CN109391343A - 一种Polar码编码方法及装置 - Google Patents

一种Polar码编码方法及装置 Download PDF

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CN109391343A
CN109391343A CN201710653425.6A CN201710653425A CN109391343A CN 109391343 A CN109391343 A CN 109391343A CN 201710653425 A CN201710653425 A CN 201710653425A CN 109391343 A CN109391343 A CN 109391343A
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sequence
reliability
polarisation channel
channel
polarisation
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CN109391343B (zh
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周悦
王俊
李榕
陈莹
王坚
张华滋
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Huawei Technologies Co Ltd
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Huawei Technologies Co Ltd
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Priority to EP18840915.5A priority patent/EP3651393B1/en
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0056—Systems characterized by the type of code used
    • H04L1/0057—Block codes
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/13—Linear codes
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0076—Distributed coding, e.g. network coding, involving channel coding
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0056—Systems characterized by the type of code used
    • H04L1/0067—Rate matching
    • H04L1/0068—Rate matching by puncturing

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  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Physics & Mathematics (AREA)
  • Probability & Statistics with Applications (AREA)
  • Theoretical Computer Science (AREA)
  • Mobile Radio Communication Systems (AREA)
  • Error Detection And Correction (AREA)

Abstract

本申请涉及通信技术领域，公开了一种Polar码编码方法及装置，用以提高极化信道的可靠度计算与排序的准确度。该方法为：获取用于对K个待编码比特进行编码的第一序列，所述第一序列中包含N个极化信道的序号，所述N个极化信道的序号在所述第一序列中是按照所述N个极化信道的可靠度进行排列的，K为正整数，N为Polar码的母码长度，N为2的正整数次幂，K≤N；根据可靠度从高到低的顺序，从所述第一序列中选择K个极化信道的序号；按照所选择的K个极化信道的序号放置所述待编码比特，并对所述待编码比特进行Polar码编码。

Description

一种Polar码编码方法及装置
技术领域
本申请实施例涉及通信技术领域，尤其涉及一种Polar码编码方法及装置。
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。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，第五代(5th generation，5G)通信系统等未来的通信系统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 mobile broadband，eMBB)、海量机器连接通信(massive machine typecommunication，mMTC)和高可靠低延迟通信(ultra reliable low latencycommunication，URLLC)。这些通信场景对于Polar码的编译码性能提出了更高的要求。
极化信道的可靠度排序对Polar码的编译码性能起到重要作用，而现阶段，极化信道的可靠度排序的准确度并不理想，从而影响了Polar码在应用过程中的编译码性能的进一步提高。
发明内容
本申请实施例提供一种Polar码编码方法及装置，用以提高极化信道的可靠度排序的准确度。
本申请实施例提供的具体技术方案如下：
第一方面，提供一种Polar码编码方法，获取待编码的比特，所述待编码的比特长度为K，K为正整数，获取用于对K个待编码比特进行编码的序列，记为第一序列，所述第一序列用于表征N个极化信道的可靠度的排序，所述第一序列中包含N个极化信道的序号，所述N个极化信道的序号在所述第一序列中是按照所述N个极化信道的可靠度进行排列的，N为Polar码的母码长度，N为2的正整数次幂，K≤N，按照可靠度从高到低的顺序，从所述第一序列中选出可靠度排序较高的前K个序号，将待编码的信息比特映射到所述前K个序号的极化信道上，并对所述待编码比特进行Polar码编码。从而实现了通过Polar码极化信道的可靠度的计算来确定信息比特与固定比特的位置，与信道参数及码率没有关系，可以降低Polar码编码的计算复杂度。
在一个可能的设计中，所述第一序列为第二序列的全部或者子集，所述第二序列中包含Nmax个极化信道的序号，所述Nmax个极化信道的序号在所述第二序列中是按照所述Nmax个极化信道的可靠度进行排列的，所述Nmax为2的正整数次幂，所述Nmax≥N。
在一个可能的设计中，所述第二序列中第i个极化信道的可靠度为
其中，0≤i≤N-1，Wi为第i个极化信道的可靠度，i满足i＝Bn-1Bn-2...B0，其中Bn- 1Bn-2...B1B0为i的二进制表示，Bj为信道序号i的二进制表示中第j位的取值,Bj∈{0,1}，其中β为实数核函数；b0、b1和b2为不同的复数核函数；a0、a1、a2为权重因子；分别表征当信道序号的二进制表达的第e1、e2位为1时相应的复数函数会对可靠度产生影响。
在一个可能的设计中，所述第二序列中第i个极化信道的可靠度为
其中，0≤i≤N-1，Wi为第i个极化信道的可靠度，i满足i＝Bn-1Bn-2...B0，其中Bn- 1Bn-2...B1B0为i的二进制表示，Bj为信道序号i的二进制表示中第j位的取值,Bj∈{0,1}，其中β为实数核函数；b0、b1和b2为不同的复数核函数；a0、a1、a2为权重因子；分别表征当信道序号的二进制表示的第e1、e2位为1时相应的复数函数会对可靠度产生影响。
在一个可能的设计中，所述权重因子和复数核函数分别为a0＝0.169，b0＝0.8805，a1＝-0.096，b1＝0.2432+0.2432I，其中I为虚数单位，e1＝6，a2＝0.038，b2＝0.8262，e2＝9，所述第二序列中第i个极化信道的可靠度为
在一个可能的设计中，所述权重因子和复数核函数分别为a0＝0.1733，b0＝0.5486，a1＝-0.0279，b1＝0.5222+0.5222I，其中I为虚数单位，e1＝5，a2＝-0.07，b2＝0，e2＝6，所述第二序列中第i个极化信道的可靠度为：
在一个可能的设计中，所述第二序列中第i个极化信道的可靠度为
其中，0≤i≤N-1，Wi为第i个极化信道的可靠度，i满足i＝Bn-1Bn-2...B0，其中Bn- 1Bn-2...B1B0为i的二进制表示，Bj为信道序号i的二进制表示中第j位的取值,Bj∈{0,1}，其中β为实数核函数；b0和b1为不同的复数核函数；a0和a1为权重因子；表征当信道序号的二进制表示的第e1、e2位为1时相应的复数函数会对可靠度产生影响。
在一个可能的设计中，所述权重因子和复数核函数分别为a0＝0.169，b0＝0.601，a1＝-0.07694，b1＝0.0769+0.0769I，其中I为虚数单位，e1＝6，所述第二序列中第i个极化信道的可靠度为：
在一个可能的设计中，所述权重因子和复数核函数分别为a0＝0.169，b0＝0.601，a1＝-0.0475，b1＝0，e1＝6，所述第二序列中第i个极化信道的可靠度为：
在一个可能的设计中，
在一个可能的设计中，所述第二序列可以为说明书序列1-序列20所示的任意一个序列的部分或全部，所述第二序列中的N个极化信道的序号是按所述N个极化信道的可靠度从小到大排列的，且所述极化信道的序号最小值为0。
第二方面，提供一种Polar码编码装置，该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所述的方法的功能。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Polar码编码装置包括：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一方面的任一种可能的设计中所述的行为；输出接口电路，用于输出编码后的比特序列。
可选的，所述Polar码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Polar码编码装置包括：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Polar码编码装置可以实现如上述第一方面和第一方面的任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Polar码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。
第三方面，提供了一种通信系统，该通信系统包网络设备和终端，所述网络设备或终端可以执行如上述第一方面及其可能的设计所述的方法。
第四方面，提供了一种计算机存储介质，存储有计算机程序，该计算机程序包括用于执行第一方面和第一方面的任一可能设计中任一种所述的方法的指令。
第五方面，本申请实施例提供了一种包含指令的计算机程序产品，当其在计算机上运行时，使得计算机执行上述各方面所述的方法。
第六方面，提供了一种无线设备，包括用于实施第一方面和第一方面的任一可能设计的编码装置，调制器和收发器，
所述调制器用于调制编码后的比特序列得到调制后的序列；
所述收发器用于处理所述调制后的序列。
在一个可能的设计中，所述无线设备为终端或者网络设备。
附图说明
图1为本申请实施例中应用的通信系统架构示意图；
图2为本申请实施例中Polar码编码方法的流程示意图；
图3为本申请实施例中Polar码编码装置结构示意图之一；
图4为本申请实施例中Polar码编码装置结构示意图之二；
图5为本申请实施例中Polar码编码装置结构示意图之三；
图6为本申请实施例中Polar码编码装置结构示意图之四。
具体实施方式
下面将结合附图，对本申请实施例进行详细描述。
本申请实施例提供一种Polar码编码方法及装置，根据极化信道的可靠度，获得可靠度排序，按照可靠度排序选择用于发送信息比特的极化信道的序号，按照所选择的信息比特序号进行Polar码编码，本申请实施例可以更确切的计算得到Polar码各子信道的可靠度。下面结合附图详细说明本发明实施例提供的编码方法和装置。
为方便对本申请实施例的理解，下面对Polar码作简单介绍。
Polar码的编码策略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，其编码矩阵为GN，编码过程为其中是一个二进制的行矢量，长度为N(即码长)；GN是一个N×N的矩阵，且 定义为log2N个矩阵F2的克罗内克(Kronecker)乘积。上述矩阵
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集合(frozen bits)，其索引的集合用的补集表示。Polar码的编码过程相当于：这里，GN(A)是GN中由集合中的索引对应的那些行得到的子矩阵，GN(AC)是GN中由集合中的索引对应的那些行得到的子矩阵。为中的信息比特集合，数量为K，一般地，包括但不限于循环冗余校验(CyclicRedundancy Check，简称CRC)比特和奇偶校验(Parity Check，简称PC)比特在内的各类校验比特也都包括在信息比特集合中；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：这里为中的信息比特集合，为长度K的行矢量，即|·|表示集合中元素的个数，K为信息块大小，是矩阵GN中由集合中的索引对应的那些行得到的子矩阵，是一个K×N的矩阵。
