015,1018,1019,992,1021,1008,1016,1020,1022,1023,1024]

序列8

[1,2,3,5,9,17,33,65,129,4,6,257,7,10,11,18,13,19,513,34,21,35,25,66,8,67,37,41,130,69,12,131,49,73,258,133,14,81,259,20,15,137,97,22,261,514,145,36,23,26,515,265,161,38,27,517,273,39,29,68,42,193,521,43,70,289,16,50,45,71,132,529,51,74,321,75,24,134,53,545,82,77,28,135,385,260,83,138,57,98,577,85,139,40,262,30,99,146,141,89,31,263,147,72,641,516,44,266,162,149,101,46,105,267,518,163,52,47,274,769,153,269,76,194,519,136,113,54,275,522,195,55,290,78,165,58,277,169,523,84,79,291,197,59,530,281,140,525,32,61,322,86,177,264,201,531,100,87,323,90,546,142,293,209,297,533,102,91,48,148,143,386,325,547,103,93,268,537,225,106,150,387,578,305,329,520,56,164,107,151,154,80,389,579,270,114,109,337,549,553,166,155,115,276,271,60,642,581,393,167,157,196,88,524,353,170,117,62,278,643,561,585,92,401,63,171,198,292,279,144,282,121,178,770,645,173,199,526,593,179,202,417,104,294,283,94,771,532,527,649,203,152,295,285,95,324,181,210,298,609,108,449,534,205,156,773,211,299,657,326,548,535,185,110,272,226,306,538,213,301,327,116,168,111,777,388,158,307,330,227,673,550,539,217,159,64,118,331,280,390,200,172,785,551,541,309,580,119,338,554,122,333,705,284,391,229,174,233,339,394,555,123,582,180,175,313,801,354,528,204,562,96,341,395,125,296,557,583,241,182,286,644,355,402,563,586,397,345,183,287,833,206,186,403,328,300,587,536,646,212,207,112,565,187,418,594,405,357,302,361,589,540,647,160,189,214,897,772,419,308,303,595,650,569,409,228,332,215,610,120,450,218,392,369,310,597,651,552,774,542,230,219,176,611,658,451,311,334,421,314,653,601,425,543,124,775,231,221,340,335,659,584,556,453,315,234,778,126,396,674,288,317,342,184,235,433,661,127,613,558,617,779,457,208,356,343,242,675,564,559,786,237,346,398,665,781,588,243,465,188,706,358,347,304,648,404,625,566,399,787,216,359,349,245,707,190,567,802,481,590,362,406,677,570,789,681,220,191,596,591,312,420,363,803,709,407,571,249,410,336,793,652,370,544,365,573,834,598,689,232,422,776,411,713,371,222,316,612,599,423,835,413,452,602,223,654,344,805,426,373,721,318,809,128,236,614,603,560,660,655,898,348,837,319,427,454,615,605,780,400,238,737,377,434,618,662,899,429,455,817,841,244,239,435,458,360,568,676,619,663,350,666,592,901,782,626,459,408,192,246,351,621,849,437,678,667,466,627,788,783,364,572,247,461,412,905,250,679,669,708,467,600,865,682,629,574,441,366,790,251,482,604,469,913,575,683,372,424,710,367,804,791,224,414,253,656,483,794,633,690,685,711,473,415,320,374,691,714,929,616,806,795,456,606,428,375,240,715,664,807,797,607,836,378,693,485,430,722,489,810,620,961,717,668,379,436,431,723,811,838,460,697,622,352,381,784,738,248,818,497,438,725,813,839,628,680,623,900,670,819,842,739,439,462,729,442,671,576,630,252,843,792,902,712,468,684,463,368,821,443,631,850,634,845,254,796,903,741,416,686,745,445,470,851,906,635,255,692,687,825,484,471,866,716,376,608,474,853,907,637,808,753,694,798,867,914,486,475,432,909,857,695,799,718,380,698,915,487,840,477,812,724,719,490,624,699,930,382,917,869,814,873,440,672,491,701,383,726,931,820,815,464,498,921,740,844,727,493,632,962,730,904,499,881,822,444,742,731,688,963,823,472,846,933,826,501,446,937,636,256,743,733,852,847,476,965,827,447,746,638,908,505,800,829,854,696,747,945,639,969,488,478,720,868,855,754,749,858,910,479,755,977,700,384,870,859,816,492,916,911,728,871,861,757,702,993,494,874,918,732,703,500,495,824,932,875,919,761,922,848,882,877,448,502,744,934,923,883,734,828,503,935,925,964,735,506,856,938,885,830,640,748,507,860,831,939,966,480,912,750,509,889,946,941,967,756,751,947,970,872,862,971,920,704,758,863,949,496,978,876,759,973,924,762,979,953,878,763,994,981,884,504,936,879,736,926,765,995,985,927,832,886,508,968,940,887,752,890,997,942,510,1001,891,948,943,511,972,864,893,760,1009,950,951,974,954,764,980,975,880,955,766,928,957,982,767,996,983,888,986,998,987,944,892,999,989,512,1002,894,952,1003,895,976,1010,1005,1011,956,984,1013,958,768,988,959,1017,1000,990,991,896,1004,1006,1012,1007,960,1014,1015,1018,1019,992,1021,1008,1016,1020,1022,1023,1024]

进行极化编码时，若所需的母码序列的长度等于1024，则发送设备可以采用上述序列3至序列8中的任意一个序列作为极化编码的母码序列。若所需的母码序列的长度小于1024，则发送设备可以从上述序列3至序列8中的任意一个序列中读取所需长度的序列作为母码序列。

例如，若发送设备进行极化编码所需的母码长度等于64，则发送设备可以从序列3至序列8中的任意一个序列中依次读取极化信道的索引小于或等于64的索引，即能构成母码序列。

在上述方式2中，发送设备在生成指示序列时，是根据冒泡算法，判断长度为2n的极化码对应的2n个极化信道的可靠度中，当前可靠度最高的极化信道的索引是否属于区间[1,n]生成指示序列的。

可选地，在另一种可能的实现方式中，发送设备可以根据PW公式计算长度为2n的极化码对应的2n个极化信道的可靠度，并根据该2n个极化信道的可靠度，对该2n个极化信道的索引进行排序，得到一个序列(以下，记作序列#A)。

其中，PW公式如下公式(6)所示：

其中，B_j∈{0,1},j∈{0,1,...,n-1},i＝B_n-1B_n-2...B₀,B_n-1B_n-2...B₀为i的二进制表示，W_i为第i个极化信道的极化权重，i∈{0,1,...,n-1}。

应理解，极化权重也可以作为衡量极化信道的可靠度的一个参量。因此，对根据公式(6)计算得到的极化信道的极化权重进行排序，也即对极化信道的可靠度进行排序。

发送设备依次读取序列#A中的索引，判断每个索引是否属于区间[1,n]。

若序列#A中的第i个索引属于区间[1,n]，则在指示序列的头部加入1，若序列#A的第i个索引不属于区间[1,n]，则在指示序列的头部加入0，直至指示序列中包括2n个索引。

相对应地，发送设备在进行极化编码时，可以首先获取序列#7，再根据序列#7确定序列#8。接下来，发送设备根据指示序列，从序列#7和序列#8中读取索引，依次遍历指示序列中的每个元素，最后将依次读取的所有索引构成的序列确定为母码序列。

