CN113810059A - 一种用于卫星通信的极化编码译码方法及装置 - Google Patents
一种用于卫星通信的极化编码译码方法及装置 Download PDFInfo
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Abstract
本申请涉及卫星通信技术领域,公开了一种用于卫星通信的极化编码译码方法及装置,该方法包括获取K个待编码比特,从第一序列中选择K个序号,该K个序号对应的极化信道放置该待编码比特,并对该K个待编码比特进行Polar码编码,得到编码后的比特,其中,该第一序列中包括N个极化信道的序号,该第一序列为说明书中提供的相关序列的全部或者子序列。该技术方案适用于北斗卫星的短报文通信系统,采用该方法可以有效提升该通信系统的性能、降低复杂度。
Description
技术领域
本申请实施例涉及卫星通信技术领域,尤其涉及一种Polar码编码方法及装置。
背景技术
北斗卫星的通信系统具有短报文通信功能,是北斗卫星的一大特色,可以看作是人们平时手机使用的“短信息”,“短信息”既能够定位,又能显示发布者的位置。卫星定位终端和北斗卫星或北斗地面服务站之间能够直接通过卫星信号进行双向的信息传递,而GPS只能单向传递(终端从卫星接收位置信号)。在08年汶川地震的时候,震区唯一的通讯方式就是北斗卫星,其短报文功能发挥了极大的搜救作用。目前第二代北斗的短报文系统采用Turbo码进行信道编码,而其性能和复杂度有待进一步的改善。
发明内容
本申请实施例提供一种用于卫星系统的极化编码方法及装置,用以提升短报文通信系统的性能、降低其复杂度。
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,该方法包括获取K个待编码比特;从第一序列中选择K个序号,所述K个序号对应的极化信道放置所述待编码比特,并对所述K个待编码比特进行Polar码编码,得到编码后的比特,其中,所述第一序列中包括N个极化信道的序号,所述第一序列为说明书中的序列Q1或Q2所示的序列的全部或者子序列,所述K为正整数,N为Polar码的母码长度,N=2n,n为正整数,K≤N。
本申请实施例提供的方案可以用于北斗卫星的短报文通信,尤其适用于出站短报文的信道编码设计,通过特别设计的信息位确定序列最大限度的提升性能和降低复杂度。另外,该序列可以适用于多个不同的待编码比特长度,在该序列中,不同长度的待编码比特对应的信道位置集合之间具有嵌套关系,借由该特点可以实现降低系统存储开销的目的,特别是母码长度特别大的情况,效果显著。
在一个可能的设计中,所述选择的K个序号对应的极化信道可靠度高于所述第一序列中剩余的(N-K)个序号对应的极化信道的可靠度。
在一个可能的设计中,所述第一序列是预先存储的。
在一个可能的设计中,当所述母码长度N为4096时,所述待编码比特的数量K为:452,536,904,1048,1808,2072,2712或3096;或者当所述母码长度N为8192时,所述待编码比特的数量K为:235,470,940,1880,2820或3760。
在一个可能的设计中,当所述母码长度为4096时,所述第一序列为说明书中的序列Q1;或者当所述母码长度为8192时,所述第一序列为说明书中的序列Q2。
在一个可能的设计中,所述方法还包括:对所述Polar码编码后的比特进行速率匹配,得到速率匹配后的比特。
在一个可能的设计中,所述N个极化信道的序号为0~(N-1)或1~N。
在一个可能的设计中,所述待编码比特中包括循环冗余校验CRC比特。
在一个可能的设计中,所述待编码比特中包括奇偶校验PC比特。
第二方面,提供一种极化Polar码译码方法,该方法包括接收待译码的比特信息,所述待译码的比特信息包括K个信息比特的信息,所述K个信息比特承载在第一序列的K个序号对应的极化信道上,所述第一序列包括N个极化信道的序号,所述第一序列为说明书中的序列Q1或Q2所示的序列的全部或者子序列,所述K为正整数,N为Polar码的母码长度,N=2n,n为正整数,K≤N;根据待译码的比特信息进行Polar码译码,得到所述K个信息比特。
在一个可能的设计中,所述选择的K个序号对应的极化信道可靠度高于所述第一序列中剩余的(N-K)个序号对应的极化信道的可靠度。
在一个可能的设计中,所述第一序列是预先存储的。
在一个可能的设计中,当所述母码长度N为4096时,所述信息比特的数量K为:452,536,904,1048,1808,2072,2712或3096;或者当所述母码长度N为8192时,所述信息比特的数量K为:235,470,940,1880,2820或3760。
在一个可能的设计中,当所述母码长度为4096时,所述第一序列为说明书中的序列Q1;或者当所述母码长度为8192时,所述第一序列为说明书中的序列Q2。
在一个可能的设计中,所述N个极化信道的序号为0~(N-1)或1~N。
在一个可能的设计中,所述待编码比特中包括循环冗余校验CRC比特。
在一个可能的设计中,所述待编码比特中包括奇偶校验PC比特。
第三方面,提供一种极化Polar码编码装置,包括获取单元,用于获取K个待编码比特;选择单元,用于从第一序列中选择K个序号,所述K个序号对应的极化信道放置所述待编码比特;编码单元,用于对所述K个待编码比特进行Polar码编码,得到编码后的比特;其中,所述第一序列中包括N个极化信道的序号,所述第一序列为说明书中的序列Q1或Q2所示的序列的全部或者子序列,所述K为正整数,N为Polar码的母码长度,N=2n,n为正整数,K≤N。
在一个可能的设计中,所述选择的K个序号对应的极化信道可靠度高于所述第一序列中剩余的(N-K)个序号对应的极化信道的可靠度。
在一个可能的设计中,所述第一序列是预先存储的。
在一个可能的设计中,当所述母码长度N为4096时,所述待编码比特的数量K为:452,536,904,1048,1808,2072,2712或3096;或者当所述母码长度N为8192时,所述待编码比特的数量K为:235,470,940,1880,2820或3760。
在一个可能的设计中,当所述母码长度为4096时,所述第一序列为说明书中的序列Q1;或者当所述母码长度为8192时,所述第一序列为说明书中的序列Q2。
在一个可能的设计中,所述装置还包括速率匹配单元,用于对所述Polar码编码后的比特进行速率匹配,得到速率匹配后的比特。
在一个可能的设计中,所述N个极化信道的序号为0~(N-1)或1~N。
在一个可能的设计中,所述待编码比特中包括循环冗余校验CRC比特。
在一个可能的设计中,所述待编码比特中包括奇偶校验PC比特。