Polar码的构造过程即集合的选取过程，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，分别对应编码矩阵的N个行，计算极化信道可靠度，将可靠度较高的前K个极化信道的索引作为集合的元素，剩余(N-K)个极化信道对应的索引作为固定比特的索引集合的元素。集合决定了信息比特的位置，集合决定了固定比特的位置。
本申请实施例提供的方案涉及如何确定极化信道可靠度。本申请实施例的基本发明思路是：极化信道可靠度可以通过可靠度来表征，从信号谱分析的角度来看，现有的可靠度对极化信道可靠度的近似可以理解为一种信号的域变换。类似于傅里叶变换采用ejw这个核来实现信号时域与频域间的转换，该方法通过采用β核来将信号从信道序号域转换到可靠度权重域。在信号的时-频分析领域里，最常见的包括傅里叶变换及小波变换。傅里叶变换因受限于三角函数核ejw的形式，其对信号时-频分析过程中，存在时域分辨力与频域分辨力不可兼得的窘境。小波变化通过采用小波变换核、函数形式多样，因此能够在进行域变换时扑捉到信号在时域上瞬间的变化，能够实现时-频域上同时兼顾的分辨能力。本申请实施例中，通过采用可改变的变换核来对极化信道可靠度进行估计，从而改善序列可靠度估计的精度。
图1为本发明实施例无线通信网络的结构示意图。图1只是一种示例，其它能用到本发明实施例的编码方法或装置的无线网络也都在本发明的保护范围内。
如图1所示，无线通信网络100包括网设备110，和终端112。当无线通信网络100包括核心网102时，该网络设备110还可以与核心网102相连。网络设备110还可以与IP网络104进行通信，例如，因特网(internet)，私有的IP网，或其它数据网等。网络设备为覆盖范围内的终端提供服务。例如，参见图1所示，网络设备110为网络设备110覆盖范围内的一个或多个终端112提供无线接入。除此之外，网络设备之间的覆盖范围可以存在重叠的区域，例如网络设备110和120。网络设备之间还可以可以互相通信，例如，网络设备110可以与网络设备120之间进行通信。
上述网络设备可以是用于与终端设备进行通信的设备。例如，可以是GSM系统或CDMA系统中的基站(Base Transceiver Station，BTS)，也可以是WCDMA系统中的基站(NodeB，NB)，还可以是LTE系统中的演进型基站(Evolved Node B，eNB或eNodeB)或未来5G网络中的网络侧设备等。或者该网络设备还可以是中继站、接入点、车载设备等。在终端对终端(Device to Device，D2D)通信系统中，该网络设备还可以是担任基站功能的终端。
上述终端可以指用户设备(User Equipment，UE)、接入终端、用户单元、移动站、远方站、远程终端、移动设备、用户终端、无线通信设备、用户代理或用户装置。接入终端可以是蜂窝电话、无绳电话、会话启动协议(Session Initiation Protocol，SIP)电话、无线本地环路(Wireless Local Loop，WLL)站、个人数字处理(Personal Digital Assistant，PDA)、具有无线通信功能的手持设备、计算设备或连接到无线调制解调器的其它处理设备、车载设备、可穿戴设备，未来5G网络中的终端设备等。基于图1所示的通信系统架构，本申请实施例中，执行Polar码编码方法的执行主体可以为上述网络设备或终端，当网络设备或终端作为发送端发送数据或信息时，均可以采用此Polar码编码方法。相应的，当网络设备或终端作为接收端接收数据或信息时，也需要根据本发明所述的方法先确认子信道序列。下面将对本申请实施例提供的Polar码编码方法做详细介绍。
基于图1所示的通信系统架构，如图2所示，本申请实施例提供的Polar码编码方法具体流程如下所述。
步骤201、获取用于对K个待编码比特进行编码的第一序列。
其中，第一序列中包含N个极化信道的序号，N个极化信道的序号在第一序列中是按照N个极化信道的可靠度进行排列的，K为正整数，N为Polar码的母码长度，N为2的正整数次幂。
步骤202、根据可靠度从高到低的顺序，从第一序列中选择K个极化信道的序号。
步骤203、按照所选择的K个极化信道的序号放置所述待编码比特，并对待编码比特进行Polar码编码。
其中，将所述K个待编码比特映射到所述N个极化信道中的K个极化信道上，其中，所述K个极化信道的可靠度高于剩余的(N-K)个极化信道的可靠度。
可选的，第一序列为第二序列的全部或者子集，第二序列中包含Nmax个极化信道的序号，Nmax个极化信道的序号在第二序列中是按照Nmax个极化信道的可靠度进行排列的，Nmax为2的正整数次幂，Nmax≥N。Nmax个极化信道的可靠度的计算方式与N个极化信道的可靠度的计算方式类似。
可选的，根据目标码长对Polar码编码后的序列进行速率匹配。
本实施例提供的编码方法，通过接收到输入的信息比特后，根据Polar码的目标码长N确定待编码比特的个数K，无论在线计算还是预先计算并存车的方式，若已知第二序列，则可以从第二序列中获取第一序列，当Nmax＝N时，第二序列即为第一序列。其中，第二序列中包含通信系统所支持的最大码长Nmax个极化信道的可靠度排序。可选的，可以从预先存储的第二序列中获取第一序列，接着根据第一序列确定出信息比特，最后对K个待编码比特进行Polar编码，获得Polar编码后的比特序列。从而实现了通过半在线计算半离线存储的方式获得Polar码极化信道的可靠度来确定信息比特与固定比特的位置。
下面具体介绍一下如何确定N(或者Nmax)个极化信道中第i个极化信道的可靠度。N个极化信道的序号可以为0～(N-1)，也可以为1～N。本申请实施例中，在确定N个极化信道的第i个极化信道的可靠度时，i的取值可以为1、2、…、N，也可以为0、1、…、N-1。
用Wi表示N个极化信道中第i个极化信道的可靠度，可靠度计算公式可以包括但不限于以下几种。可以理解的是，本申请实施例中涉及的公式只是一种举例，本领域技术人员可以在对公式进行简单的变形而不影响公式的性能的基础上获得的方案，均属于本申请实施例保护的范围。
以下公式中，不失一般性0≤i≤N-1，Wi为第i个极化信道的可靠度，N＝2n，i满足i＝Bn-1Bn-2...B0，其中Bn-1Bn-2...B1B0为i的二进制表示，Bj为信道序号i的二进制表示中第j位的取值,Bj∈{0,1}。当然，极化信道序号i的取值范围也可以选为1≤i≤N，此时i-1＝Bn- 1Bn-2...B0，即Bn-1Bn-2...B1B0为i-1的二进制表示，其他性质及各极化信道的先后关系均保持不变。因此本申请中，还是以0≤i≤N-1为例说明。
第i个极化信道的可靠度Wi为：
其中β为通常计算极化权重所采用的核函数，例如，β取b0、b1和b2为不同的核函数，其可在复数域内取值；a0、a1、a2为对应核函数的权重因子，表征各个核函数对最终极化权重影响的相对大小；分别表征当信道序号的二进制表示的第e1、e2位为1时相应乘积内的核函数会对极化权重产生影响。这里的核(Kernel)函数描述了一个空间到另一个空间的映射关系，本发明中的β，b1，b2等约束了信道序号域到可靠度域的映射关系，完成了信道序号域到可靠度域的变换，因此称为核函数。本发明对核函数的具体数学形式(如数值)进行了举例，在实际应用中可以表现为常数。
当核函数包括虚部时(非实数时)，序列最后的排序按照计算得出的极化权重的幅值进行排序、如果包括两个幅值相同的项则按照相位在内从小到大的顺序来进行排序，当然，也可以采用从大到小的顺序进行排序，这里不做具体的限定，不失一般性，本申请中的序列还是以从小到大的顺序进行排序。
例如：公式(1)中仅包含4个核函数：
根据公式(2)，当所述权重因子和复数核函数分别为a0＝0.169，b0＝0.8805，a1＝-0.096，b1＝0.2432+0.2432I，其中I为虚数单位，e1＝6，a2＝0.038，b2＝0.8262，e2＝9时公式为：
这里需要说明的是，例如当N＝128的时候，n＝7，则n-1<e2，可将取为0。例如当N＝32的时候，n＝5，则n-1<e1，可将和均取为0。即当e2>n-1时，当e1>n-1时， 以下各公式均类似，不再赘述。
根据公式(2)，当所述权重因子和复数核函数分别为a0＝0.1733，b0＝0.5486，a1＝-0.0279，b1＝0.5222+0.5222I，其中I为虚数单位，e1＝5，a2＝-0.07，b2＝0，e2＝6时公式具体化为：
注意这里b2＝0表明该核函数仅对信道序号二进制位的最低位产生加权(其中令00＝1，下同)。
例如：公式(1)中还可以仅包含3个核函数：
根据公式(5)，当所述权重因子和复数核函数分别为a0＝0.169，b0＝0.601，a1＝-0.07694，b1＝0.0769+0.0769I，其中I为虚数单位，e1＝6时公式具体化为：
根据公式(5)，当所述权重因子和复数核函数分别为a0＝0.169，b0＝0.601，a1＝-0.0475，b1＝0，e1＝6时公式具体化为：
具体的序列例子可以参见如下序列1～序列20。
序列1：
以N＝1024为例,利用公式(3)生成的序列为:
[0,1,2,4,8,16,32,3,5,6,64,9,10,17,12,128,18,33,20,34,24,65,36,7,256,66,40,11,68,13,48,129,19,14,72,130,21,512,35,132,22,80,25,37,257,136,26,67,38,96,258,41,28,69,144,42,260,49,70,73,44,15,264,160,50,131,74,513,81,52,133,23,272,514,76,134,82,192,56,516,137,27,97,39,288,84,259,138,29,520,98,145,43,261,140,30,88,71,146,100,528,262,320,45,265,161,51,148,75,46,104,266,162,53,544,77,273,152,515,83,268,193,164,54,112,135,384,274,57,78,517,85,194,289,168,58,276,576,139,518,99,521,290,86,89,196,60,141,31,280,101,176,522,321,147,292,263,142,90,200,529,524,102,105,149,640,322,530,47,296,92,267,163,150,208,106,153,545,532,324,113,269,165,55,304,79,385,546,275,154,108,195,270,536,328,166,114,224,386,577,169,548,59,277,156,768,87,197,519,116,291,170,388,278,336,61,578,552,281,177,91,198,523,201,293,172,62,120,143,392,282,580,103,178,323,294,525,560,93,352,202,641,297,284,531,209,180,584,107,526,325,151,400,642,298,94,204,533,210,109,305,184,326,644,155,329,592,115,300,547,534,225,271,167,416,537,306,212,387,110,157,549,648,330,769,117,226,538,337,308,579,171,389,279,158,608,550,216,770,199,332,553,540,118,121,228,390,656,338,448,173,63,581,312,772,393,283,554,179,353,203,295,174,122,232,340,561,394,582,585,285,556,776,181,672,95,354,205,401,527,562,124,211,299,396,643,286,344,182,327,586,240,402,593,185,356,564,206,784,645,301,213,535,111,588,417,307,186,404,331,704,227,646,594,302,360,568,649,418,214,217,609,539,309,188,800,159,333,408,119,229,596,551,650,339,771,449,420,310,541,368,391,218,610,657,313,334,652,773,123,230,600,233,341,555,542,450,658,175,424,583,314,220,612,395,832,355,774,125,557,777,234,342,345,452,673,660,316,241,563,397,287,587,616,183,357,558,432,207,778,403,674,126,236,398,346,565,664,456,785,242,589,780,705,358,187,361,405,676,595,896,624,566,786,215,303,647,348,569,244,419,590,406,464,189,706,597,362,680,409,801,788,570,369,219,651,421,611,311,190,335,248,410,802,231,708,598,364,451,601,572,792,422,370,653,221,688,480,613,543,833,425,315,412,804,659,235,712,343,453