下面给出根据PW公式计算长度为2n的极化码对应的2n个极化信道的可靠度，进而确定得到母码序列的示例。例如下面的序列9。

序列9

[1,2,3,5,9,17,33,4,6,7,10,65,11,18,13,19,129,34,21,35,25,8,37,66,12,257,67,41,14,49,69,20,130,15,22,73,131,23,36,26,513,133,38,81,27,39,258,97,137,29,42,259,68,70,16,43,145,50,261,71,45,74,161,51,24,265,75,132,514,134,53,82,28,77,515,135,57,273,83,138,40,30,517,289,193,98,139,85,31,44,146,260,99,262,89,521,141,46,72,147,52,263,101,47,266,76,162,529,149,54,321,267,105,78,163,545,153,55,274,113,136,58,269,84,516,165,518,275,194,79,140,86,59,32,519,385,290,195,87,277,169,100,522,142,61,90,177,291,577,281,197,102,523,148,48,264,91,143,530,150,293,103,322,525,268,201,93,106,151,531,164,56,323,154,297,80,270,107,641,546,166,533,305,209,114,155,325,60,276,109,547,167,537,386,271,225,115,278,157,88,520,170,62,329,549,387,279,196,578,292,198,144,117,524,171,63,282,92,178,769,579,389,294,199,121,553,337,173,526,283,202,104,94,179,561,152,295,581,353,532,393,285,203,95,298,108,642,527,181,534,210,324,156,326,272,585,299,205,110,643,535,185,548,401,306,211,116,168,327,538,158,301,111,330,645,550,417,307,226,593,280,213,159,118,539,172,64,331,551,388,770,227,609,390,309,217,649,119,541,338,174,554,284,200,122,333,180,771,580,391,313,229,582,528,339,175,555,394,296,204,123,286,96,657,562,182,773,583,449,354,557,395,341,287,233,586,300,206,125,673,563,183,536,402,241,355,186,345,777,587,397,302,212,112,644,328,646,565,403,308,207,594,214,187,357,540,160,303,589,332,647,569,418,785,215,595,405,310,228,650,120,552,189,542,218,361,334,419,801,705,610,409,311,230,651,597,543,369,176,556,392,314,219,124,340,658,772,611,421,774,231,601,450,335,653,558,396,342,315,221,584,288,234,126,659,564,184,775,613,451,343,559,425,356,778,208,588,398,317,235,127,674,346,661,566,433,242,833,453,188,358,779,617,404,304,237,590,675,347,665,567,399,786,243,625,406,216,648,359,570,190,781,596,457,349,677,362,407,787,706,591,420,312,245,652,598,571,191,544,410,220,336,363,897,802,707,599,422,789,249,681,612,465,370,654,573,411,316,232,602,222,365,689,803,423,793,709,614,481,371,660,560,413,344,776,223,603,426,318,236,128,655,662,805,615,452,834,454,400,373,780,713,605,427,319,238,618,663,348,676,568,434,244,835,455,666,377,809,592,429,782,239,619,458,360,678,350,435,817,721,626,408,246,667,837,572,192,788,621,459,351,679,364,898,783,737,627,437,790,247,669,600,466,682,574,412,250,841,461,366,899,791,708,441,804,710,656,629,467,372,683,575,424,794,251,604,414,224,367,690,901,806,711,633,482,849,685,469,415,374,795,714,616,428,320,253,606,691,664,807,483,865,473,905,375,797,715,607,430,810,240,620,456,378,693,436,722,836,485,668,838,784,431,811,717,622,460,379,697,352,913,818,723,628,438,248,680,839,670,813,623,489,842,462,381,929,819,738,439,792,725,671,630,497,684,576,442,252,843,468,368,900,739,902,821,729,631,463,850,686,470,443,796,712,634,416,254,845,692,903,825,741,471,851,687,484,906,376,808,716,635,445,798,255,608,474,694,961,866,486,907,853,799,745,432,812,718,637,475,380,695,914,753,867,487,698,857,909,814,724,624,477,840,490,382,915,820,719,440,726,699,869,672,815,464,844,491,383,930,727,917,822,740,632,498,701,444,730,873,493,846,931,921,823,742,499,881,688,472,904,826,731,636,446,256,852,933,743,962,847,501,908,854,827,733,447,800,746,638,476,696,963,855,505,937,868,720,910,829,747,639,488,858,478,945,754,965,700,870,916,816,749,479,859,492,384,911,755,918,728,871,702,969,861,494,874,919,932,824,757,500,703,922,732,848,495,875,934,761,977,882,502,923,828,744,448,734,877,935,993,883,503,925,856,735,938,830,748,640,506,964,966,912,885,939,831,750,507,860,480,946,756,967,889,941,751,970,872,509,862,947,920,758,704,971,863,496,876,949,759,978,924,762,973,878,953,979,884,504,936,763,926,736,879,994,981,927,886,940,832,765,508,995,985,887,942,752,968,890,510,948,997,943,972,891,511,864,950,760,1001,974,893,951,1009,954,764,980,880,975,982,955,928,766,983,996,888,957,767,986,998,944,987,892,512,999,989,1002,894,952,976,1003,895,1010,956,1005,1011,984,958,768,1013,959,988,1017,1000,990,991,1004,896,1006,1012,1007,1014,960,1015,1018,1019,992,1021,1008,1016,1020,1022,1023,1024]

序列10

[1,2,3,5,9,17,33,4,6,7,10,65,11,18,13,19,129,34,21,35,25,37,41,66,8,257,67,49,12,14,69,20,130,15,22,73,131,23,36,26,513,133,38,81,27,39,258,97,137,29,42,259,68,70,43,50,145,16,261,71,45,74,161,51,53,265,75,132,514,134,24,82,57,77,515,135,28,273,83,138,40,30,517,289,193,98,139,85,31,44,146,260,99,262,89,521,141,46,101,147,52,263,105,47,266,72,162,529,149,54,321,267,113,76,163,545,153,55,274,78,165,58,269,84,516,169,518,275,194,79,136,86,59,32,519,385,290,195,87,277,177,100,522,140,61,90,142,291,577,281,197,102,523,148,48,293,91,143,530,150,297,103,322,525,264,201,93,106,151,531,164,56,323,154,305,107,268,114,641,546,166,533,270,209,80,155,325,60,276,109,547,167,537,386,271,225,115,278,157,117,549,170,62,329,553,387,279,196,578,292,198,171,88,520,178,63,282,121,144,769,579,389,294,199,92,561,337,173,524,283,202,104,94,179,526,181,295,581,353,532,393,285,203,95,298,108,642,527,152,534,210,324,185,326,299,585,306,205,110,643,535,156,548,401,272,211,116,168,327,538,158,301,111,330,645,550,417,307,226,593,309,213,159,118,539,172,64,331,551,388,770,227,609,390,280,217,649,119,541,338,174,554,313,229,122,333,180,771,580,391,284,233,582,555,339,175,562,394,296,200,123,286,96,657,528,182,773,583,449,354,557,395,341,287,241,586,300,204,125,673,563,183,565,402,206,355,186,345,777,587,397,302,212,112,644,357,646,536,403,308,207,594,214,187,361,569,160,303,589,328,647,540,418,785,215,595,405,310,228,650,120,552,189,542,218,369,332,419,801,705,610,409,311,230,651,597,543,334,176,556,421,314,219,124,340,658,772,611,425,774,231,601,450,335,653,558,392,342,315,221,613,288,234,126,659,564,184,775,617,451,343,559,433,356,778,235,584,396,317,242,127,674,346,661,566,398,208,833,453,188,358,779,625,404,304,237,588,675,347,665,567,399,786,243,590,406,245,677,359,570,190,781,596,457,349,681,362,407,787,706,591,420,312,216,648,598,571,191,544,410,249,363,370,897,802,707,599,422,789,220,689,612,465,336,652,573,411,316,232,602,222,365,654,803,423,793,709,614,481,371,660,560,413,373,805,223,603,426,318,236,128,655,662,809,615,452,834,454,427,344,776,713,605,434,319,238,618,663,377,676,568,400,244,835,455,666,348,817,619,429,780,239,626,458,360,678,350,435,782,721,592,437,246,667,837,572,192,788,621,459,351,679,364,898,783,737,627,408,790,247,669,629,466,682,574,441,250,841,461,366,899,791,708,412,804,710,683,600,467,372,690,575,424,794,251,633,414,224,367,656,901,806,711,604,482,849,685,469,415,374,795,714,616,428,320,253,606,691,693,807,483,865,473,905,375,797,715,607,430,810,240,620,485,378,664,436,722,836,489,697,838,811,431,818,717,622,456,379,668,352,913,784,723,628,438,248,680,839,670,813,623,497,842,460,381,929,819,738,439,821,725,671,630,462,684,576,442,252,843,468,368,900,739,902,792,729,631,463,850,686,470,443,825,741,634,416,254,845,692,903,796,745,471,851,687,484,906,376,808,712,635,445,798,255,608,474,694,961,866,486,907,853,799,753,432,812,716,637,475,380,695,914,718,867,487,698,857,909,814,724,624,477,869,490,382,915,820,719,440,726,699,873,672,815,491,840,498,383,930,727,917,822,740,632,464,701,444,730,881,493,844,931,921,823,742,499,846,688,501,933,826,731,636,446,256,852,937,743,962,847,472,904,854,827,733,447,800,746,638,505,696,963,855,476,945,868,747,908,829,754,639,488,858,478,910,720,965,700,870,916,816,749,479,859,492,384,911,755,918,757,871,702,969,861,494,874,919,932,824,728,500,703,922,761,875,495,882,934,732,977,848,502,923,828,744,448,734,877,935,993,883,503,925,885,735,938,830,748,640,506,964,966,939,856,946,831,750,507,889,480,912,756,967,860,941,751,970,872,509,862,947,949,758,704,971,863,496,876,920,759,978,953,762,973,878,924,979,884,504,936,763,926,736,879,994,981,927,886,940,832,765,508,995,985,887,942,752,997,890,510,948,1001,943,968,891,511,864,950,760,1009,972,893,951,974,954,764,980,880,975,982,955,928,766,983,996,888,957,767,986,998,944,987,892,512,999,989,1002,894,952,1003,1010,895,976,956,1005,1011,1013,958,768,984,959,1017,988,1000,990,991,1004,896,1006,1012,1007,1014,960,1015,1018,1019,992,1021,1008,1016,1020,1022,1023,1024]