第四方面,提供一种极化Polar码译码装置,包括接收单元,用于接收待译码的比特信息,所述待译码的比特信息包括K个信息比特的信息,所述K个信息比特承载在第一序列的K个序号对应的极化信道上,所述第一序列包括N个极化信道的序号,所述第一序列为说明书中的序列Q1或Q2所示的序列的全部或者子序列,所述K为正整数,N为Polar码的母码长度,N=2n,n为正整数,K≤N,译码单元,用于根据待译码的比特信息进行Polar码译码,得到所述K个信息比特。
在一个可能的设计中,所述选择的K个序号对应的极化信道可靠度高于所述第一序列中剩余的(N-K)个序号对应的极化信道的可靠度。
在一个可能的设计中,所述第一序列是预先存储的。
在一个可能的设计中,当所述母码长度N为4096时,所述信息比特的数量K为:452,536,904,1048,1808,2072,2712或3096;或者当所述母码长度N为8192时,所述信息比特的数量K为:235,470,940,1880,2820或3760。
在一个可能的设计中,当所述母码长度为4096时,所述第一序列为说明书中的序列Q1;或者当所述母码长度为8192时,所述第一序列为说明书中的序列Q2。
在一个可能的设计中,所述N个极化信道的序号为0~(N-1)或1~N。
在一个可能的设计中,所述待编码比特中包括循环冗余校验CRC比特。
在一个可能的设计中,所述待编码比特中包括奇偶校验PC比特。
第五方面,提供一种极化Polar码处理装置,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,所述处理器用于执行如上述第一方面或第一方面可能的设计任一项所述的方法,或者执行如上述第二方面或第二方面可能的设计任一项所述的方法。
在一个可能的设计中,所述Polar码编码装置为芯片或集成电路。
第六方面,提供一种Polar码处理装置,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如上述第一方面或第一方面可能的设计任一项所述的方法,得到基于Polar码编码后的比特序列;或者执行如上述第二方面或第二方面可能的设计任一项所述的方法,得到基于Polar码译码后的比特序列;输出接口电路,用于输出比特序列。
第七方面,提供一种无线设备,其特征在于,包括如第五方面所述的处理装置、调制解调器、收发器:所述调制解调器用于调制编码后的比特序列得到调制后的序列,或者解调编码后的比特信息;所述收发器用于发送所述调制后的序列,或者接收编码后的比特信息。
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为适用本申请实施例提供方案的无线通信网络场景示意图;
图2为适用本申请实施例中无线通信网络的系统框架示意图;
图3为本申请实施例提供的的信息比特位置集合的确定方法示意图;
图4为本申请实施例提供的一种Polar码编码方法示意图;
图5为本申请实施例提供的一种Polar码译码方法示意图;
图6为本申请实施例提供的一种Polar码编码装置600示意图;
图7为本申请实施例提供的一种Polar码编码装置700示意图;
图8为本申请实施例提供的一种Polar码译码装置800示意图;
图9为本申请实施例提供的一种Polar码译码装置900示意图;
图10为本申请实施例提供的一种Polar码编码装置800示意图;
图11为本申请实施例提供的一种Polar码译码装置1100示意图。
具体实施方式
本申请的说明书和权利要求书及所述附图中的术语“第一”、“第二”、“第三”和“第四”等是用于区别不同对象,而不是用于描述特定顺序。此外,术语“包括”和“具有”以及它们任何变形,意图在于覆盖不排他的包含。例如包含了一系列步骤或单元的过程、方法、系统、产品或设备没有限定于已列出的步骤或单元,而是可选地还包括没有列出的步骤或单元,或可选地还包括对于这些过程、方法、产品或设备固有的其它步骤或单元。
在本文中提及“实施例”意味着,结合实施例描述的特定特征、结构或特性可以包含在本申请的至少一个实施例中。在说明书中的各个位置出现该短语并不一定均是指相同的实施例,也不是与其它实施例互斥的独立的或备选的实施例。本领域技术人员显式地和隐式地理解的是,本文所描述的实施例可以与其它实施例相结合。
在本申请中,“至少一个(项)”是指一个或者多个,“多个”是指两个或两个以上,“至少两个(项)”是指两个或三个及三个以上,“和/或”,用于描述关联对象的关联关系,表示可以存在三种关系,例如,“A和/或B”可以表示:只存在A,只存在B以及同时存在A和B三种情况,其中A,B可以是单数或者复数。字符“/”一般表示前后关联对象是一种“或”的关系。“以下至少一项(个)”或其类似表达,是指这些项中的任意组合,包括单项(个)或复数项(个)的任意组合。例如,a,b或c中的至少一项(个),可以表示:a,b,c,“a和b”,“a和c”,“b和c”,或“a和b和c”,其中a,b,c可以是单个,也可以是多个。
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极化编码译码方法及装置,适用于卫星通信,本申请以北斗卫星的短报文通信功能为例进行说明,其他类似通信系统也可以采用本申请提供的方法和装置。一种短报文的工作流程如下:1.短报文发送方首先将包含接收方ID号和通讯内容的通讯申请信号加密后通过卫星转发入站;2.地面中心站接收到通讯申请信号后,经脱密和再加密后加入持续广播的出站广播电文中,经卫星广播给用户;3.接收方用户机接收出站信号,解调解密出站电文,完成一次通讯。针对北斗卫星的特定出站(地面中心站发送给卫星,卫星转发给终端)信息比特数和码长,可以采用特别设计的固定的速率匹配和嵌套的极化码的信息位确定方法,最大限度的提升性能和降低复杂度。
为方便对本申请实施例的理解,下面对极化码作简单介绍。
极化(Polar)码的编码策略是利用无噪信道传输用户有用的信息,噪声信道传输约定的信息或者不传信息,以提高数据传输的可靠性,以保证通信的质量。Polar码也是一种线性块码,具有低的编译码复杂度。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log2 N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。极化信道的序号即为信息比特或者固定比特的位置索引,也即在中的位置索引。