,654,602,775,372,426,222,614,317,617,834,661,808,127,237,433,604,347,454,559,457,779,243,720,428,318,675,662,376,399,359,836,618,434,665,625,238,781,816,349,458,677,245,897,567,666,465,787,591,436,620,363,840,707,782,407,736,678,626,898,350,460,681,668,246,249,789,571,466,191,365,440,709,599,411,900,628,848,371,682,481,803,790,423,573,250,793,468,689,366,710,413,713,684,603,805,904,373,632,223,574,482,794,655,690,615,252,835,427,414,864,472,806,455,714,605,809,796,374,721,377,484,692,912,429,319,837,619,663,239,810,435,716,459,606,430,722,378,488,696,817,621,838,841,812,737,667,437,627,351,928,461,247,783,818,724,380,679,467,899,438,622,496,842,669,738,629,441,849,820,462,251,901,728,469,683,670,791,367,844,442,711,740,960,483,630,902,633,850,824,253,685,905,470,473,575,865,795,444,691,415,715,375,744,485,852,686,634,807,906,254,797,474,866,693,913,717,607,908,379,486,636,489,856,723,811,798,752,694,431,914,839,476,868,697,718,381,813,725,490,929,916,497,698,819,623,843,872,439,739,814,463,930,382,492,726,729,700,821,920,498,845,741,671,961,443,631,932,851,880,822,471,730,903,825,500,846,445,742,745,962,853,635,936,255,826,475,732,687,907,446,867,504,487,964,746,637,854,857,828,753,477,909,944,869,799,695,915,719,748,491,968,638,910,858,754,478,870,873,917,699,383,493,860,727,815,756,499,976,931,918,874,701,921,881,494,731,933,501,760,702,823,922,847,876,743,963,992,934,882,733,502,937,924,505,827,447,965,747,855,884,938,734,829,506,945,749,966,969,639,940,859,888,479,755,830,911,946,871,508,750,970,861,757,977,948,875,919,495,972,862,758,761,978,952,877,703,993,923,883,503,980,762,935,878,925,994,885,735,507,764,984,939,926,967,996,886,889,509,941,831,947,751,971,1000,942,890,510,949,973,863,892,759,979,1008,950,953,974,981,763,954,879,995,765,982,985,956,997,927,887,766,986,998,1001,891,511,988,943,1002,893,1009,951,975,1004,894,1010,955,983,1012,957,767,987,1016,958,999,989,1003,990,1005,895,1011,1006,1013,1014,1017,959,1018,991,1020,1007,1015,1019,1021,1022,1023]
序列2：
以N＝1024为例,利用公式(4)生成的序列为:
[1,2,3,5,9,17,33,4,6,7,65,10,11,18,13,129,19,34,21,35,25,257,37,8,66,67,41,12,69,14,130,49,20,15,73,513,131,22,133,36,23,81,26,258,38,137,27,259,39,97,68,42,29,145,261,70,43,50,71,265,45,16,74,514,161,132,51,75,515,134,273,53,24,82,77,517,135,193,83,138,57,28,289,260,40,98,521,139,85,30,146,262,99,141,44,31,89,529,147,263,321,101,72,266,46,162,149,52,267,47,105,545,76,516,163,274,54,153,269,385,78,518,165,136,275,194,55,113,84,58,79,519,577,290,195,277,522,169,140,86,59,291,197,100,523,87,142,281,61,32,90,530,177,148,293,264,322,102,525,143,201,641,91,531,150,323,103,297,268,48,106,546,164,93,533,151,209,325,154,270,107,547,386,166,305,276,56,114,537,155,271,329,769,109,549,387,80,520,167,578,225,196,278,115,170,157,60,579,389,292,553,279,198,524,337,171,117,88,282,62,178,581,294,199,393,526,173,144,283,202,642,63,121,561,92,532,179,295,353,324,104,527,585,298,203,643,285,401,94,534,181,152,210,326,299,205,108,645,548,95,535,593,306,211,538,327,185,156,301,272,330,770,417,110,550,388,168,307,226,649,213,116,539,158,331,771,111,551,609,580,390,227,309,554,280,338,172,118,541,159,217,657,333,773,391,449,582,229,555,200,339,394,119,174,313,284,64,122,562,180,583,296,354,777,557,395,528,341,175,586,233,673,204,644,286,123,563,402,182,355,587,397,300,287,206,646,345,785,125,565,403,96,536,183,594,241,212,357,328,186,589,302,207,647,705,418,595,405,308,650,569,214,540,187,303,361,801,332,772,419,112,552,610,228,651,597,310,215,409,542,189,160,218,658,334,774,611,421,392,450,311,230,653,556,369,340,120,543,601,314,219,659,335,775,833,613,451,584,231,778,425,558,396,342,176,315,234,674,221,124,661,564,453,356,779,559,617,343,588,398,235,675,317,288,346,786,433,126,566,404,184,242,665,358,781,399,457,897,590,237,677,208,648,347,787,706,127,567,625,596,406,243,570,359,188,591,304,362,802,707,420,349,789,681,407,652,465,598,245,571,216,410,190,363,803,709,612,422,599,312,654,370,793,573,411,544,191,602,249,689,220,660,365,805,336,776,423,834,481,614,452,232,655,371,713,426,603,413,316,222,662,835,615,809,454,780,427,560,373,618,344,236,676,605,318,223,663,721,434,837,666,455,782,619,429,400,458,898,319,238,678,377,817,348,788,435,128,568,626,244,667,360,783,841,621,459,899,592,239,679,737,708,350,790,627,437,682,408,466,246,669,572,461,364,901,804,351,791,710,849,683,629,467,600,247,794,441,574,412,192,250,690,366,806,711,424,482,905,685,656,469,372,795,714,575,633,604,414,251,691,367,807,865,836,483,616,810,715,428,374,797,415,473,913,606,253,693,224,664,722,838,485,811,456,375,717,620,430,607,320,378,818,723,436,839,697,668,813,784,431,842,489,929,622,460,900,240,680,379,819,738,725,628,438,670,843,623,462,902,739,381,821,352,792,439,850,684,497,630,468,248,671,729,442,845,463,903,961,741,712,851,906,631,686,825,470,796,443,576,634,252,692,368,808,866,484,907,853,687,745,471,716,798,635,445,416,474,914,254,694,867,486,909,812,376,799,718,857,637,475,915,608,255,695,753,724,869,840,698,487,814,719,432,490,930,477,380,917,820,726,699,815,873,844,491,931,624,740,382,822,727,440,498,921,701,672,730,846,493,933,464,904,962,383,823,742,881,852,499,632,826,731,444,847,963,743,937,908,854,688,501,827,746,472,733,636,446,965,868,855,910,747,829,800,447,858,505,945,638,476,916,256,696,754,870,488,911,969,749,720,859,639,478,918,755,871,700,816,874,492,932,861,479,919,977,757,728,922,702,875,494,934,384,824,882,500,923,703,761,732,877,848,495,935,993,964,744,883,938,502,925,828,734,966,939,885,856,503,748,830,735,448,506,946,967,941,912,970,831,750,889,860,507,947,640,756,872,971,751,862,509,949,480,920,978,758,973,876,863,979,759,953,924,704,762,878,496,936,994,981,884,926,763,879,995,940,886,504,927,985,765,736,997,968,887,942,832,890,508,948,943,1001,972,752,891,510,950,974,893,864,511,951,1009,980,760,954,975,982,955,764,880,996,983,957,928,986,766,998,888,987,767,999,944,1002,989,892,1003,894,512,952,1010,1005,976,895,1011,956,1013,984,958,959,1017,988,768,1000,990,1004,991,1006,896,1012,1007,1014,1015,960,1018,1019,1021,992,1008,1016,1020,1022,1023,1024]