序列11

[1,2,3,5,9,17,33,4,6,7,10,65,11,18,13,19,129,34,21,35,25,37,8,66,41,257,67,12,49,14,69,20,130,15,22,73,131,23,36,26,513,133,38,81,27,39,258,97,137,29,42,259,68,70,43,16,145,50,261,71,45,74,161,51,24,265,75,132,514,134,53,82,57,77,515,135,28,273,83,138,40,30,517,289,193,98,139,85,31,44,146,260,99,262,89,521,141,46,101,147,52,263,72,47,266,105,162,529,149,54,321,267,76,113,163,545,153,55,274,78,165,58,269,84,516,136,518,275,194,79,169,86,59,32,519,385,290,195,87,277,140,100,522,177,61,90,142,291,577,281,197,102,523,148,48,293,91,143,530,150,264,103,322,525,297,201,93,106,151,531,164,56,323,154,268,107,305,80,641,546,166,533,270,209,114,155,325,60,276,109,547,167,537,386,271,225,115,278,157,88,549,170,62,329,520,387,279,196,578,292,198,171,117,553,144,63,282,121,178,769,579,389,294,199,92,524,337,173,561,283,202,104,94,179,526,152,295,581,353,532,393,285,203,95,298,108,642,527,181,534,210,324,185,326,299,585,272,205,110,643,535,156,548,401,306,211,116,168,327,538,158,301,111,330,645,550,417,307,226,593,280,213,159,118,539,172,64,331,551,388,770,227,609,390,309,217,649,119,541,338,174,554,313,229,122,333,180,771,580,391,284,200,582,555,339,175,528,394,296,233,123,286,96,657,562,182,773,583,449,354,557,395,341,287,204,586,300,241,125,673,563,183,536,402,206,355,186,345,777,587,397,302,212,112,644,357,646,565,403,308,207,594,214,187,328,569,160,303,589,361,647,540,418,785,215,595,405,310,228,650,120,552,189,542,218,332,369,419,801,705,610,409,311,230,651,597,543,334,176,556,421,314,219,124,340,658,772,611,392,774,231,601,450,335,653,558,425,342,315,221,613,288,234,126,659,564,184,775,584,451,343,559,396,356,778,235,617,433,317,208,127,674,346,661,566,398,242,833,453,188,358,779,588,404,304,237,625,675,347,665,567,399,786,243,590,406,216,677,359,570,190,781,596,457,349,648,362,407,787,706,591,420,312,245,681,598,571,191,544,410,249,363,336,897,802,707,599,422,789,220,652,612,465,370,689,573,411,316,232,602,222,365,654,803,423,793,709,614,481,371,660,560,413,344,805,223,603,426,318,236,128,655,662,776,615,452,834,454,427,373,809,713,605,400,319,238,618,663,377,676,568,434,244,835,455,666,348,780,619,429,817,239,592,458,360,678,350,435,782,721,626,408,246,667,837,572,192,788,621,459,351,679,364,898,783,737,627,437,790,247,669,600,466,682,574,441,250,841,461,366,899,791,708,412,804,710,683,629,467,372,656,575,424,794,251,633,414,224,367,690,901,806,711,604,482,849,685,469,415,374,795,714,616,428,320,253,606,691,664,807,483,865,473,905,375,797,715,607,430,810,240,620,485,378,693,436,722,836,456,697,838,811,431,784,717,622,489,379,668,352,913,818,723,628,438,248,680,839,670,813,623,460,842,497,381,929,819,738,439,792,725,671,630,462,684,576,442,252,843,468,368,900,739,902,821,729,631,463,850,686,470,443,825,741,634,416,254,845,692,903,796,712,471,851,687,484,906,376,808,745,635,445,798,255,608,474,694,961,866,486,907,853,799,716,432,812,753,637,475,380,695,914,718,867,487,698,857,909,814,724,624,477,869,490,382,915,820,719,440,726,699,840,672,815,491,873,464,383,930,727,917,822,740,632,498,701,444,730,844,493,881,931,921,823,742,499,846,688,472,933,826,731,636,446,256,852,904,743,962,847,501,937,854,827,733,447,800,746,638,505,696,963,855,476,908,868,747,945,829,720,639,488,858,478,910,754,965,700,870,916,816,749,479,859,492,384,911,755,918,728,871,702,969,861,494,874,919,932,824,757,500,703,922,761,875,495,848,934,732,977,882,502,923,828,744,448,734,877,935,993,883,503,925,856,735,938,830,748,640,506,964,966,939,885,912,831,750,507,889,480,946,756,967,860,941,751,970,872,509,862,947,920,758,704,971,863,496,876,949,759,978,953,762,973,878,924,979,884,504,936,763,926,736,879,994,981,927,886,940,832,765,508,995,985,887,942,752,997,890,510,948,968,943,1001,891,511,864,950,760,972,1009,893,951,974,954,764,980,880,975,982,955,928,766,983,996,888,957,767,986,998,944,987,892,512,999,989,1002,894,952,1003,976,895,1010,956,1005,1011,984,958,768,1013,959,1017,988,1000,990,991,1004,896,1006,1012,1007,1014,960,1015,1018,1019,992,1021,1008,1016,1020,1022,1023,1024]