Polar码的构造方法可以采用在线构造的方式,此时在线构造的参数有信噪比有关,发送和接收端无法同时获得准确的信噪比参数(或者需要通过额外的开销获得),并且在线构造需要额外的复杂度。同时,针对不同的编码长度和信息比特长度均需要单独保存信息比特位置。还可以采用与信噪比无关的构造方法,比如PW(英文:PolarizationWeight,中文:极化权重)值。PW值的排序序列本身即是Polar码的一种可靠度排序序列,用于信息比特的选取。PW选择信息比特长度时,性能可以进一步提高。
从编码矩阵可以看出,原始Polar码(母码)的码长为2的整数次幂,在实际应用中需要通过速率匹配实现任意码长的Polar码。采用打孔(puncture)或缩短(shorten)的方案实现速率匹配。在编码时通过对超过目标码长的母码进行打孔或缩短达到目标码长,译码时填充恢复至母码码长。针对北斗出站(地面中心站发送给卫星,卫星转发给终端)的特定出站信息比特数和码长,可以采用固定的速率匹配方式和信息比特位置作为码的设计方案。
在介绍具体方案之前,先对适用本申请实施例提供方案的场景和系统架构作简单介绍。
图1为适用本申请实施例提供方案的无线通信网络场景示意图。本申请提供的方案可以应用于NTN通信系统,如图1所示,该通信系统100可由终端设备101、卫星(或称卫星基站)102以及地面站(或称关口站、信关站)(gateway)103组成。
其中,终端设备101,也可称为用户设备(user equipment,UE)、终端、终端装置等。终端设备是一种具有无线收发功能的设备或者芯片或者通信系统,可以部署在陆地上,包括室内或室外、手持、穿戴或车载;也可以部署在水面上,如轮船上等;还可以部署在空中,例如部署在飞机、气球或卫星上等。终端设备可以是手机(mobile phone)、平板电脑(Pad)、带无线收发功能的电脑、虚拟现实(virtual reality,VR)终端设备、增强现实(augmentedreality,AR)终端设备、工业控制(industrial control)中的无线终端、无人驾驶(selfdriving)中的无线终端、远程医疗(remote medical)中的无线终端、智能电网(smartgrid)中的无线终端、运输安全(transportation safety)中的无线终端、智慧城市(smartcity)中的无线终端、智慧家庭(smart home)中的无线终端等等。可理解,该终端设备还可是未来5G网络中的终端设备或者未来演进的公共陆地移动网络(public land mobilenetwork,PLMN)中的终端设备等。为便于描述,以下将以终端设备为UE为例,来说明本申请实施例所涉及的方法。
可选的,图1所示的通信系统中,终端设备和终端设备之间可以通过设备到设备(device to device,D2D)、车与任何事物(vehicle-to-everything,V2X)或机器到机器(machine to machine,M2M)等通信技术进行通信,本申请实施例对于终端设备之间的通信方法不作限定。
其中,卫星102可为终端设备提供无线接入服务,调度无线资源给接入的终端设备,提供可靠的无线传输协议和数据加密协议等。卫星可以是将人造地球卫星和高空飞行器等作为无线通信的基站,例如演进型基站(evolutional NodeB,eNB)和5G基站(gNB)等。或者,卫星也可以作为这些基站的中继,向终端设备透传这些基站的无线信号,此时,地面站可视为无线通信的基站。因此,在一些实施例中,比如在卫星的再生场景下,网络设备可以为图1所示的卫星基站;在另一些实施例中,比如在卫星的透传场景下,该网络设备可以为图1所示的地面站。为便于描述,下文中以网络设备为基站为例说明本申请所涉及的方法。
本申请提供的实施例中,网络设备可以包括但不限于以上所示的卫星基站,例如该网络设备还可以是未来通信系统如第六代通信系统中的基站。可选的,该网络设备还可以为无线局域网(wireless fidelity,WiFi)系统中的接入节点、无线中继节点、无线回传节点等。可选的,该网络设备还可以是云无线接入网络(cloud radio access network,CRAN)场景下的无线控制器。可选的,该网络设备还可以是可穿戴设备或车载设备等。可选的,该网络设备还可以是小站,传输节点(transmission reception point,TRP)(或也可以称为传输接收点)等。可理解,该网络设备还可以是未来演进的PLMN中的基站等等。
可选的,卫星102可以是静止轨道(geostationary earth orbit,GEO)卫星,也可以是非静止轨道(none-geostationary earth orbit,NGEO)的中轨道(medium earthorbit,MEO)卫星和低轨道(low earth orbit,LEO)卫星,还可以是高空通信平台(HighAltitude Platform Station,HAPS)等。
其中,地面站103可用于连接卫星与核心网。例如,当卫星作为无线通信的基站时,地面站可透传卫星与核心网之间的信令。又或者,地面站可作为无线通信的基站,卫星可透传终端设备与地面站之间的信令。示例性的,当进行通信时,地面站可将来自于核心网的信令通过反馈链路(或称馈电链路)(feeder link)发送至卫星;并由卫星通过该卫星与终端设备之间的服务链路(service link)向该终端设备发送该信令。相应的,终端设备也可以通过服务链路向卫星发送信令,由该卫星通过地面站向核心网发送该信令。
可理解,图1仅示出了一个卫星以及一个地面站,在实际使用中,可根据需要采取多卫星和/或多地面站的架构。其中,每个卫星可向一个或多个终端设备提供服务,每个卫星可对应于一个或多个地面站,每个地面站可对应于一个或多个卫星等等,本申请中不予具体限定。基于图1所示的通信场景,本申请实施例中,执行极化码编码译码方法的执行主体可以为上述地面站或终端,当网络设备或终端作为发送端发送数据或信息时,可以采用此极化码编码方法。相应的,当网络设备或终端作为接收端接收数据或信息时,可以采用此极化码译码方法。
图2为适用本申请实施例提供方案的无线通信网络的系统框架示意图,如图2所示,发送端确定待编码的信息比特后,将所述待编码的信息比特进行Polar编码,经过速率匹配后发送出去,编码后的信息经过信道传输,接收端接收来自信道的信息,解速率匹配后用于译码,译码完成后输出译码得到的信息比特。本申请提供的方案可以应用到现有的通信系统中,特别是卫星通信的场景,代替原有的编译码或者作为现有的编译码的增强方案。
下面将对本申请实施例提供的极化码编码译码方法做详细介绍。