序列3：
以N＝1024为例,利用公式(6)生成的序列为:
[0,1,2,4,8,16,32,3,5,6,64,9,10,17,12,128,18,33,20,34,24,36,65,7,256,66,40,11,68,13,48,129,19,14,72,130,512,21,35,132,22,80,25,37,257,136,26,38,67,96,258,41,28,144,69,42,260,49,70,44,73,15,264,160,50,131,513,74,52,81,133,514,23,272,76,134,192,82,516,56,137,27,97,39,288,84,259,138,520,29,145,98,43,261,140,30,88,146,71,528,100,262,320,45,265,161,51,148,46,75,104,266,162,544,53,515,273,152,77,268,164,54,193,83,112,135,384,274,517,57,78,85,194,518,289,168,58,276,576,139,521,99,290,196,86,60,89,141,522,31,280,176,147,101,292,529,321,263,142,200,90,524,640,149,530,102,105,322,47,296,92,267,163,150,208,545,532,153,106,324,269,113,165,546,55,304,385,275,154,79,536,108,270,328,166,195,224,114,548,386,577,519,169,768,59,277,156,197,87,116,291,170,388,278,578,336,552,61,523,281,177,198,293,172,62,201,580,91,120,143,392,282,525,178,103,560,294,641,531,323,352,93,202,526,297,284,584,180,209,642,151,400,533,107,325,298,204,94,210,547,644,534,305,184,592,155,109,326,300,537,329,271,225,115,167,416,306,212,549,387,769,648,157,538,110,330,117,226,550,308,579,608,337,171,389,770,279,158,216,553,540,332,199,656,228,118,390,581,121,448,338,173,554,772,63,312,393,283,179,561,353,295,174,203,582,232,122,340,556,394,585,527,776,285,672,181,562,643,401,354,205,95,124,299,396,286,586,344,182,211,240,564,402,593,645,535,185,327,784,356,206,301,588,213,646,417,307,186,404,704,594,111,568,302,649,539,331,360,227,418,609,214,551,800,309,188,217,596,771,650,159,408,541,333,229,119,420,310,657,449,610,339,368,391,218,555,773,652,542,313,600,334,658,230,583,233,612,123,341,450,175,774,424,314,832,220,557,395,777,673,563,660,355,125,234,452,342,558,316,587,616,345,397,778,287,241,674,183,432,565,403,357,207,785,664,236,126,398,589,456,346,780,242,676,566,705,595,624,647,896,187,405,786,358,569,361,303,590,348,215,244,419,406,597,706,464,801,680,189,570,788,651,409,362,611,369,421,802,311,190,708,219,598,248,572,410,601,653,543,335,792,364,231,688,422,659,613,451,480,370,804,833,221,775,654,425,315,412,712,602,661,235,453,614,343,372,426,617,834,222,559,808,317,604,779,675,662,433,720,237,127,454,428,318,665,457,618,836,347,376,399,243,781,434,625,677,567,359,816,897,787,666,238,591,620,349,458,782,840,245,678,436,707,736,465,626,898,407,681,571,789,668,363,460,350,246,709,599,249,628,466,803,682,900,191,790,440,848,573,411,365,793,689,481,371,423,710,250,468,805,684,574,713,603,632,655,904,413,794,366,690,615,373,482,806,835,223,864,252,427,414,605,714,472,809,796,692,721,663,455,912,484,374,619,837,377,429,810,319,716,606,435,722,239,817,696,430,667,621,459,838,488,378,812,841,783,737,627,679,928,437,818,724,899,669,461,622,351,380,842,247,438,629,738,467,496,820,849,683,901,791,670,441,728,462,844,711,740,251,469,630,902,442,633,960,850,685,575,367,824,905,795,691,483,865,253,470,807,686,444,715,744,473,634,852,906,415,797,693,485,375,913,866,254,717,607,636,474,811,908,798,856,694,723,752,914,486,697,839,489,868,379,431,718,476,813,725,929,819,698,916,623,381,490,814,843,872,739,497,930,439,726,821,700,729,671,463,920,492,382,845,741,631,498,932,822,961,851,880,903,443,730,825,846,742,471,500,745,635,853,962,687,936,445,826,732,907,867,255,446,637,746,964,475,854,504,828,857,909,799,753,695,487,944,915,869,719,748,477,638,910,968,858,754,699,917,491,870,873,478,815,860,727,756,931,918,976,701,493,383,921,874,499,881,933,823,702,731,760,922,494,847,876,743,501,934,963,992,882,733,937,827,924,502,747,965,855,505,884,938,447,734,829,945,749,639,966,506,940,830,969,859,888,911,755,946,871,750,479,508,861,970,757,948,977,919,875,972,862,758,761,978,703,495,952,923,877,993,883,935,762,980,925,878,503,885,994,735,764,939,926,984,967,996,507,886,889,941,831,947,751,509,942,971,1000,890,949,510,973,863,892,759,950,979,1008,953,974,763,981,954,879,995,765,982,956,985,927,997,887,766,986,998,1001,891,943,988,511,893,1002,1009,951,975,1004,894,1010,955,983,1012,957,767,958,987,1016,999,989,1003,990,1005,895,1011,1006,1013,1014,1017,959,1018,991,1020,1007,1015,1019,1021,1022,1023]
序列4：
以N＝1024为例,利用公式(7)生成的序列为:
[0,1,2,4,8,16,32,3,5,6,64,9,10,17,12,128,18,33,20,34,24,65,36,7,256,66,40,11,68,13,48,129,19,14,72,130,512,21,35,132,22,80,25,37,257,136,26,67,38,96,258,41,28,144,69,42,260,49,70,73,44,15,264,160,50,131,513,74,81,52,133,514,23,272,76,134,192,82,516,56,137,27,97,39,288,84,259,138,520,29,145,98,43,261,140,30,88,146,71,528,100,262,320,45,265,161,51,148,75,46,104,266,162,544,53,515,273,152,77,268,193,83,164,54,112,135,384,274,517,57,78,85,194,518,289,168,58,276,576,139,521,99,290,196,86,89,60,141,522,31,280,176,101,147,321,292,529,263,142,200,90,524,640,149,530,102,105,322,47,296,92,267,163,150,208,545,532,153,106,324,113,269,165,546,55,304,385,275,154,79,536,108,270,195,328,166,224,114,577,548,386,519,169,768,59,277,156,197,87,116,291,170,388,278,578,336,552,61,523,281,177,198,201,91,293,172,62,580,120,143,392,282,525,178,103,560,323,294,641,531,352,93,202,526,297,284,584,209,180,642,151,400,107,325,533,298,204,94,210,547,644,534,305,184,109,592,155,326,329,300,537,225,115,271,167,416,306,212,549,387,769,648,157,538,110,330,117,226,579,550,337,308,608,171,389,770,279,158,216,553,540,199,332,656,228,118,581,121,390,448,338,173,554,772,63,312,393,283,179,353,561,203,295,174,582,232,122,585,340,556,394,527,776,285,672,181,562,643,401,354,205,95,124,299,396,286,586,211,344,182,240,593,564,402,327,645,535,185,784,356,206,301,588,213,646,417,307,186,404,111,704,594,568,331,302,649,539,227,360,609,418,214,551,217,800,309,188,596,771,650,159,408,333,541,229,119,449,339,420,310,657,610,368,391,218,555,773,652,542,313,600,334,658,230,583,233,123,341,612,450,175,774,424,314,832,220,557,395,777,355,673,563,660,125,234,587,452,342,558,345,316,616,241,397,778,287,674,183,432,357,565,403,207,785,664,236,126,589,398,456,346,780,242,705,595,676,566,624,647,896