序列12

[1,2,3,5,9,17,33,4,6,7,10,65,11,18,13,19,129,34,21,35,25,37,8,66,41,257,67,49,12,14,69,20,130,15,22,73,131,36,23,26,513,133,38,81,27,39,258,97,137,29,42,259,68,70,43,16,145,50,261,71,45,74,161,51,24,265,75,132,514,134,53,82,57,77,515,135,28,273,83,138,40,30,517,289,193,98,139,85,31,44,146,260,99,262,89,521,141,46,101,147,52,263,72,47,266,105,162,529,149,54,321,267,113,76,163,545,153,55,274,78,165,58,269,84,516,136,518,275,194,79,169,86,59,32,519,385,290,195,100,277,177,87,522,140,61,90,142,291,577,281,197,102,523,148,48,293,91,143,530,150,264,103,322,525,297,201,93,106,164,531,151,56,323,154,305,107,268,80,641,546,166,533,270,209,114,155,325,60,276,109,547,167,537,386,271,225,115,278,157,88,549,170,62,329,520,387,292,196,578,279,198,171,117,553,144,63,282,121,178,769,579,389,294,199,92,561,337,173,524,283,202,104,94,179,526,152,295,581,353,532,393,285,203,95,298,108,642,527,181,534,210,324,185,326,299,585,272,205,110,643,548,156,535,401,306,211,116,168,327,538,158,301,111,330,645,550,417,307,226,593,280,213,159,118,539,172,64,331,551,388,770,227,609,390,309,217,649,119,541,338,174,554,313,229,122,333,180,771,580,391,284,200,582,555,339,175,528,394,296,233,123,286,96,657,562,182,773,583,449,354,557,395,341,287,241,586,300,204,125,673,563,183,536,402,206,355,186,345,777,587,397,302,212,112,644,357,646,565,403,308,207,594,214,187,328,569,160,303,589,361,647,540,418,785,228,595,405,310,215,650,120,552,189,542,218,369,332,419,801,705,610,409,311,230,651,597,543,334,176,556,421,314,219,124,340,658,772,611,392,774,231,601,450,335,653,558,425,342,315,221,613,288,234,126,659,564,184,775,584,451,356,559,433,343,778,235,617,396,317,208,127,674,346,661,566,398,242,833,453,188,358,779,625,404,304,237,588,675,347,665,567,399,786,243,590,406,216,677,359,570,190,781,596,457,349,648,362,420,787,706,591,407,312,245,681,598,571,191,544,410,249,363,336,897,802,707,612,422,789,220,689,599,465,370,652,573,411,316,232,602,222,365,654,803,423,793,709,614,481,371,660,560,413,344,805,223,603,426,318,236,128,655,662,776,615,452,834,454,427,373,809,713,605,400,319,238,618,676,377,663,568,434,244,835,455,666,348,817,619,429,780,239,592,458,360,678,350,435,782,721,626,408,246,667,837,572,192,788,621,459,351,679,364,898,783,737,627,437,790,247,669,600,466,682,574,441,250,841,461,366,899,804,708,412,791,710,683,629,467,372,656,575,424,794,251,633,414,224,367,690,901,806,711,604,482,849,685,469,415,374,795,714,616,428,320,253,606,691,664,807,483,865,473,905,375,797,715,607,430,810,240,620,485,378,693,436,722,836,456,697,838,811,431,784,717,622,489,379,668,352,913,818,723,628,438,248,680,839,670,813,623,497,842,460,381,929,819,738,439,792,725,671,630,462,684,576,442,252,843,468,368,900,739,902,821,729,631,463,850,686,470,443,825,741,634,416,254,845,692,903,796,712,484,851,687,471,906,376,808,745,635,445,798,255,608,474,694,961,866,486,907,853,799,753,432,812,716,637,475,380,695,914,718,867,487,698,857,909,814,724,624,477,869,490,382,915,820,719,440,726,699,840,672,815,491,873,464,383,930,740,917,822,727,632,498,701,444,730,881,493,844,931,921,823,742,499,846,688,472,933,826,731,636,446,256,852,904,743,962,847,501,937,854,827,733,447,800,746,638,505,696,963,868,476,945,855,747,908,829,720,639,488,858,478,910,754,965,700,870,916,816,749,479,859,492,384,911,755,918,728,871,702,969,861,494,874,932,919,824,757,500,703,922,761,875,495,848,934,732,977,882,502,923,828,744,448,734,877,935,993,883,503,925,856,735,938,830,748,640,506,964,966,939,885,912,831,750,507,889,480,946,756,967,860,941,751,970,872,509,862,947,920,758,704,971,863,496,876,949,759,978,953,762,973,878,924,979,884,504,936,763,926,736,879,994,981,927,886,940,832,765,508,995,985,887,942,752,997,890,510,948,968,943,1001,891,511,864,950,760,1009,972,893,951,974,954,764,980,880,975,982,955,928,766,996,983,888,957,767,986,998,944,987,892,512,999,989,1002,894,952,1003,976,895,1010,956,1005,1011,984,958,768,1013,959,1017,988,1000,990,991,1004,896,1006,1012,1007,1014,960,1015,1018,1019,992,1021,1008,1016,1020,1022,1023,1024]

序列13

[1,2,3,5,9,17,33,4,6,7,10,65,11,18,13,19,129,34,21,35,25,8,37,66,41,257,67,12,49,14,69,20,130,15,22,73,131,36,23,26,513,133,38,81,27,39,258,97,137,29,42,259,68,70,43,16,145,50,261,71,45,74,161,51,24,265,75,132,514,134,53,82,28,77,515,135,57,273,83,138,40,30,517,289,193,98,139,85,31,44,146,260,99,262,89,521,141,46,72,147,52,263,101,47,266,105,162,529,149,54,321,267,76,113,163,545,153,55,274,78,136,58,269,84,516,165,518,275,194,79,169,86,59,32,519,385,290,195,100,277,140,87,522,177,61,90,142,291,577,281,197,102,523,148,48,264,91,143,530,150,293,103,322,525,297,201,93,106,164,531,151,56,323,154,268,107,305,80,641,546,166,533,270,209,114,155,325,60,276,109,547,167,537,386,271,225,115,278,157,88,520,170,62,329,549,387,292,196,578,279,198,171,117,553,144,63,282,92,178,769,579,389,294,199,121,524,337,173,561,283,202,104,94,179,526,152,295,581,353,532,393,285,203,95,298,108,642,527,181,534,210,324,156,326,299,585,272,205,110,643,548,185,535,401,306,211,116,168,327,538,158,301,111,330,645,550,417,307,226,593,280,213,159,118,539,172,64,331,551,388,770,227,609,390,309,217,649,119,541,338,174,554,284,200,122,333,180,771,580,391,313,229,582,555,339,175,528,394,296,233,123,286,96,657,562,182,773,583,449,354,557,395,341,287,204,586,300,241,125,673,563,183,536,402,206,355,186,345,777,587,397,302,212,112,644,328,646,565,403,308,207,594,214,187,357,540,160,303,589,361,647,569,418,785,228,595,405,310,215,650,120,552,189,542,218,332,369,419,801,705,610,409,311,230,651,597,543,334,176,556,392,314,219,124,340,658,772,611,421,774,231,601,450,335,653,558,425,342,315,221,584,288,234,126,659,564,184,775,613,451,356,559,396,343,778,235,617,433,317,208,127,674,346,661,566,398,242,833,453,188,358,779,588,404,304,237,625,675,347,665,567,399,786,243,590,406,216,648,359,570,190,781,596,457,349,677,362,420,787,706,591,407,312,245,681,598,571,191,544,410,220,363,336,897,802,707,612,422,789,249,652,599,465,370,689,573,411,316,232,602,222,365,654,803,423,793,709,614,481,371,660,560,413,344,776,223,603,426,318,236,128,655,662,805,615,452,834,454,427,373,809,713,605,400,319,238,618,676,348,663,568,434,244,835,455,666,377,780,619,429,817,239,592,458,360,678,350,435,782,721,626,408,246,667,837,572,192,788,621,459,351,679,364,898,783,737,627,437,790,247,669,600,466,682,574,412,250,841,461,366,899,804,708,441,791,710,683,629,467,372,656,575,424,794,251,604,414,224,367,690,901,806,711,633,482,849,685,469,415,374,795,714,616,428,320,253,606,691,664,807,483,865,473,905,375,797,715,607,430,810,240,620,456,378,693,436,722,836,485,668,838,811,431,784,717,622,489,379,697,352,913,818,723,628,438,248,680,839,670,813,623,460,842,497,381,929,819,738,439,792,725,671,630,462,684,576,442,252,843,468,368,900,739,902,821,729,631,463,850,686,470,443,796,712,634,416,254,845,692,903,825,741,484,851,687,471,906,376,808,745,635,445,798,255,608,474,694,961,866,486,907,853,799,716,432,812,753,637,475,380,695,914,718,867,487,698,857,909,814,724,624,477,840,490,382,915,820,719,440,726,699,869,672,815,491,873,464,383,930,740,917,822,727,632,498,701,444,730,844,493,881,931,921,823,742,499,846,688,472,904,826,731,636,446,256,852,933,743,962,847,501,937,854,827,733,447,800,746,638,476,696,963,868,505,908,855,747,945,829,720,639,488,858,478,910,754,965,700,870,916,816,749,479,859,492,384,911,755,918,728,871,702,969,861,494,874,932,919,824,757,500,703,922,732,875,495,848,934,761,977,882,502,923,828,744,448,734,877,935,993,883,503,925,856,735,938,830,748,640,506,964,966,939,885,912,831,750,507,860,480,946,756,967,889,941,751,970,872,509,862,947,920,758,704,971,863,496,876,949,759,978,924,762,973,878,953,979,884,504,936,763,926,736,879,994,981,927,886,940,832,765,508,995,985,887,942,752,968,890,510,948,997,943,1001,891,511,864,950,760,972,1009,893,951,974,954,764,980,880,975,982,955,928,766,996,983,888,957,767,986,998,944,987,892,512,999,989,1002,894,952,1003,976,895,1010,956,1005,1011,984,958,768,1013,959,988,1017,1000,990,991,1004,896,1006,1012,1007,1014,960,1015,1018,1019,992,1021,1008,1016,1020,1022,1023,1024]。