图3为本申请实施例提供的的信息比特位置集合的确定方法示意图,其中,Polar码的最大母码长度为Nmax,信息比特长度为K时,编码后(速率匹配后或输出)的比特长度为M,当前信息比特对应的Polar码的母码长度为N=2^ceil(log2(M))。本申请实施例提供的方案涉及如何在给定信息比特数和码长(母码码长、速率匹配后的码长、或其他规定的输出码长)的情况下,提升码的性能并降低复杂度。本申请实施例提供的方案可以用于北斗卫星的短报文通信,尤其适用于出站短报文的信道编码设计,通过特别设计的固定的速率匹配和信息位确定方法,最大限度的提升性能和降低复杂度。此时,需要速率匹配(打孔或者缩短)的比特数为(N-M),固定速率匹配位置集合,速率匹配位置集合记录了速率匹配的位置序号(可选的,序号从0开始,最大为Nmax-1),根据速率匹配位置集合,确定信息比特位置集合。由于出站编码后的比特数M固定时,可以有多个不同的信息比特长度,而不同长度的信息比特对应的信道位置集合之间具有嵌套关系,可以降低系统存储开销,特别是母码长度特别大的情况,效果显著,图中不同长度的K1,K2,K3长度信息比特序号集合是K4长度的信息比特序号集合的子集。取子集的方式可以为从后往前取,也可以从前往后取,图示取子集的方式仅为举例。
基于图1所示的无线通信网络场景和图2所示的通信系统框架,如图4所示本申请实施例提供的一种Polar码编码方法,具体流程如下:
步骤401、获取K个待编码比特。
步骤402、从第一序列中选择K个序号,该K个序号对应的极化信道放置该待编码比特。
步骤403、对该K个待编码比特进行Polar码编码,得到编码后的比特。
其中,该第一序列中包括N个极化信道的序号,该第一序列为说明书中的序列Q1或Q2所示的序列的全部或者子序列,该K为正整数,N为Polar码的母码长度,N=2n,n为正整数,K≤N。第一序列Q1和Q2参见说明书后段的相关部分,下文不再赘述。
这里所述的第一序列或者所述的子序列是按照可靠度进行排列,具有排序关系,极化信道的可靠度的计算方式可以参考前述的方法,序列的排序可以是按可靠度从低到高排列,也可以是按可靠度从高到低排列,还可以是分成2个或者2个以上的组,每组内部按可靠度从低到高或从高到低排列,具体的分组方式可以是以极化信道的序号大小分组或者其他按同余的序号进行分组(例如分3组,将按除于3后同余的序号分为一组),不做具体限定。下文相同术语同样适用。
可选的,该第一序列是预先存储的。
可选的,当该母码长度N为4096时,该待编码比特的数量K为:452,536,904,1048,1808,2072,2712或3096;或者当该母码长度N为8192时,该待编码比特的数量K为:235,470,940,1880,2820或3760。
可选的,所述K可以在上述值的基础上浮动,例如,增加或者减少10,12,15或者20后的某个K值。更具体地,以452为基础,所述信息比特的数量K可以为432至472之间的某个整数:433,434,435,436,437,438,439,440,…,470,471,472,同样的,536为基础,所述信息比特的数量K可以为516至556之间的整数:516,517,…,555,556,3096为基础,所述信息比特的数量K可以为3076至3116之间的整数:3076,3077,…,3115,3116,235为基础,所述信息比特的数量K可以为215至255之间的整数:215,216,…,254,255;470为基础,所述信息比特的数量K可以为450至490之间的整数:450,451,…,489,490;940为基础,所述信息比特的数量K可以为920至960之间的整数:920,921,…,959,960,其他K值同样适用。
可选的,当该母码长度为4096时,该第一序列为说明书中的序列Q1;或者当该母码长度为8192时,该第一序列为说明书中的序列Q2。
可选的,该方法还包括:对该Polar码编码后的比特进行速率匹配,得到速率匹配后的比特。例如,根据目标码长对Polar码编码后的序列进行打孔。在本申请提供的第一序列中的序号如果设为速率匹配(打孔或者缩短)的位置,该序号或这些序号将被跳过。可选的,可以按照序号从小到大的顺序进行速率匹配,例如打孔,需要打掉的比特的数量可以根据母码码长和目标码长之差确定,例如,如果母码长度为8192,发送的目标码长为7520,则需要打掉的比特数量为672(8192-7520)个。可选的,还可以根据说明书后段提供的缩短位置集合S1进行速率匹配。
可以理解,假设被打孔或者缩短的比特位置排除后的第一序列具有M个元素,则选择的K个序号对应的极化信道可靠度高于该序列中剩余的(M-K)个序号对应的极化信道的可靠度。优选的,所述序列中包含M个极化信道的序号,所述M个极化信道的序号在所述序列中是按照所述M个极化信道的可靠度进行排列的,M为正整数,但是可以理解的是,该序列中的可靠度排序可能由于速率匹配的影响,提前排除掉需要打孔或者缩短的比特位置而并不连续。另该序列中某些位置的调整也并不会影响在该场景下信道传输的可靠性,例如,所选择的K个序号之间的互换并不影响对该K个序号的选择,只需要满足选择的K个序号对应的极化信道可靠度高于该序列中剩余的(M-K)个序号对应的极化信道的可靠度。可选的,该选择的K个序号为该第一序列中的后K个序号,或者该选择的K个序号为该第一序列中的前K个序号。
可选的,该待编码比特中包括循环冗余校验CRC比特。
可选的,该待编码比特中包括奇偶校验PC比特。
本实施例提供的编码方法,通过接收到输入的信息比特后,确定待编码比特的个数K,除了在线计算或预先计算并存储一个第一序列之外,该第一序列的长度对应极化码的母码长度;还可以在线计算或者存储多个第二序列,该多个第二序列分别存储了对应于不同长度K的待编码比特的信息比特位置序号集合,所述第二序列为第三序列的全部或者子集,此时第三序列是某种情况下的最长的信息比特位置序号集合,例如某特定速率匹配后的比特长度下的最长的信息比特位置序号集合,所述第二序列中的极化信道的序号排序与第三序列中的极化信道的序号排序一致。
无论在线计算还是预先计算并存储的方式,确定出信息比特的位置后,剩余位置可以认为是冻结比特或称固定比特的位置,对K个待编码比特进行Polar编码,获得Polar编码后的比特序列。
下面具体介绍根据N个极化信道中第i个极化信道的可靠度进行排序得到的极化信道序号的序列。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。
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。
第一序列可以是按照不同准则确定的序列Q1、序列Q2所示的任意一个序列的部分或全部,可选的,这些序列也可以用相应的表格来表示,如果是表格形式,其包含的表项是“可靠度或可靠度序号”和“极化信道序号”,其中的“可靠度或可靠度序号”即为可靠度由低到高或者由高到低的自然顺序,而“极化信道序号”则为对应序列中的极化信道序号。