,187,405,786,358,361,569,303,590,215,348,244,597,419,406,706,464,801,680,189,570,788,651,409,362,611,369,219,421,802,311,190,708,598,248,601,572,410,335,653,543,792,231,364,688,613,451,422,659,480,370,833,221,804,775,654,425,315,412,712,602,235,453,343,661,614,617,372,426,834,222,559,808,317,604,779,675,662,433,237,127,720,454,457,347,428,318,665,618,836,243,376,399,625,781,434,359,677,567,816,897,787,666,238,591,349,620,458,245,782,707,840,678,465,436,736,626,898,407,363,681,571,789,668,460,350,246,709,599,249,628,466,803,682,900,191,790,440,365,848,573,411,793,481,371,689,423,710,250,713,603,468,805,684,574,632,655,904,413,794,366,690,615,373,482,835,223,806,864,252,605,427,414,714,472,809,796,721,692,455,663,912,619,484,374,837,377,429,810,319,716,606,435,239,722,817,696,621,459,430,667,838,488,378,841,812,737,627,783,679,928,437,818,724,899,461,351,669,622,247,380,842,629,467,438,738,496,849,820,683,901,791,670,441,728,462,711,844,251,469,740,630,633,902,442,367,960,850,685,575,824,905,795,483,691,865,253,715,470,807,686,473,444,744,634,852,906,415,797,485,375,693,913,866,254,717,607,636,474,811,908,798,723,856,694,752,914,486,839,489,379,697,868,431,718,476,813,725,929,819,698,916,623,381,490,843,814,739,872,497,930,439,726,729,821,700,463,671,920,492,382,845,741,631,498,961,851,932,822,880,903,443,730,825,846,471,742,745,635,500,853,962,687,936,445,826,732,907,867,255,637,475,446,746,964,854,504,857,828,753,909,799,487,695,944,869,915,719,477,748,638,910,968,858,754,491,699,917,870,873,478,815,727,860,756,931,918,493,383,976,701,921,874,499,881,731,933,823,702,760,922,494,847,743,876,501,963,934,992,882,733,937,827,924,747,502,965,855,505,884,938,447,734,829,945,749,639,966,506,969,859,940,830,755,888,911,946,871,479,750,508,861,970,757,977,948,919,875,972,862,758,761,495,978,703,952,877,923,993,883,935,762,980,925,878,503,885,994,735,764,939,926,984,967,507,996,886,889,941,831,947,751,509,971,942,1000,890,949,510,973,863,759,892,979,950,1008,953,974,763,981,954,879,995,765,982,985,956,927,997,887,766,986,998,1001,891,943,988,511,893,1002,1009,951,975,1004,894,1010,955,983,1012,957,767,987,958,1016,999,989,1003,990,1005,895,1011,1006,1013,1014,1017,959,1018,991,1020,1007,1015,1019,1021,1022,1023]
序列5：
以N＝512为例,利用公式(3)生成的序列为:
[0,1,2,4,8,16,32,3,5,6,64,9,10,17,12,128,18,33,20,34,24,65,36,7,256,66,40,11,68,13,48,129,19,14,72,130,21,35,132,22,80,25,37,257,136,26,67,38,96,258,41,28,69,144,42,260,49,70,73,44,15,264,160,50,131,74,81,52,133,23,272,76,134,82,192,56,137,27,97,39,288,84,259,138,29,98,145,43,261,140,30,88,71,146,100,262,320,45,265,161,51,148,75,46,104,266,162,53,77,273,152,83,268,193,164,54,112,135,384,274,57,78,85,194,289,168,58,276,139,99,290,86,89,196,60,141,31,280,101,176,321,147,292,263,142,90,200,102,105,149,322,47,296,92,267,163,150,208,106,153,324,113,269,165,55,304,79,385,275,154,108,195,270,328,166,114,224,386,169,59,277,156,87,197,116,291,170,388,278,336,61,281,177,91,198,201,293,172,62,120,143,392,282,103,178,323,294,93,352,202,297,284,209,180,107,325,151,400,298,94,204,210,109,305,184,326,155,329,115,300,225,271,167,416,306,212,387,110,157,330,117,226,337,308,171,389,279,158,216,199,332,118,121,228,390,338,448,173,63,312,393,283,179,353,203,295,174,122,232,340,394,285,181,95,354,205,401,124,211,299,396,286,344,182,327,240,402,185,356,206,301,213,111,417,307,186,404,331,227,302,360,418,214,217,309,188,159,333,408,119,229,339,449,420,310,368,391,218,313,334,123,230,233,341,450,175,424,314,220,395,355,125,234,342,345,452,316,241,397,287,183,357,432,207,403,126,236,398,346,456,242,358,187,361,405,215,303,348,244,419,406,464,189,362,409,369,219,421,311,190,335,248,410,231,364,451,422,370,221,480,425,315,412,235,343,453,372,426,222,317,127,237,433,347,454,457,243,428,318,376,399,359,434,238,349,458,245,465,436,363,407,350,460,246,249,466,191,365,440,411,371,481,423,250,468,366,413,373,223,482,252,427,414,472,455,374,377,484,429,319,239,435,459,430,378,488,437,351,461,247,380,467,438,496,441,462,251,469,367,442,483,253,470,473,444,415,375,485,254,474,379,486,489,431,476,381,490,497,439,463,382,492,498,443,471,500,445,255,475,446,504,487,477,491,478,383,493,499,494,501,502,505,447,506,479,508,495,503,507,509,510,511]
序列6：
以N＝512为例,利用公式(4)方法生成的序列为:
[0,1,2,4,8,16,32,3,5,6,64,9,10,17,12,128,18,33,20,34,24,65,36,256,7,66,40,11,68,13,48,129,19,14,72,130,21,35,132,22,80,25,37,136,257,26,38,67,96,258,41,28,144,69,42,260,49,70,73,44,264,15,160,50,131,74,81,52,133,272,23,76,134,192,82,56,137,27,97,39,288,84,138,259,29,98,145,43,140,261,30,88,146,71,100,262,320,45,265,161,51,148,46,75,104,266,162,53,152,273,77,268,193,164,54,83,112,384,135,274,57,78,85,289,194,168,276,58,139,99,290,196,86,89,60,141,280,31,101,176,147,321,292,142,263,200,90,102,149,105,47,322,296,92,163,267,150,208,153,106,324,113,269,165,55,304,385,154,275,79,108,270,328,166,195,224,114,386,169,59,156,277,197,87,291,116,170,388,278,336,61,281,177,293,198,201,91,172,62,120,392,143,282,103,178,294,323,352,93,202,297,284,209,180,107,400,151,325,298,204,94,210,305,109,184,155,326,329,300,225,115,167,271,416,306,212,387,157,110,330,117,226,337,171,308,389,158,279,216,332,199,228,118,121,390,173,448,63,338,312,393,283,179,353,295,174,203,232,340,122,394,285,181,354,401,205,95,299,124,396,286,344,182,211,240,402,327,185,356,206,301,213,417,307,111,186,404,302,227,331,360,418,214,309,217,188,408,159,333,229,119,449,420,310,339,368,391,218,313,334,230,233,123,341,175,450,424,314,220,395,355,125,234,452,342,345,316,241,397,287,183,357,432,403,207,236,126,398,456,346,242,187,358,405,361,303,348,215,419,244,406,464,189,409,362,369,421,311,219,190,248,410,231,335,364,422,451,480,370,221,425,315,412,235,453,343,372,426,222,317,433,237,127,454,457,428,347,318,243,376,399,359,434,238,349,458,245,465,436,363,407,460,350,246,249,191,466,365,440,411,481,371,423,250,468,413,366,373,482,223,427,252,414,472,455,484,374,377,429,319,435,239,430,459,488,378,437,461,351,247,380,438,467,496,441,462,251,469,367,442,483,253,470,473,444,415,485,375,254,474,486,489,379,431,476,381,490,497,439,463,492,382,498,443,471,500,445,255,475,446,504,487,477,491,478,493,383,499,494,501,502,505,447,506,479,508,495,503,507,509,510,511]