在上述方式2中，发送设备根据第一序列和指示序列，可以确定出极化编码所需的母码序列。即，发送设备在进行极化编码时，首先需要获取第一序列和指示序列。其中，发送设备可以预先存储第一序列和指示序列，这样，在进行极化编码时，可以获取预先存储的第一序列和指示序列，进而确定母码序列。后续，发送设备采用该母码序列对待编码比特进行极化编码。

在另一种可能的实现方式中，发送设备在进行极化编码时，可以通过在线计算或查表的方式，确定第一序列，再根据第一序列和指示序列确定极化编码所需的母码序列。

在本申请实施例中，对发送设备获取第一序列的方式不作限定。

可选地，发送设备获取第一序列，包括：

发送设备从第三序列中读取第一序列，第一序列包括的n个信道的索引为第三序列中第(i·n+1)个位置的索引至第(i+1)·n个位置的索引分别减去i·n得到的，i≥0且为整数，第三序列包括的索引的个数大于或等于n，第三序列中的索引是按照各自对应的极化信道的可靠度或者信道容量的大小顺序排列的。

类似地，发送设备获取指示序列，包括：

发送设备从第四序列中读取第五序列，第五序列包括2n个索引，所述2n个索引为第四序列中第(j·2n+1)个位置的索引至第(j+1)·2n个位置的索引，j≥0且为整数，第四序列包括的索引的个数大于或等于2n，第四序列中的索引是按照各自对应的极化信道的可靠度的大小顺序排列的；

发送设备根据第五序列，生成指示序列。

需要说明的是，这里的第三序列、第四序列和第五序列仅仅是为了区分不同的序列。其中，第三序列、第四序列和第五序列中包括极化信道的索引。

另外，这里的第三序列和第四序列的长度可以相等或者不相等，本申请实施例对此不作特别限定。第五序列的长度小于或等于第四序列的长度。

进一步地，第三序列中包括的极化信道的索引是按照各自对应的极化信道的可靠度的大小顺序排列的。第四序列中包括的极化信道的索引是也按照这些索引对应的极化信道的可靠度的大小顺序排列的。

下面再给出几种母码序列的示例。

序列14

[1,2,3,5,9,17,33,65,4,129,6,7,257,10,11,513,18,13,19,34,21,35,25,66,37,8,67,41,130,69,12,49,131,73,14,258,20,15,133,81,259,22,137,97,23,36,514,261,26,145,38,27,515,265,161,39,29,68,517,42,273,193,43,70,16,50,521,289,45,71,132,51,74,529,24,321,75,53,134,82,77,57,135,545,28,385,260,83,138,98,40,85,577,30,139,262,99,146,31,89,141,44,263,641,101,147,516,266,72,46,162,105,149,267,52,47,769,518,163,274,153,76,113,269,54,194,519,165,275,55,78,522,136,195,58,290,84,169,79,277,523,59,197,291,32,177,86,140,281,530,61,525,322,87,100,201,293,531,142,90,323,264,148,48,209,143,297,102,546,91,533,386,103,93,325,150,225,547,305,106,268,537,151,56,164,387,578,329,107,549,154,270,114,80,109,389,520,166,155,579,337,276,60,271,553,115,167,157,642,196,393,581,117,62,170,88,278,353,561,524,63,171,279,121,292,198,643,401,585,282,178,144,92,173,199,526,770,645,294,283,179,202,104,417,593,532,94,527,295,285,203,181,324,152,95,771,649,298,210,108,534,449,609,205,185,773,299,326,211,156,535,110,548,657,272,306,538,301,226,327,116,168,111,213,388,158,307,330,777,550,539,673,227,64,217,118,159,309,331,551,172,280,390,541,580,229,119,338,785,554,122,333,705,313,391,200,174,233,339,123,284,555,394,582,180,175,801,96,354,562,528,125,296,241,341,557,395,583,204,286,644,182,355,563,586,402,345,287,183,397,833,206,300,565,186,357,587,403,112,536,646,212,207,594,187,418,328,302,589,569,361,160,405,897,647,214,189,308,772,303,595,650,540,120,419,215,228,409,369,610,332,552,450,597,218,310,651,421,542,774,611,176,230,219,311,658,124,334,392,543,601,451,653,314,425,775,231,221,340,556,335,613,659,126,234,315,453,778,288,433,184,674,584,342,558,127,396,235,317,617,661,779,564,208,242,343,457,559,356,237,675,398,786,625,665,346,188,781,243,588,566,404,304,465,399,706,358,347,677,787,190,245,567,216,359,590,349,648,707,481,406,802,191,570,681,362,249,789,596,591,312,407,420,571,220,363,709,803,689,544,410,793,598,370,652,336,232,573,365,222,834,422,411,713,805,316,599,612,371,223,654,602,423,413,452,128,835,776,721,236,373,318,426,344,809,660,560,655,614,603,319,898,427,837,377,454,238,615,605,737,817,662,400,434,618,244,780,348,239,429,455,899,841,663,568,676,360,435,458,619,192,350,666,246,782,626,592,901,437,459,621,351,408,849,678,247,667,788,572,783,466,364,627,250,461,441,679,669,708,905,865,467,629,574,251,682,412,790,600,366,224,575,372,482,424,367,253,683,469,791,633,804,710,913,414,656,794,690,604,483,320,685,711,473,374,415,806,428,795,616,929,691,714,375,485,606,240,378,807,797,715,693,836,456,664,607,430,489,810,620,961,379,722,436,431,352,717,697,811,497,838,381,248,723,668,460,622,818,438,784,813,628,738,839,680,623,725,900,439,670,462,819,842,252,442,739,368,576,729,630,468,671,463,843,684,792,821,443,902,631,741,416,254,850,470,634,445,845,825,712,903,686,255,745,376,471,484,851,635,796,906,692,687,608,474,866,637,808,753,853,716,432,907,798,486,475,380,694,867,914,799,857,487,695,477,909,718,812,382,490,698,869,624,915,724,719,440,383,699,491,840,930,814,672,873,917,464,498,726,820,701,815,493,931,632,444,727,740,921,499,881,844,730,822,962,933,446,501,472,688,742,823,731,636,846,256,904,447,826,963,937,743,852,505,733,847,638,827,746,476,965,800,945,696,854,908,639,747,829,488,478,720,754,855,969,868,749,910,858,700,479,755,384,492,916,816,911,870,977,859,702,728,757,871,861,494,918,703,993,874,761,500,824,495,919,932,732,875,922,848,448,744,882,502,877,734,934,923,828,883,503,735,935,925,640,964,506,748,830,856,938,885,831,507,939,750,480,966,889,912,860,756,946,509,751,941,967,872,947,970,704,862,758,920,863,971,496,949,759,876,978,762,973,953,924,878,763,979,736,884,504,936,879,994,765,926,981,832,886,995,927,985,940,508,887,752,997,890,968,942,510,891,948,1001,943,864,511,760,893,972,950,1009,951,974,880,764,954,980,975,955,928,766,982,957,888,767,983,996,986,944,998,892,987,999,989,512,894,1002,952,895,1003,976,1010,956,1005,1011,958,984,1013,768,959,988,1017,1000,990,991,1004,896,1006,1012,1007,960,1014,1015,1018,992,1019,1021,1008,1016,1020,1022,1023,1024]