对应的,基于图1所示的无线通信网络场景和图2所示的通信系统框架,如图5所示本申请实施例提供的一种Polar码译码方法,具体流程如下:
步骤501、接收待译码的比特信息,所述待译码的比特信息包括K个信息比特的信息,所述K个信息比特承载在第一序列的K个序号对应的极化信道上,所述第一序列包括N个极化信道的序号,所述第一序列为说明书中的序列Q1或Q2所示的序列的全部或者子序列,所述K为正整数,N为Polar码的母码长度,N=2n,n为正整数,K≤N;
步骤502、根据待译码的比特信息进行Polar码译码,得到所述K个信息比特。
可以理解,假设被打孔或者缩短的比特位置排除后的第一序列具有M个元素,则选择的K个序号对应的极化信道可靠度高于该序列中剩余的(M-K)个序号对应的极化信道的可靠度。优选的,所述序列中包含M个极化信道的序号,所述M个极化信道的序号在所述序列中是按照所述M个极化信道的可靠度进行排列的,M为正整数,但是可以理解的是,该序列中的可靠度排序可能由于速率匹配的影响,提前排除掉需要打孔或者缩短的比特位置而并不连续。另该序列中某些位置的调整也并不会影响在该场景下信道传输的可靠性,例如,所选择的K个序号之间的互换并不影响对该K个序号的选择,只需要满足选择的K个序号对应的极化信道可靠度高于该序列中剩余的(M-K)个序号对应的极化信道的可靠度。可选的,该选择的K个序号为该第一序列中的后K个序号,或者该选择的K个序号为该第一序列中的前K个序号。
可选的,所述第一序列是预先存储的。
可选的,当所述母码长度N为4096时,所述信息比特的数量K为:452,536,904,1048,1808,2072,2712或3096;可选的,所述K可以在上述值的基础上浮动,例如,增加或者减少20,452为基础,述信息比特的数量K可以为432至472之间的整数:433,434,435,436,437,438,439,440,…,470,471,472,同样的,536为基础,所述信息比特的数量K可以为516至556之间的整数:516,517,…,555,556,3096为基础,所述信息比特的数量K可以为3076至3116之间的整数:3076,3077,…,3115,3116,其他K值同样适用。
或者当所述母码长度N为8192时,所述信息比特的数量K为:235,470,940,1880,2820或3760。可选的,所述K可以在上述值的基础上浮动,例如,增加或者减少20。235为基础,所述信息比特的数量K可以为215至255之间的整数:215,216,…,254,255;470为基础,所述信息比特的数量K可以为450至490之间的整数:450,451,…,489,490;940为基础,所述信息比特的数量K可以为920至960之间的整数:920,921,…,959,960,其他K值同样适用。
可选的,当所述母码长度为4096时,所述第一序列为说明书中的序列Q1;或者当所述母码长度为8192时,所述第一序列为说明书中的序列Q2。
可选的,所述N个极化信道的序号为0~(N-1)或1~N。
可选的,所述待编码比特中包括循环冗余校验CRC比特。
可选的,所述待编码比特中包括奇偶校验PC比特。
基于图4所示的Polar码编码方法的同一发明构思,如图6所示,本申请实施例中还提供一种Polar码编码装置600,该Polar码编码装置600用于执行图4所示的Polar码编码方法。图4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600包括:输入接口电路601,用于获取待编码比特;逻辑电路602,用于执行上述图4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603,用于输出编码后的比特序列。
进一步地,该编码装置600输出的编码后的比特序列经过调制器610调制后输出给收发器620,收发器620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630发送出去。容易理解,从产品集成的角度看,在某些条件允许的情况下,调制器610和收发器620可以是一个功能实现模块或实现单元,或者收发器620和天线660可以是一个功能实现模块或实现单元。可选的,上述系统还可以包括解调器611,用于对收发器获取的编码比特信息进行解调,图中未示出611,同样,调制器和解调器可以使用一个物理实体实现功能,例如所述610还可以是调制解调器,编码装置和译码装置也可以是同一个物理实体。
可选的,Polar码编码装置600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7所示,Polar码编码装置700包括:存储器701,用于存储程序;处理器702,用于执行存储器701存储的程序,当程序被执行时,使得Polar码编码装置700可以实现上述图4实施例提供的Polar码编码方法。
可选的,上述存储器701可以是物理上独立的单元,也可以如图7所示,存储器701与处理器702集成在一起。
可选的,当上述图4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700也可以只包括处理器702。用于存储程序的存储器701位于Polar码编码装置700之外,处理器702通过电路/电线与存储器701连接,用于读取并执行存储器701中存储的程序。
类似的,基于图5所示的Polar码译码方法的同一发明构思,如图8所示,本申请实施例中还提供一种Polar码译码装置800,该Polar码译码装置800用于执行图5所示的Polar码译码方法。图8所示的Polar码译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码译码装置800包括:输入接口电路801,用于获取待译码比特;逻辑电路802,用于执行上述图5所示的Polar码译码方法,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803,用于输出译码后的比特序列。
进一步地,该译码装置800还与解调器810和收发器820联接,收发器820还与天线830联接。天线接收到编码后的比特信息通过收发器进行相应处理传输给解调器,解调器810对经处理的编码后比特信息进行解调提供给译码装置进行下一步处理。容易理解,从产品集成的角度看,在某些条件允许的情况下,解调器810和收发器820可以是一个功能实现模块或实现单元,或者收发器820和天线830可以是一个功能实现模块或实现单元。