序列7：
以N＝512为例,利用公式(6)生成的序列为:
[0,1,2,4,8,16,32,3,5,6,64,9,10,17,12,128,18,33,20,34,24,36,65,7,256,66,40,11,68,13,48,129,19,14,72,130,21,35,132,22,80,25,37,257,136,26,38,67,96,258,41,28,144,69,42,260,49,70,44,73,15,264,160,50,131,74,52,81,133,23,272,76,134,192,82,56,137,27,97,39,288,84,259,138,29,145,98,43,261,140,30,88,146,71,100,262,320,45,265,161,51,148,46,75,104,266,162,53,273,152,77,268,164,54,193,83,112,135,384,274,57,78,85,194,289,168,58,276,139,99,290,196,86,60,89,141,31,280,176,147,101,292,321,263,142,200,90,149,102,105,322,47,296,92,267,163,150,208,153,106,324,269,113,165,55,304,385,275,154,79,108,270,328,166,195,224,114,386,169,59,277,156,197,87,116,291,170,388,278,336,61,281,177,198,293,172,62,201,91,120,143,392,282,178,103,294,323,352,93,202,297,284,180,209,151,400,107,325,298,204,94,210,305,184,155,109,326,300,329,271,225,115,167,416,306,212,387,157,110,330,117,226,308,337,171,389,279,158,216,332,199,228,118,390,121,448,338,173,63,312,393,283,179,353,295,174,203,232,122,340,394,285,181,401,354,205,95,124,299,396,286,344,182,211,240,402,185,327,356,206,301,213,417,307,186,404,111,302,331,360,227,418,214,309,188,217,159,408,333,229,119,420,310,449,339,368,391,218,313,334,230,233,123,341,450,175,424,314,220,395,355,125,234,452,342,316,345,397,287,241,183,432,403,357,207,236,126,398,456,346,242,187,405,358,361,303,348,215,244,419,406,464,189,409,362,369,421,311,190,219,248,410,335,364,231,422,451,480,370,221,425,315,412,235,453,343,372,426,222,317,433,237,127,454,428,318,457,347,376,399,243,434,359,238,349,458,245,436,465,407,363,460,350,246,249,466,191,440,411,365,481,371,423,250,468,413,366,373,482,223,252,427,414,472,455,484,374,377,429,319,435,239,430,459,488,378,437,461,351,380,247,438,467,496,441,462,251,469,442,367,483,253,470,444,473,415,485,375,254,474,486,489,379,431,476,381,490,497,439,463,492,382,498,443,471,500,445,255,446,475,504,487,477,491,478,493,383,499,494,501,502,505,447,506,479,508,495,503,507,509,510,511]
序列8：
以N＝512为例,利用公式(7)生成的序列为:
[0,1,2,4,8,16,32,3,5,6,64,9,10,17,12,128,18,33,20,34,24,65,36,7,256,66,40,11,68,13,48,129,19,14,72,130,21,35,132,22,80,25,37,257,136,26,67,38,96,258,41,28,144,69,42,260,49,70,73,44,15,264,160,50,131,74,81,52,133,23,272,76,134,192,82,56,137,27,97,39,288,84,259,138,29,145,98,43,261,140,30,88,146,71,100,262,320,45,265,161,51,148,75,46,104,266,162,53,273,152,77,268,193,83,164,54,112,135,384,274,57,78,85,194,289,168,58,276,139,99,290,196,86,89,60,141,31,280,176,101,147,321,292,263,142,200,90,149,102,105,322,47,296,92,267,163,150,208,153,106,324,113,269,165,55,304,385,275,154,79,108,270,195,328,166,224,114,386,169,59,277,156,197,87,116,291,170,388,278,336,61,281,177,198,201,91,293,172,62,120,143,392,282,178,103,323,294,352,93,202,297,284,209,180,151,400,107,325,298,204,94,210,305,184,109,155,326,329,300,225,115,271,167,416,306,212,387,157,110,330,117,226,337,308,171,389,279,158,216,199,332,228,118,121,390,448,338,173,63,312,393,283,179,353,203,295,174,232,122,340,394,285,181,401,354,205,95,124,299,396,286,211,344,182,240,402,327,185,356,206,301,213,417,307,186,404,111,331,302,227,360,418,214,217,309,188,159,408,333,229,119,449,339,420,310,368,391,218,313,334,230,233,123,341,450,175,424,314,220,395,355,125,234,452,342,345,316,241,397,287,183,432,357,403,207,236,126,398,456,346,242,187,405,358,361,303,215,348,244,419,406,464,189,409,362,369,219,421,311,190,248,410,335,231,364,451,422,480,370,221,425,315,412,235,453,343,372,426,222,317,433,237,127,454,457,347,428,318,243,376,399,434,359,238,349,458,245,465,436,407,363,460,350,246,249,466,191,440,365,411,481,371,423,250,468,413,366,373,482,223,252,427,414,472,455,484,374,377,429,319,435,239,459,430,488,378,437,461,351,247,380,467,438,496,441,462,251,469,442,367,483,253,470,473,444,415,485,375,254,474,486,489,379,431,476,381,490,497,439,463,492,382,498,443,471,500,445,255,475,446,504,487,477,491,478,493,383,499,494,501,502,505,447,506,479,508,495,503,507,509,510,511]
序列9：
以N＝256为例，利用公式(3)生成的序列为:
[0,1,2,4,8,16,32,3,5,6,64,9,10,17,12,128,18,33,20,34,24,65,36,7,66,40,11,68,13,48,129,19,14,72,130,21,35,132,22,80,25,37,136,26,67,38,96,41,28,69,144,42,49,70,73,44,15,160,50,131,74,81,52,133,23,76,134,82,192,56,137,27,97,39,84,138,29,98,145,43,140,30,88,71,146,100,45,161,51,148,75,46,104,162,53,77,152,83,193,164,54,112,135,57,78,85,194,168,58,139,99,86,89,196,60,141,31,101,176,147,142,90,200,102,105,149,47,92,163,150,208,106,153,113,165,55,79,154,108,195,166,114,224,169,59,156,87,197,116,170,61,177,91,198,201,172,62,120,143,103,178,93,202,209,180,107,151,94,204,210,109,184,155,115,225,167,212,110,157,117,226,171,158,216,199,118,121,228,173,63,179,203,174,122,232,181,95,205,124,211,182,240,185,206,213,111,186,227,214,217,188,159,119,229,218,123,230,233,175,220,125,234,241,183,207,126,236,242,187,215,244,189,219,190,248,231,221,235,222,127,237,243,238,245,246,249,191,250,223,252,239,247,251,253,254,255]
序列10：
以N＝256为例，利用公式(4)方法生成的序列为:
[0,1,2,4,8,16,32,3,5,6,64,9,10,17,12,128,18,33,20,34,24,65,36,7,66,40,11,68,13,48,129,19,14,72,130,21,35,132,22,80,25,37,136,26,38,67,96,41,28,144,69,42,49,70,73,44,15,160,50,131,74,81,52,133,23,76,134,192,82,56,137,27,97,39,84,138,29,98,145,43,140,30,88,146,71,100,45,161,51,148,46,75,104,162,53,152,77,193,164,54,83,112,135,57,78,85,194,168,58,139,99,196,86,89,60,141,31,101,176,147,142,200,90,102,149,105,47,92,163,150,208,153,106,113,165,55,154,79,108,166,195,224,114,169,59,156,197,87,116,170,61,177,198,201,91,172,62,120,143,103,178,93,202,209,180,107,151,204,94,210,109,184,155,225,115,167,212,157,110,117,226,171,158,216,199,228,118,121,173,63,179,174,203,232,122,181,205,95,124,182,211,240,185,206,213,111,186,227,214,217,188,159,229,119,218,230,233,123,175,220,125,234,241,183,207,236,126,242,187,215,244,189,219,190,248,231,221,235,222,237,127,243,238,245,246,249,191,250,223,252,239,247,251,253,254,255]