序列15

[1,2,3,5,9,17,33,65,129,4,257,6,7,10,513,11,18,13,19,34,21,35,25,66,37,8,67,41,130,69,49,12,131,73,14,258,133,20,15,81,259,137,22,97,514,36,23,261,145,26,515,38,27,265,161,39,29,68,517,42,273,193,43,70,521,16,50,289,45,71,132,74,51,529,321,75,24,53,134,82,77,545,57,135,385,260,28,83,138,40,98,577,85,30,139,262,99,146,31,89,141,44,263,641,101,147,516,266,72,46,162,149,105,52,267,47,769,518,163,274,153,113,76,269,54,194,519,165,275,55,78,522,136,195,58,290,84,169,79,277,59,523,32,197,291,140,86,177,530,281,61,525,322,100,87,201,293,142,90,531,264,323,148,48,143,102,91,209,546,297,533,386,103,93,325,150,547,305,268,225,106,537,56,151,164,387,107,578,329,154,549,270,80,114,109,520,166,389,155,60,276,579,271,337,115,553,167,157,196,62,642,393,88,278,170,117,581,353,561,524,63,279,171,292,198,121,643,144,401,282,92,585,178,173,526,199,104,770,294,283,202,179,645,94,532,527,417,593,295,285,152,324,203,181,95,771,298,108,649,210,534,449,205,609,185,299,326,156,211,110,548,535,773,272,306,657,538,116,301,226,168,327,111,213,388,158,307,330,550,539,777,64,227,159,118,673,217,172,331,280,309,551,390,541,119,580,229,338,554,122,785,333,200,313,174,391,705,284,233,123,339,555,180,582,394,175,96,528,296,562,354,801,125,204,341,241,557,286,583,395,182,644,586,563,355,402,287,183,345,397,206,300,833,186,112,536,587,565,357,212,403,207,646,328,187,594,302,160,418,589,569,405,361,647,214,308,303,189,897,772,540,595,120,650,419,228,215,409,369,332,552,610,310,218,597,450,542,651,421,176,774,311,230,219,124,334,611,658,543,392,314,601,451,653,340,556,231,425,335,221,775,126,613,315,234,659,288,778,453,184,584,558,433,396,342,127,674,317,235,661,617,564,208,779,559,343,356,242,457,237,675,398,188,346,786,665,625,588,243,781,566,404,304,399,358,706,465,347,677,190,216,787,245,567,590,359,349,648,406,191,570,707,481,362,802,596,681,249,591,789,312,407,420,571,220,363,544,709,410,803,598,336,689,652,232,370,793,573,365,222,422,411,316,834,612,599,713,371,805,223,654,602,423,413,452,128,236,776,318,344,426,373,835,660,560,655,614,603,721,809,319,427,238,454,898,377,615,605,837,662,400,348,434,244,780,737,618,817,239,429,455,568,663,676,360,899,435,619,458,841,192,350,666,246,782,592,626,459,408,621,437,351,678,247,901,667,572,788,783,364,849,627,466,250,461,441,679,669,708,574,412,905,600,366,682,629,467,251,790,224,865,575,372,424,482,367,791,683,253,804,710,469,633,414,913,656,794,690,604,320,483,685,415,374,711,473,616,428,806,795,714,691,606,375,240,485,929,378,807,797,664,456,836,715,607,693,430,810,620,489,379,436,722,431,352,961,717,697,811,838,381,248,668,723,622,497,460,784,438,818,628,813,680,738,623,839,725,900,439,670,462,842,819,252,442,368,576,739,671,630,468,463,729,684,843,792,821,443,902,631,416,741,254,850,470,634,445,845,712,825,686,903,376,255,484,471,796,745,635,851,692,906,687,608,474,808,866,637,853,753,716,432,798,907,486,475,380,694,867,914,799,487,695,857,477,718,909,812,382,698,490,624,869,724,915,719,440,383,699,840,491,814,930,672,464,917,873,726,498,820,701,815,493,632,444,931,727,740,499,921,881,844,822,730,962,446,933,472,688,501,823,742,731,636,846,256,904,447,826,963,852,743,937,505,847,733,638,827,746,476,800,965,696,908,854,945,639,829,747,488,478,720,868,855,754,969,749,910,700,858,479,755,384,492,916,816,911,870,859,977,702,728,757,871,861,494,918,703,874,993,761,500,824,495,932,919,732,875,922,848,744,448,882,502,877,734,934,923,828,883,503,735,935,925,964,640,748,506,830,856,938,885,507,831,939,750,480,966,889,912,860,946,756,509,751,941,967,872,970,947,704,862,758,920,971,949,863,496,759,876,978,762,973,953,924,979,878,763,736,884,504,936,994,879,765,981,926,832,995,927,886,985,940,508,887,752,997,890,968,942,510,1001,891,948,943,864,511,893,760,972,1009,950,951,974,954,764,880,980,975,955,928,766,982,957,888,767,983,996,986,944,998,987,892,999,989,512,894,1002,952,895,1003,976,1010,1005,956,1011,958,984,1013,768,959,1017,988,1000,990,991,896,1004,1006,1012,1007,960,1014,1015,1018,1019,992,1021,1008,1016,1020,1022,1023,1024]