可选的,Polar码译码装置800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码译码方法中的部分或全部通过软件来实现时,如图9所示,Polar码译码装置900包括:存储器901,用于存储程序;处理器902,用于执行存储器901存储的程序,当程序被执行时,使得Polar码译码装置900可以实现上述图5实施例提供的Polar码译码方法。
可选的,上述存储器901可以是物理上独立的单元,也可以存储器901与处理器902集成在一起。
可选的,当上述图5实施例的译码方法中的部分或全部通过软件实现时,Polar码传输装置900也可以只包括处理器902。用于存储程序的存储器901位于Polar码译码装置900之外,处理器902通过电路/电线与存储器901连接,用于读取并执行存储器901中存储的程序。
上述处理器可以是中央处理器(central processing unit,CPU),网络处理器(network processor,NP)或者CPU和NP的组合。上述处理器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(programmable logic device,PLD)或其组合。上述PLD可以是复杂可编程逻辑器件(complex programmable logic device,CPLD),现场可编程逻辑门阵列(field-programmable gate array,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4所示的Polar码编码方法,如图10所示,本申请实施例还提供了一种Polar码编码装置1000,Polar码编码装置1000用于执行图4所示的Polar码编码方法,Polar码编码装置1000包括:
获取单元1001,用于获取K个待编码比特;
选择单元1002,用于从第一序列中选择K个序号,所述K个序号对应的极化信道放置所述待编码比特;
编码单元1003,用于对所述K个待编码比特进行Polar码编码,得到编码后的比特。
其中,所述第一序列中包括N个极化信道的序号,所述第一序列为说明书中的序列Q1或Q2所示的序列的全部或者子序列,所述K为正整数,N为Polar码的母码长度,N=2n,n为正整数,K≤N。
该Polar码编码装置1000的获取单元1001,选择单元1002和/或编码单元1003还用于执行图4所示的Polar码编码方法中的部分或全部方法,具体实现的功能可以参考前述的Polar码编码方法。
基于图5所示的Polar码译码方法,如图11所示,本申请实施例还提供了一种Polar码译码装置1100,Polar码译码装置1100用于执行图5所示的Polar码译码方法,Polar码译码装置1100包括:
接收单元1101,用于用于接收待译码的比特信息,所述待译码的比特信息包括K个信息比特的信息,所述K个信息比特承载在第一序列的K个序号对应的极化信道上,所述第一序列包括N个极化信道的序号,所述第一序列为说明书中的序列Q1或Q2所示的序列的全部或者子序列,所述K为正整数,N为Polar码的母码长度,N=2n,n为正整数,K≤N;
译码单元1102,用于根据待译码的比特信息进行Polar码译码,得到所述K个信息比特。
该Polar码译码装置1100的获取单元1101和/或译码单元1102还用于执行图5所示的Polar码译码方法中的部分或全部方法,具体实现的功能可以参考前述的Polar码译码方法。
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4所示的Polar码编码方法,或者执行图5所示的Polar码译码方法。
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4所示的Polar码编码方法,或者执行图5所示的Polar码译码方法。
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。
第一序列Q1通过均衡考虑待编码比特长度K为536,1048,2072,3096,452,904,1808,2712下码的性能得到,序列长度为4096,Q1=[0,1,2,4,8,16,3,32,5,6,9,64,10,17,12,18,128,33,20,34,7,24,36,65,11,256,66,40,13,19,68,14,129,48,21,72,130,35,22,25,512,132,37,80,26,38,257,67,136,41,28,258,96,69,42,15,144,49,260,70,44,73,131,50,23,1024,264,74,160,513,133,52,81,27,76,514,134,39,272,82,137,56,29,516,259,192,97,138,84,43,30,145,288,98,261,71,520,140,45,88,146,51,262,100,1025,46,265,75,2048,161,528,148,53,320,1026,266,104,77,162,515,135,54,273,83,152,57,1028,268,78,544,164,517,274,193,112,139,85,58,31,1032,518,384,289,194,99,276,168,86,521,141,60,89,147,290,576,263,196,101,522,142,1040,47,280,90,2049,176,529,149,292,102,321,1027,524,267,200,105,2050,92,163,530,150,55,322,1056,153,296,1029,106,269,79,640,545,2052,165,532,275,208,113,154,324,59,1030,270,108,546,1033,166,519,385,304,195,114,2056,277,169,87,536,156,61,1088,328,1034,548,386,291,224,577,278,197,170,116,523,143,1041,62,281,91,2064,177,1036,768,578,388,293,198,103,552,336,172,1042,525,282,201,120,2051,93,178,531,151,294,580,323,1152,1057,526,392,297,202,1044,107,284,2080,94,641,560,2053,180,533,209,352,1058