序列11：
以N＝256为例，利用公式(6)生成的序列为:
[0,1,2,4,8,16,32,3,5,6,64,9,10,17,12,128,18,33,20,34,24,36,65,7,66,40,11,68,13,48,129,19,14,72,130,21,35,132,22,80,25,37,136,26,38,67,96,41,28,144,69,42,49,70,44,73,15,160,50,131,74,52,81,133,23,76,134,192,82,56,137,27,97,39,84,138,29,145,98,43,140,30,88,146,71,100,45,161,51,148,46,75,104,162,53,152,77,164,54,193,83,112,135,57,78,85,194,168,58,139,99,196,86,60,89,141,31,176,147,101,142,200,90,149,102,105,47,92,163,150,208,153,106,113,165,55,154,79,108,166,195,224,114,169,59,156,197,87,116,170,61,177,198,172,62,201,91,120,143,178,103,93,202,180,209,151,107,204,94,210,184,155,109,225,115,167,212,157,110,117,226,171,158,216,199,228,118,121,173,63,179,174,203,232,122,181,205,95,124,182,211,240,185,206,213,186,111,227,214,188,217,159,229,119,218,230,233,123,175,220,125,234,241,183,207,236,126,242,187,215,244,189,190,219,248,231,221,235,222,237,127,243,238,245,246,249,191,250,223,252,239,247,251,253,254,255]
序列12：
以N＝256为例，利用公式(7)生成的序列为:
[0,1,2,4,8,16,32,3,5,6,64,9,10,17,12,128,18,33,20,34,24,65,36,7,66,40,11,68,13,48,129,19,14,72,130,21,35,132,22,80,25,37,136,26,67,38,96,41,28,144,69,42,49,70,73,44,15,160,50,131,74,81,52,133,23,76,134,192,82,56,137,27,97,39,84,138,29,145,98,43,140,30,88,146,71,100,45,161,51,148,75,46,104,162,53,152,77,193,83,164,54,112,135,57,78,85,194,168,58,139,99,196,86,89,60,141,31,176,101,147,142,200,90,149,102,105,47,92,163,150,208,153,106,113,165,55,154,79,108,195,166,224,114,169,59,156,197,87,116,170,61,177,198,201,91,172,62,120,143,178,103,93,202,209,180,151,107,204,94,210,184,109,155,225,115,167,212,157,110,117,226,171,158,216,199,228,118,121,173,63,179,203,174,232,122,181,205,95,124,211,182,240,185,206,213,186,111,227,214,217,188,159,229,119,218,230,233,123,175,220,125,234,241,183,207,236,126,242,187,215,244,189,219,190,248,231,221,235,222,237,127,243,238,245,246,249,191,250,223,252,239,247,251,253,254,255]
序列13：
以N＝128为例，利用公式(3)生成的序列为:
[0,1,2,4,8,16,32,3,5,6,64,9,10,17,12,18,33,20,34,24,65,36,7,66,40,11,68,13,48,19,14,72,21,35,22,80,25,37,26,67,38,96,41,28,69,42,49,70,73,44,15,50,74,81,52,23,76,82,56,27,97,39,84,29,98,43,30,88,71,100,45,51,75,46,104,53,77,83,54,112,57,78,85,58,99,86,89,60,31,101,90,102,105,47,92,106,113,55,79,108,114,59,87,116,61,91,62,120,103,93,107,94,109,115,110,117,118,121,63,122,95,124,111,119,123,125,126,127]
序列14：
以N＝128为例，利用公式(4)生成的序列为:
[0,1,2,4,8,16,32,3,5,6,64,9,10,17,12,18,33,20,34,24,65,36,7,66,40,11,68,13,48,19,14,72,21,35,22,80,25,37,26,38,67,96,41,28,69,42,49,70,73,44,15,50,74,81,52,23,76,82,56,27,97,39,84,29,98,43,30,88,71,100,45,51,46,75,104,53,77,54,83,112,57,78,85,58,99,86,89,60,31,101,90,102,105,47,92,106,113,55,79,108,114,59,87,116,61,91,62,120,103,93,107,94,109,115,110,117,118,121,63,122,95,124,111,119,123,125,126,127]
序列15：
以N＝128为例，利用公式(6)生成的序列为:
[0,1,2,4,8,16,32,3,5,6,64,9,10,17,12,18,33,20,34,24,36,65,7,66,40,11,68,13,48,19,14,72,21,35,22,80,25,37,26,38,67,96,41,28,69,42,49,70,44,73,15,50,74,52,81,23,76,82,56,27,97,39,84,29,98,43,30,88,71,100,45,51,46,75,104,53,77,54,83,112,57,78,85,58,99,86,60,89,31,101,90,102,105,47,92,106,113,55,79,108,114,59,87,116,61,62,91,120,103,93,107,94,109,115,110,117,118,121,63,122,95,124,111,119,123,125,126,127]
序列16：
以N＝128为例，利用公式(7)生成的序列为:
[0,1,2,4,8,16,32,3,5,6,64,9,10,17,12,18,33,20,34,24,65,36,7,66,40,11,68,13,48,19,14,72,21,35,22,80,25,37,26,67,38,96,41,28,69,42,49,70,73,44,15,50,74,81,52,23,76,82,56,27,97,39,84,29,98,43,30,88,71,100,45,51,75,46,104,53,77,83,54,112,57,78,85,58,99,86,89,60,31,101,90,102,105,47,92,106,113,55,79,108,114,59,87,116,61,91,62,120,103,93,107,94,109,115,110,117,118,121,63,122,95,124,111,119,123,125,126,127]
序列17：
以N＝64为例，利用公式(3)生成的序列为:
[0,1,2,4,8,16,32,3,5,6,9,10,17,12,18,33,20,34,24,36,7,40,11,13,48,19,14,21,35,22,25,37,26,38,41,28,42,49,44,15,50,52,23,56,27,39,29,43,30,45,51,46,53,54,57,58,60,31,47,55,59,61,62,63]
序列18：
以N＝64为例，利用公式(4)生成的序列为：
[0,1,2,4,8,16,32,3,5,6,9,10,17,12,18,33,20,34,24,36,7,40,11,13,48,19,14,21,35,22,25,37,26,38,41,28,42,49,44,15,50,52,23,56,27,39,29,43,30,45,51,46,53,54,57,58,60,31,47,55,59,61,62,63]
序列19：
以N＝64为例，利用公式(6)生成的序列为:
[0,1,2,4,8,16,32,3,5,6,9,10,17,12,18,33,20,34,24,36,7,40,11,13,48,19,14,21,35,22,25,37,26,38,41,28,42,49,44,15,50,52,23,56,27,39,29,43,30,45,51,46,53,54,57,58,60,31,47,55,59,61,62,63]
序列20：
以N＝64为例，利用公式(7)生成的序列为:
[0,1,2,4,8,16,32,3,5,6,9,10,17,12,18,33,20,34,24,36,7,40,11,13,48,19,14,21,35,22,25,37,26,38,41,28,42,49,44,15,50,52,23,56,27,39,29,43,30,45,51,46,53,54,57,58,60,31,47,55,59,61,62,63]
需要说明的是，上述一些序列只是一些举例，其应用到Polar编码过程中会有助于提高Poalr码编译码性能。任一种举例的序列中，在不影响其整体效果的前提下，可以做包括但不限于如下几方面的调整或者等同替换：
1、序列中少数元素之间的位置互换。例如，序号位置可以在设定幅度内调整，例如，设定幅度为5，将序号为10的元素位置在左右5个位置内调整均可；
2、序列中的部分元素进行调整，但是根据该序列选择出用于传输T比特信息的信道集合是一致或相似的。
3、序列中包含从0开始到N-1结束的N个元素，从0开始到N-1结束的N个元素代表N个极化信道的序号。实际上，N个极化信道的序号也可以从1开始到N结束，将上述序列中各序号均加1即可，这也是上述各计算方式中的序号形式。当然，也可以采取其他方式表示上述极化信道的序号或者标识，该具体表达方式不影响序列中所表示的极化信道的具体位置。
4、上述序列中的N个极化信道的序号是按照N个极化信道可靠度从小到大排列的，这时按可靠度从高到低选取K个极化信道即为取上述任一序列的最后K个序号对应的极化信道，实际上，N个极化信道的序号也可以按照N个极化信道可靠度从大到小排列，将上述序列中的元素逆序排列或者反序排列即可，这时按可靠度从高到低选取K个极化信道即为取最开始K个序号对应的极化信道。
5、上述序列还可以利用各个信道的归一化可靠度或等效可靠度序列进行表征。例如：信道x在上述序列的排序位置为n(最左面的记为1)则该信道的可靠度可以表示为n或者归一化的n/N，其中N为序列的长度。
基于图2所示的Polar码编码方法的同一发明构思，如图3所示，本申请实施例中还提供一种Polar码编码装置300，该Polar码编码装置300用于执行图2所示的Polar码编码方法。图3所示的Polar码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，Polar码编码装置300包括：输入接口电路301，用于获取待编码比特；逻辑电路302，用于执行上述图2所示的Polar码编码方法，具体请见前面方法实施例中的描述，此处不再赘述；输出接口电路303，用于输出编码后的比特序列。
进一步地，该编码装置300输出的编码后的比特序列经过调制器310调制后输出给收发器320，收发器320对调制后的序列进行相应处理(包括但不限于数模变换和/或变频等处理)后通过天线330发送出去。
可选的，Polar码编码装置300在具体实现时可以是芯片或者集成电路。
可选的，当上述实施例的Polar码编码方法中的部分或全部通过软件来实现时，如图4所示，Polar码编码装置300包括：存储器401，用于存储程序；处理器402，用于执行存储器401存储的程序，当程序被执行时，使得Polar码编码装置300可以实现上述图2实施例提供的Polar码编码方法。
可选的，上述存储器401可以是物理上独立的单元，也可以如图5所示，存储器501与处理器502集成在一起。
可选的，当上述图2实施例的编码方法中的部分或全部通过软件实现时，Polar码传输装置300也可以只包括处理器402。用于存储程序的存储器401位于Polar码传输装置300之外，处理器402通过电路/电线与存储器401连接，用于读取并执行存储器401中存储的程序。