序列16

[1,2,3,5,9,17,33,4,6,65,7,10,129,11,18,13,19,34,21,35,25,257,513,66,8,37,67,41,12,130,69,49,14,131,20,73,15,258,133,22,81,259,137,36,23,26,97,261,514,38,145,27,515,39,265,68,29,42,161,517,43,70,273,16,50,193,71,45,521,132,74,51,289,24,75,53,134,529,82,321,77,135,28,57,83,138,260,545,40,98,385,30,85,139,262,146,31,99,577,44,89,141,263,147,101,266,516,72,46,162,641,52,149,47,105,267,163,518,274,76,54,153,113,269,194,769,165,275,519,78,55,136,522,58,84,195,290,79,169,277,523,59,32,86,140,197,291,61,177,281,530,525,100,87,322,293,142,201,531,90,264,148,323,48,102,143,91,297,546,209,533,103,386,150,93,325,547,106,268,305,164,151,56,225,537,387,107,154,329,578,549,270,80,114,166,60,109,276,155,271,389,579,520,115,337,553,167,196,157,393,170,278,642,581,88,62,117,353,561,524,171,292,279,63,198,144,92,121,643,282,178,401,585,199,173,526,294,283,104,202,179,770,645,532,593,94,295,417,527,324,152,203,285,181,298,95,771,649,108,210,534,205,609,185,299,326,449,548,156,110,211,535,773,306,657,272,301,327,538,168,116,226,111,388,158,213,330,307,550,777,539,64,118,159,227,673,331,172,217,280,309,551,390,580,541,338,119,229,554,333,785,200,122,313,391,705,174,339,555,582,284,394,180,123,175,233,562,354,801,96,296,341,528,583,557,204,395,286,182,125,241,644,586,563,355,402,287,345,397,206,183,300,587,833,565,186,403,212,357,646,536,112,207,594,328,302,187,418,589,569,405,647,160,361,897,595,308,214,650,772,303,540,189,419,120,228,215,332,409,369,610,597,552,651,310,218,450,421,542,774,611,658,311,230,601,334,176,219,653,392,124,314,451,543,340,425,556,775,335,231,659,613,221,778,315,234,126,453,674,584,288,342,396,184,433,558,661,617,127,235,317,779,564,356,343,208,242,457,675,559,786,398,346,188,237,665,625,588,781,706,677,404,243,566,358,399,304,347,465,787,567,590,707,216,190,359,245,802,681,648,406,349,570,596,362,191,481,789,591,420,407,312,220,249,571,709,803,363,410,689,598,652,544,793,336,370,573,834,232,422,365,411,713,599,805,612,316,222,371,654,602,423,452,413,835,776,223,128,660,809,721,426,614,655,236,318,344,373,603,560,898,427,837,615,454,319,662,605,238,377,817,737,618,780,400,434,348,244,429,455,663,676,899,239,568,841,619,360,458,435,666,782,626,350,192,246,592,901,678,621,408,459,667,788,437,849,783,351,572,247,627,364,466,679,250,461,708,669,441,905,682,865,790,629,412,467,574,600,366,251,683,804,791,710,224,424,372,482,575,633,367,414,469,913,253,794,690,656,685,604,711,320,483,806,374,415,428,473,795,714,691,616,929,375,240,485,606,807,836,715,797,693,664,456,378,810,607,430,722,620,436,489,717,379,697,961,811,838,431,723,352,460,248,438,381,497,818,668,622,784,813,839,738,680,628,725,900,623,842,819,670,462,439,739,252,729,442,843,576,630,671,468,368,821,463,684,792,902,850,443,741,631,416,254,845,825,470,903,634,712,686,851,445,745,255,906,796,376,484,471,692,635,687,866,474,608,808,853,907,716,637,798,753,694,486,432,475,867,914,380,857,799,909,695,718,487,812,477,915,869,698,490,724,382,624,719,930,840,814,440,699,383,491,917,873,672,726,820,815,464,498,701,931,493,632,727,740,844,921,444,881,499,822,730,962,933,823,742,846,472,446,256,501,688,731,904,636,826,963,852,937,847,447,743,733,476,505,827,746,638,965,800,854,908,696,945,639,747,829,488,868,855,478,720,754,969,910,858,749,700,479,916,384,755,870,492,911,816,859,977,702,728,871,757,918,861,494,874,703,993,500,932,919,824,761,495,875,732,922,848,882,448,502,744,934,877,923,734,828,883,503,935,964,925,735,640,506,938,748,830,856,885,507,939,831,966,480,750,889,912,946,860,509,756,941,967,751,872,970,947,862,704,758,971,920,496,949,863,759,876,978,762,973,953,924,979,878,763,504,936,736,884,994,879,926,981,765,995,832,886,927,508,940,985,887,752,997,968,890,942,510,948,1001,891,943,511,864,972,760,950,893,1009,974,951,764,954,980,880,975,955,928,766,982,957,767,888,996,983,986,998,944,987,892,512,999,989,1002,894,952,895,1003,976,1010,956,1005,1011,984,958,768,1013,959,988,1017,1000,990,991,896,1004,1006,1012,1007,960,1014,1015,1018,1019,992,1021,1008,1016,1020,1022,1023,1024]。

以上，对本申请实施例中发送设备如何确定极化编码时的母码序列的过程作了详细说明，并且针对不同的实现方式，给出了确定的母码序列的示例。

可以理解的是，上文都是以发送设备所作的说明。而对于接收设备而言，确定母码序列的过程和发送设备是完全一样的。因此，不再详述。

发送设备确定了母码序列之后，根据母码序列可以进一步确定信息比特索引集合。

接下来，就可以根据信息比特索引集合对待编码比特进行极化编码，得到编码后的序列。

后续，发送设备可以将编码后的序列发送给接收设备、相对应地，接收设备执行步骤130-140。

130、接收设备获取待译码序列。

应理解，发送设备对待编码比特进行极化编码，得到编码后的序列。该编码后的序列经发送设备发送，被接收设备接收到的序列为待译码序列。

140、接收设备采用长度为N的母码序列对待译码序列进行译码，得到译码后的序列。

接收设备对获取到的待译码序列进行译码的过程，实际上正是发送设备根据母码序列对待编码比特进行极化编码的逆过程。

类似地，接收设备首先确定母码序列，再根据母码序列确定信息比特索引集合。接下来，接收设备根据信息比特索引集合对待译码序列进行译码，得到译码后的序列。

接收设备确定母码序列的过程与发送设备确定母码序列的过程相同，这里不再赘述。

另外，本申请实施例提供的母码序列在串行抵消(Successive Cancellation，SC)译码时具有较优的性能。

以上结合图1至图4，对本申请实施例提供的极化码编码的方法作了详细说明。下面结合图5至图8，对本申请实施例提供的装置和设备进行说明。

图5为本申请实施例提供的极化码编码的装置300的示意性框图。如图5所示，装置300主要包括接收单元310和处理单元320。

接收单元310，用于获取待编码比特；

处理单元320，还用于采用长度为N的母码序列对待编码比特进行极化编码，得到编码后的序列。

图6为本申请实施例提供的设备500的示意性结构图，如图6所示，设备500包括：一个或多个处理器501，一个或多个存储器502，一个或多个收发器(每个收发器包括发射机503和接收机504)。发射机503或接收机504通过天线505收发信号。存储器502中存储计算机程序指令(或者说，代码)。处理器501执行存储在存储器502中的计算机程序指令，以实现本申请提供的极化码编码的方法实施例中的相应流程和/或操作。为了简洁，此处不再赘述。

图5中所示的装置300可以通过图6中所示的设备500来实现。例如，图5中所示的接收单元310可以由图6中所示的接收机504实现，处理单元320可以由图6中所示的处理器501实现。

本申请实施例还提供一种设备600，用于实现编码的功能。如图7所示，图7为本申请实施例提供的设备600的示意图。该设备600包括收发器608和处理装置604。

收发器608，用于获取待编码比特；

处理装置604用于采用长度为N的母码序列对待编码比特进行极化编码，得到编码后的序列。

可选的，处理装置604可以是芯片或者集成电路。

本申请实施例还提供了一种用于编码的处理装置604，用于实现上述实施例中的极化码编码的方法。上述实施例的编码方法中的部分或全部可以通过硬件来实现也可以通过软件来实现，当通过硬件实现时，参见图8所示，图8为处理装置的内部结构示意图。该处理装置604包括：

输入接口电路6142，用于获取输入的待编码比特；

逻辑电路6144，用于采用长度为N的母码序列对待编码比特进行极化编码，得到编码后的序列。

输出接口电路6146，用于输出极化编码后的比特序列。

以上实施例中，处理器可以为中央处理器(Central Processing Unit，CPU)、微处理器、特定应用集成电路(Application-Specific Integrated Circuit，ASIC)，或一个或多个用于控制本申请方案程序执行的集成电路等。例如，处理器可以包括数字信号处理器设备、微处理器设备、模数转换器、数模转换器等。处理器可以根据这些设备各自的功能而在这些设备之间分配移动设备的控制和信号处理的功能。此外，处理器可以包括操作一个或多个软件程序的功能，软件程序可以存储在存储器中。

处理器的所述功能可以通过硬件实现，也可以通过硬件执行相应的软件实现。所述硬件或软件包括一个或多个与上述功能相对应的模块。

存储器可以是只读存储器(Read-Only Memory，ROM)或可存储静态信息和指令的其他类型的静态存储设备，随机存取存储器(Random Access Memory，RAM)或者可存储信息和指令的其他类型的动态存储设备。也可以是电可擦可编程只读存储器(ElectricallyErasable Programmable Read-Only Memory，EEPROM)、只读光盘(Compact Disc Read-Only Memory，CD-ROM)或其他光盘存储、光碟存储(包括压缩光碟、激光碟、光碟、数字通用光碟、蓝光光碟等)、磁盘存储介质或者其他磁存储设备、或者能够用于携带或存储具有指令或数据结构形式的期望的程序代码并能够由计算机存取的任何其他介质，但不限于此。

可选的，上述的存储器与存储器可以是物理上相互独立的单元，或者，存储器也可以和处理器集成在一起。

本领域普通技术人员可以意识到，结合本文中所公开的实施例描述的各示例的单元及算法步骤，能够以电子硬件、或者计算机软件和电子硬件的结合来实现。这些功能究竟以硬件还是软件方式来执行，取决于技术方案的特定应用和设计约束条件。专业技术人员可以对每个特定的应用来使用不同方法来实现所描述的功能，但是这种实现不应认为超出本申请的范围。