,155,325,298,1031,584,271,204,109,642,547,2054,1048,167,534,400,305,210,115,2057,184,326,537,1060,157,300,1089,110,329,1035,644,549,387,2112,306,225,592,2058,279,212,171,117,538,158,1280,63,1090,330,1064,2065,550,416,1037,769,226,579,389,308,199,648,118,553,2060,337,173,1043,540,283,216,121,1092,2066,332,179,1038,770,608,390,295,228,581,554,338,1153,174,1072,527,393,312,203,1045,122,2176,285,2081,95,656,561,2068,181,1096,772,582,448,353,1154,1059,556,394,340,299,232,1046,585,286,205,2082,124,643,562,2055,1049,182,535,401,211,354,2072,1536,185,327,1156,776,1061,586,396,301,206,1104,111,672,344,2084,1050,645,564,402,2113,307,240,593,2059,213,186,356,539,1062,159,1281,302,1091,588,331,1160,1065,646,2304,551,417,2114,1052,784,227,594,404,2088,309,214,649,119,568,2061,188,1282,541,1120,217,360,1093,1066,2067,333,418,1039,771,704,609,391,2116,310,229,650,596,555,2062,339,1168,175,1073,542,408,313,218,1284,123,1094,2177,2096,334,657,1068,800,2069,610,420,1097,773,230,583,449,368,1155,652,1074,557,395,2120,341,314,233,1047,600,2178,287,220,2083,125,658,563,2070,1288,183,1098,774,612,450,355,1184,2073,1537,558,424,342,1157,777,234,1076,587,397,316,207,2560,1105,126,673,2180,345,2085,1051,660,565,403,2128,241,1100,832,2074,1538,452,187,357,1158,778,1063,616,398,1296,303,236,1106,589,674,346,1161,2086,1080,647,2305,566,432,2115,1053,785,242,2184,595,405,2089,215,664,358,569,2076,1540,189,1283,1216,780,1121,590,456,361,1162,1108,1067,676,2306,348,419,2144,1054,786,705,624,406,2117,2090,311,244,651,597,570,2063,1169,190,1312,543,409,1122,219,1285,362,1095,2192,1544,2097,335,1164,896,1069,801,706,2308,611,421,2118,1112,788,231,680,598,464,2092,369,1170,653,1075,572,410,2121,315,248,1286,601,1124,2179,221,2098,364,659,1070,802,2071,1289,422,1099,775,708,613,451,3072,370,1185,654,2312,1552,559,425,2122,343,1172,792,235,1077,602,412,2208,317,222,2561,1344,127,688,2181,2100,1290,661,1128,804,2129,614,480,1101,833,1186,2075,1539,453,426,372,1159,779,712,1078,617,399,2124,1297,318,237,2562,1107,604,675,2182,347,1176,2087,1081,662,2320,567,433,2130,1292,243,1102,2185,834,2104,1568,454,665,359,1188,808,2077,1541,618,428,1298,1217,781,238,1136,591,457,376,1163,2564,1109,1082,677,2307,2240,349,434,2145,1055,787,720,2186,625,407,2132,2091,245,666,836,571,2078,1542,1408,191,1313,1218,782,1123,620,458,1300,363,1192,1110,2193,1545,678,2336,350,1165,897,2146,1084,816,707,2309,626,436,2119,2568,1113,789,246,681,2188,599,465,2093,1171,668,1314,573,411,2136,1600,249,1287,1220,840,1125,2194,1546,460,2099,365,1166,898,1071,803,736,2310,1304,423,2148,1114,790,709,682,628,466,3073,2094,371,1200,655,2313,1553,574,440,2123,1173,793,250,1316,603,413,1126,2209,223,2576,1345,366,689,2196,1548,2101,1291,1224,900,1129,805,710,2368,615,481,3074,1116,848,1187,684,2314,1554,468,427,2152,373,1174,794,713,1079,632,414,2125,2210,319,252,