处理器402可以是中央处理器(central processing unit，CPU)，网络处理器(network processor，NP)或者CPU和NP的组合。
处理器402还可以进一步包括硬件芯片。上述硬件芯片可以是专用集成电路(application-specific integrated circuit，ASIC)，可编程逻辑器件(programmablelogic device，PLD)或其组合。上述PLD可以是复杂可编程逻辑器件(complexprogrammable logic device，CPLD)，现场可编程逻辑门阵列(field-programmable gatearray，FPGA)，通用阵列逻辑(generic array logic,GAL)或其任意组合。
上述实施例中的存储器可以包括易失性存储器(volatile memory)，例如随机存取存储器(random-access memory，RAM)；存储器也可以包括非易失性存储器(non-volatile memory)，例如快闪存储器(flash memory)，硬盘(hard disk drive，HDD)或固态硬盘(solid-state drive，SSD)；存储器还可以包括上述种类的存储器的组合。
基于图2所示的Polar码编码方法，如图6所示，本申请实施例还提供了一种Polar码编码装置300，Polar码编码装置300用于执行图2所示的Polar码编码方法，Polar码编码装置300包括：
获取单元601，用于获取用于对K个待编码比特进行编码的第一序列，第一序列中包含N个极化信道的序号，N个极化信道的序号在第一序列中是按照N个极化信道的可靠度进行排列的，K为正整数，N为Polar码的母码长度，N为2的正整数次幂，K≤N；
选择单元602，用于根据可靠度从低到高的顺序，从第一序列中选择K个极化信道的序号；
编码单元603，用于按照所选择的K个极化信道的序号放置待编码比特，并对待编码比特进行Polar码编码。
其中，第一序列可以为上述任一种举例的序列，也可以是从长度为Nmax的第二序列中取出序号小于N的序号(序号从0开始)，第二序列可以为上述任一种举例的序列。N个极化信道中第i个极化信道的可靠度也可以通过上述任一种举例的公式来确定。
本申请实施例还提供了一种计算机存储介质，存储有计算机程序，该计算机程序包括用于执行图2所示的Polar码编码方法。
本申请实施例还提供了一种包含指令的计算机程序产品，当其在计算机上运行时，使得计算机执行图2所示的Polar码编码方法。
本领域内的技术人员应明白，本申请的实施例可提供为方法、系统、或计算机程序产品。因此，本申请可采用完全硬件实施例、完全软件实施例、或结合软件和硬件方面的实施例的形式。而且，本申请可采用在一个或多个其中包含有计算机可用程序代码的计算机可用存储介质(包括但不限于磁盘存储器、CD-ROM、光学存储器等)上实施的计算机程序产品的形式。
本申请是参照根据本申请实施例的方法、设备(系统)、和计算机程序产品的流程图和/或方框图来描述的。应理解可由计算机程序指令实现流程图和/或方框图中的每一流程和/或方框、以及流程图和/或方框图中的流程和/或方框的结合。可提供这些计算机程序指令到通用计算机、专用计算机、嵌入式处理机或其他可编程数据处理设备的处理器以产生一个机器，使得通过计算机或其他可编程数据处理设备的处理器执行的指令产生用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的装置。
这些计算机程序指令也可存储在能引导计算机或其他可编程数据处理设备以特定方式工作的计算机可读存储器中，使得存储在该计算机可读存储器中的指令产生包括指令装置的制造品，该指令装置实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能。
这些计算机程序指令也可装载到计算机或其他可编程数据处理设备上，使得在计算机或其他可编程设备上执行一系列操作步骤以产生计算机实现的处理，从而在计算机或其他可编程设备上执行的指令提供用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的步骤。
尽管已描述了本申请的优选实施例，但本领域内的技术人员一旦得知了基本创造性概念，则可对这些实施例作出另外的变更和修改。所以，所附权利要求意欲解释为包括优选实施例以及落入本申请范围的所有变更和修改。
显然，本领域的技术人员可以对本申请实施例进行各种改动和变型而不脱离本申请实施例的精神和范围。这样，倘若本申请实施例的这些修改和变型属于本申请权利要求及其等同技术的范围之内，则本申请也意图包含这些改动和变型在内。

Claims (28)

1.一种极化Polar码编码方法，其特征在于，包括：
获取用于对K个待编码比特进行编码的第一序列，所述第一序列中包含N个极化信道的序号，所述N个极化信道的序号在所述第一序列中是按照所述N个极化信道的可靠度进行排列的，K为正整数，N为Polar码的母码长度，N＝2n，n为正整数，K≤N；
根据可靠度从高到低的顺序，从所述第一序列中选择K个极化信道的序号；
按照所选择的K个极化信道的序号放置所述待编码比特，并对所述待编码比特进行Polar码编码。
2.如权利要求1所述的方法，其特征在于，所述第一序列为第二序列的全部或者子集，所述第二序列中包含Nmax个极化信道的序号，所述Nmax个极化信道的序号在所述第二序列中是按照所述Nmax个极化信道的可靠度进行排列的，所述Nmax为2的正整数次幂，所述Nmax≥N。
3.如权利要求2所述的方法，其特征在于，所述第二序列中第i个极化信道的可靠度为
其中，0≤i≤N-1，Wi为第i个极化信道的可靠度，i满足i＝Bn-1Bn-2...B0，其中Bn-1Bn- 2...B1B0为i的二进制表示，Bj为信道序号i的二进制表示中第j位的取值,Bj∈{0,1}，其中β为实数核函数；b0、b1和b2为不同的复数核函数；a0、a1、a2为权重因子；分别表征当信道序号的二进制表达的第e1、e2位为1时相应的复数函数会对可靠度产生影响。
4.如权利要求2所述的方法，其特征在于，所述第二序列中第i个极化信道的可靠度为
其中，0≤i≤N-1，Wi为第i个极化信道的可靠度，i满足i＝Bn-1Bn-2...B0，其中Bn-1Bn- 2...B1B0为i的二进制表示，Bj为信道序号i的二进制表示中第j位的取值,Bj∈{0,1}，其中β为实数核函数；b0、b1和b2为不同的复数核函数；a0、a1、a2为权重因子；分别表征当信道序号的二进制表达的第e1、e2位为1时相应的复数函数会对可靠度产生影响。
5.如权利要求4所述的方法，其特征在于，所述权重因子和复数核函数分别为a0＝0.169，b0＝0.8805，a1＝-0.096，b1＝0.2432+0.2432I，其中I为虚数单位，e1＝6，a2＝0.038，b2＝0.8262，e2＝9，所述第二序列中第i个极化信道的可靠度为
6.如权利要求4所述的方法，其特征在于，所述权重因子和复数核函数分别为a0＝0.1733，b0＝0.5486，a1＝-0.0279，b1＝0.5222+0.5222I，其中I为虚数单位，e1＝5，a2＝-0.07，b2＝0，e2＝6，所述第二序列中第i个极化信道的可靠度为
7.如权利要求2所述的方法，其特征在于，所述第二序列中第i个极化信道的可靠度为
其中，0≤i≤N-1，Wi为第i个极化信道的可靠度，i满足i＝Bn-1Bn-2...B0，其中Bn-1Bn- 2...B1B0为i的二进制表示，Bj为信道序号i的二进制表示中第j位的取值,Bj∈{0,1}，其中β为实数核函数；b0和b1为不同的复数核函数；a0和a1为权重因子；表征当信道序号的二进制表示的第e1、e2位为1时相应的复数函数会对可靠度产生影响。
8.如权利要求7所述的方法，其特征在于，所述权重因子和复数核函数分别为a0＝0.169，b0＝0.601，a1＝-0.07694，b1＝0.0769+0.0769I，其中I为虚数单位，e1＝6，所述第二序列中第i个极化信道的可靠度为：
9.如权利要求7所述的方法，其特征在于，所述权重因子和复数核函数分别为a0＝0.169，b0＝0.601，a1＝-0.0475，b1＝0，e1＝6，所述第二序列中第i个极化信道的可靠度为：
10.如权利要求3-9中任一权利要求所述的方法，
11.根据权利要求1或2所述的方法，其特征在于，所述第二序列为说明书序列1-序列20所示的任意一个序列的部分或全部，所述第二序列中的N个极化信道的序号是按所述N个极化信道的可靠度从小到大排列的，且所述极化信道的序号最小值为0。
12.一种极化Polar码编码装置，其特征在于，包括：
获取单元，用于获取用于对K个待编码比特进行编码的第一序列，所述第一序列中包含N个极化信道的序号，所述N个极化信道的序号在所述第一序列中是按照所述N个极化信道的可靠度进行排列的，K为正整数，N为Polar码的母码长度，N＝2n，n为正整数，K≤N；
选择单元，用于根据可靠度从高到低的顺序，从所述第一序列中选择K个极化信道的序号；
编码单元，用于按照所选择的K个极化信道的序号放置所述待编码比特，并对所述待编码比特进行Polar码编码。
13.如权利要求12所述的装置，其特征在于，所述第一序列为第二序列的全部或者子集，所述第二序列中包含Nmax个极化信道的序号，所述Nmax个极化信道的序号在所述第二序列中是按照所述Nmax个极化信道的可靠度进行排列的，所述Nmax为2的正整数次幂，所述Nmax≥N。
14.如权利要求13所述的装置，其特征在于，所述第二序列中第i个极化信道的可靠度为
其中，0≤i≤N-1，Wi为第i个极化信道的可靠度，i满足i＝Bn-1Bn-2...B0，其中Bn-1Bn- 2...B1B0为i的二进制表示，Bj为信道序号i的二进制表示中第j位的取值,Bj∈{0,1}，其中β为实数核函数；b0、b1和b2为不同的复数核函数；a0、a1、a2为权重因子；分别表征当信道序号的二进制表示的第e1、e2位为1时相应的复数函数会对可靠度产生影响。
15.如权利要求13所述的装置，其特征在于，所述第二序列中第i个极化信道的可靠度为
其中，0≤i≤N-1，Wi为第i个极化信道的可靠度，i满足i＝Bn-1Bn-2...B0，其中Bn-1Bn- 2...B1B0为i的二进制表示，Bj为信道序号i的二进制表示中第j位的取值,Bj∈{0,1}，其中β为实数核函数；b0、b1和b2为不同的复数核函数；a0、a1、a2为权重因子；分别表征当信道序号的二进制表示的第e1、e2位为1时相应的复数函数会对可靠度产生影响。
16.如权利要求15所述的装置，其特征在于，所述权重因子和复数核函数分别为a0＝0.169，b0＝0.8805，a1＝-0.096，b1＝0.2432+0.2432I，其中I为虚数单位，e1＝6，a2＝0.038，b2＝0.8262，e2＝9，所述第二序列中第i个极化信道的可靠度为
17.如权利要求15所述的装置，其特征在于，所述权重因子和复数核函数分别为a0＝0.1733，b0＝0.5486，a1＝-0.0279，b1＝0.5222+0.5222I，其中I为虚数单位，e1＝5，a2＝-0.07，b2＝0，e2＝6，所述第二序列中第i个极化信道的可靠度为：
18.如权利要求13所述的装置，其特征在于，所述第二序列中第i个极化信道的可靠度为
其中，0≤i≤N-1，Wi为第i个极化信道的可靠度，i满足i＝Bn-1Bn-2...B0，其中Bn-1Bn- 2...B1B0为i的二进制表示，Bj为信道序号i的二进制表示中第j位的取值,Bj∈{0,1}，其中β为实数核函数；b0和b1为不同的复数核函数；a0和a1为权重因子；表征当信道序号的二进制表示的第e1、e2位为1时相应的复数函数会对可靠度产生影响。
19.如权利要求18所述的装置，其特征在于，所述权重因子和复数核函数分别为a0＝0.169，b0＝0.601，a1＝-0.07694，b1＝0.0769+0.0769I，其中I为虚数单位，e1＝6，所述第二序列中第i个极化信道的可靠度为：
20.如权利要求18所述的装置，其特征在于，所述权重因子和复数核函数分别为a0＝0.169，b0＝0.601，a1＝-0.0475，b1＝0，e1＝6，所述第二序列中第i个极化信道的可靠度为：
21.如权利要求14-20中任一权利要求所述的装置，
22.根据权利要求12或13所述的装置，其特征在于，所述第二序列为说明书序列1-序列20所示的任意一个序列的部分或全部，所述第二序列中的N个极化信道的序号是按所述N个极化信道的可靠度从小到大排列的，且所述极化信道的序号最小值为0。
23.如权利要求12-22任意一项所述的装置，其特征在于，所述装置为芯片或集成电路。
24.一种极化Polar码编码装置，其特征在于，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，所述处理器用于执行如权利要求1～11任一项所述的方法。
25.如权利要求24所述的装置，其特征在于，所述Polar码编码装置为芯片或集成电路。
26.一种Polar码编码装置，其特征在于，包括：
输入接口电路，用于获取待编码比特；
逻辑电路，用于基于获取的待编码比特执行所述权利要求1～11任一项所述的方法，得到基于Polar码编码后的比特序列；
输出接口电路，用于输出Polar码编码后的比特序列。
27.一种无线设备，其特征在于，包括如权利要求12-23所述的编码装置、调制器、收发器：
所述调制器用于调制编码后的比特序列得到调制后的序列；
所述收发器用于处理所述调制后的序列。
28.如权利要求27所述的设备，其特征在于，所述无线设备为终端或者网络设备。
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