所属领域的技术人员可以清楚地了解到，为描述的方便和简洁，上述描述的系统、装置和单元的具体工作过程，可以参考前述方法实施例中的对应过程，在此不再赘述。

在本申请所提供的几个实施例中，应该理解到，所揭露的系统、装置和方法，可以通过其它的方式实现。例如，以上所描述的装置实施例仅仅是示意性的，例如，所述单元的划分，仅仅为一种逻辑功能划分，实际实现时可以有另外的划分方式，例如多个单元或组件可以结合或者可以集成到另一个系统，或一些特征可以忽略，或不执行。另一点，所显示或讨论的相互之间的耦合或直接耦合或通信连接可以是通过一些接口，装置或单元的间接耦合或通信连接，可以是电性，机械或其它的形式。

所述作为分离部件说明的单元可以是或者也可以不是物理上分开的，作为单元显示的部件可以是或者也可以不是物理单元，即可以位于一个地方，或者也可以分布到多个网络单元上。可以根据实际的需要选择其中的部分或者全部单元来实现本实施例方案的目的。

另外，在本申请各个实施例中的各功能单元可以集成在一个处理单元中，也可以是各个单元单独物理存在，也可以两个或两个以上单元集成在一个单元中。

所述功能如果以软件功能单元的形式实现并作为独立的产品销售或使用时，可以存储在一个计算机可读取存储介质中。基于这样的理解，本申请的技术方案本质上或者说对现有技术做出贡献的部分或者该技术方案的部分可以以软件产品的形式体现出来，该计算机软件产品存储在一个存储介质中，包括若干指令用以使得一台计算机设备(可以是个人计算机，服务器，或者网络设备等)执行本申请各个实施例所述方法的全部或部分步骤。而前述的存储介质包括：U盘、移动硬盘、只读存储器(Read Only Memory,ROM)、随机存取存储器(Random Access Memory,RAM)、磁碟或者光盘等各种可以存储程序代码的介质。

以上所述，仅为本申请的具体实施方式，但本申请的保护范围并不局限于此，任何熟悉本技术领域的技术人员在本申请揭露的技术范围内，可轻易想到变化或替换，都应涵盖在本申请的保护范围之内。因此，本申请的保护范围应以权利要求的保护范围为准。

Claims

1.一种极化码编码的方法，其特征在于，所述方法包括：

发送设备获取第一序列，所述第一序列包括n个信道的索引，n≥1且为整数；

所述发送设备根据所述第一序列，确定M-1个第二序列，所述M-1个第二序列中每个第二序列包括n个信道的索引；

所述发送设备根据指示序列，对所述第一序列和所述M-1个第二序列中的索引进行排序，生成长度为M·n的母码序列，所述M·n为2的整数次幂；

所述发送设备采用所述长度为M·n的母码序列对待编码比特进行极化编码，得到编码后的序列。

2.根据权利要求1所述的方法，其特征在于，所述发送设备根据所述第一序列，确定M-1第二个序列，包括：

所述发送设备对所述第一序列中的每个索引依次增加偏移量q·n，得到所述M-1个第二序列中的第q个第二序列，所述q为大于或等于1的整数。

3.根据权利要求1或2所述的方法，其特征在于，所述指示序列包括M·n个元素，所述指示序列中的每个元素等于第一数值或第二数值，

以及，所述发送设备根据所述指示序列，对所述第一序列和所述M-1个第二序列中的索引进行排序，生成长度为M·n的母码序列，包括：

所述发送设备依次读取所述指示序列中的所述M·n个元素；

若所述指示序列中第i个元素等于所述第一数值，则所述发送设备从所述第一序列中读取索引，若所述指示序列中的第i个元素等于第二数值，则所述发送设备从所述M-1个第二序列中读取索引，i遍历[1,M·n]；

所述发送设备将依次读取的索引构成的序列确定为所述母码序列。

4.根据权利要求1或2所述的方法，其特征在于，所述发送设备获取所述第一序列，包括：

所述发送设备从第三序列中读取所述第一序列，所述第一序列包括的n个信道的索引为所述第三序列中第(i·n+1)个位置的索引至第(i+1)·n个位置的索引分别减去i·n得到的，i≥0且为整数，所述第三序列包括的索引的个数大于或等于n，所述第三序列中的索引是按照各自对应的极化信道的可靠度或者信道容量的大小顺序排列的。

5.根据权利要求1或2所述的方法，其特征在于，所述方法还包括：

所述发送设备从第四序列中读取第五序列，所述第五序列包括2n个索引，所述2n个索引为所述第四序列中第(j·2n+1)个位置的索引至第(j+1)·2n个位置的索引，j≥0且为整数，所述第四序列包括的索引的个数大于或等于2n，所述第四序列中的索引是按照各自对应的极化信道的可靠度的大小顺序排列的；

所述发送设备根据所述第五序列，生成所述指示序列。

6.一种极化码编码的装置，其特征在于，包括：

接收单元，用于获取第一序列，所述第一序列包括n个极化信道的索引，n≥1且为整数；

处理单元，还用于根据所述第一序列，确定M-1个第二序列，所述M-1个第二序列中每个第二序列包括n个信道的索引；

所述处理单元，还用于根据指示序列，对所述第一序列和所述M-1个第二序列中的索引进行排序，生成长度为M·n的母码序列，所述M·n为2的整数次幂；

以及，所述处理单元，还用于采用所述长度为M·n的母码序列对待编码比特进行极化编码，得到编码后的序列。

7.根据权利要求6所述的装置，其特征在于，所述处理单元具体用于：

对所述第一序列中的每个索引依次增加偏移量q·n，得到所述M-1个第二序列中的第q个第二序列，所述q为大于或等于1的整数。

8.根据权利要求6或7所述的装置，其特征在于，所述指示序列包括M·n个元素，所述指示序列中的每个元素等于第一数值或第二数值，

以及，所述处理单元具体用于：

依次读取所述指示序列中的所述M·n个元素；

若所述指示序列中第i个元素等于所述第一数值，则从所述第一序列中读取索引，若所述指示序列中的第i个元素等于第二数值，则从所述M-1个第二序列中读取索引，i遍历[1,M·n]；

将所述依次读取的索引构成的序列确定为所述母码序列。

9.根据权利要求6或7所述的装置，其特征在于，所述处理单元具体用于：

从第三序列中读取所述第一序列，所述第一序列包括的n个信道的索引为所述第三序列中第(i·n+1)个位置的索引至第(i+1)·n个位置的索引分别减去i·n得到的，i≥0且为整数，所述第三序列包括的索引的个数大于或等于n，所述第三序列中的索引是按照各自对应的极化信道的可靠度或者信道容量的大小顺序排列的。

10.根据权利要求6或7所述的装置，其特征在于，所述处理单元具体用于：

从第四序列中读取第五序列，所述第五序列包括2n个索引，所述2n个索引为所述第四序列中第(j·2n+1)个位置的索引至第(j+1)·2n个位置的索引，j≥0且为整数，所述第四序列包括的索引的个数大于或等于2n，所述第四序列中的索引是按照各自对应的极化信道的可靠度的大小顺序排列的；

根据所述第五序列，生成所述指示序列。

11.一种计算机可读存储介质，其特征在于，所述计算机可读存储介质中存储有计算机指令，当所述计算机指令在计算机上运行时，使得所述计算机执行如权利要求1-5中任一项所述的方法。

12.一种编码装置，其特征在于，包括接口电路和处理电路，其中，所述接口电路用于获取待编码比特，并将所述待编码比特传输至所述处理电路；所述处理电路执行如权利要求1-5中任一项所述的极化码编码的方法，对所述待编码比特进行所述极化码编码，得到编码后的序列；所述接口电路还用于输出所述编码后的序列。

13.一种芯片，其特征在于，包括存储器和处理器，所述存储器用于存储计算机程序，所述处理器用于从所述存储器中调用并运行所述计算机程序，使得如权利要求1-5中任一项所述的方法被实现。