2563,1346,605,690,2183,1177,2102,1320,663,2321,1130,806,2131,1293,482,1103,2200,835,1664,2105,1569,455,3076,904,374,1189,809,714,2316,1556,619,429,2126,1299,1232,796,239,2592,1137,606,472,2212,377,1178,2565,1348,1083,692,2322,2241,435,2160,1294,721,1132,2187,864,2133,2106,1570,484,667,837,1190,810,2079,1543,1409,430,1328,1219,783,716,1138,621,459,3080,1301,378,1193,2566,1111,2432,1560,679,2337,2242,351,1180,912,2147,1085,817,722,2324,2216,627,437,2134,2569,1352,247,696,2189,838,2108,1572,1410,669,1315,1248,812,2137,1601,622,488,1302,1221,841,1194,1140,2195,1547,461,2338,380,1167,899,2624,1086,818,737,2311,2244,1305,438,2149,2570,1115,791,724,683,2190,629,467,3088,2095,1201,670,2328,1792,575,441,2138,1602,1412,251,1317,1222,842,1127,2224,1576,462,2577,1360,367,1196,928,2197,1549,738,2340,1306,1225,901,2150,1144,820,711,2369,630,496,3075,2572,1117,849,1202,685,2315,2248,1555,469,442,2153,1175,795,728,1318,633,415,2140,1604,2211,253,2578,1347,844,691,2198,1550,1416,2103,1321,1226,902,1131,807,740,2370,1308,483,3104,1118,2201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519,3872,1886,2969,3682,3492,2779,3845,3302,2922,1972,3655,3521,2542,1782,3440,2895,3724,2001,1022,3629,3467,3413,3386,3305,2981,1947,3672,2791,1785,3359,3292,3024,3197,2929,3730,1996,3635,2549,1901,2970,3255,2875,2808,3846,2495,1959,3684,3522,2781,3427,2924,2002,3630,3496,1907,3414,3849,3306,2982,1527,1976,3659,3469,1786,3388,3279,3011,1949,3198,2930,3745,1759,3417,2550,1902,2985,2903,3732,2795,3637,3475,2972,3313,2877,2782,3904,2687,2553,2017,3524,3259,3429,3850,2004,1963,3688,3470,1909,3375,3308,3040,1950,3661,3746,1855,1788,3418,3013,2986,1531,2932,3719,3638,3504,2959,3857,3314,2878,2797,3667,3477,2554,2018,3287,2907,3736,3430,3641,2527,1991,3261,1910,2993,3852,2803,1965,3662,3528,1775,3433,3014,2008,2919,3748,1913,3420,3491,2988,1533,3858,3777,2798,1971,3696,3478,3017,3383,3316,2936,3723,3669,3642,2556,2020,2909,3262,2994,3615,3481,1966,3291,2967,3434,2805,1995,1914,3407,3968,2751,1534,3873,3778,1887,3683,3493,3018,3860,3303,2923,3752,1973,3670,3536,2543,1783,3441,2910,3725,1023,3644,3482,3387,3320,2996,3673,2806,2024,3293,3025,3436,3731,1997,3874,1916,2971,3494,2809,3847,3780,1974,3685,3523,3020,3442,2925,3726,2003,3631,3497,3415,3864,3307,2983,1977,3674,3484,1787,3389,3294,3026,3199,2931,3760,1998,2551,1903,3000,3733,2810,3876,2973,3686,3552,2783,3905,2926,2032,3525,3498,3444,3851,3784,2005,1978,3689,3471,3390,3309,3041,1951,3676,3747,1789,3419,3028,2987,2933,3734,3639,3505,2974,3315,2879,2812,3906,2555,2019,3526,3737,3431,3880,2006,3690,3500,1911,3853,3310,3042,1980,3663,3529,1790,3448,3015,2009,2934,3749,3421,3506,2989,3859,3792,2799,3697,3479,3032,3317,2937,3738,3908,3643,2557,2021,3263,2995,3854,1967,3692,3530,3435,3044,2010,3750,1915,3422,3969,2990,1535,3888,3779,3698,3508,3019,3861,3318,2938,3753,3671,3537,2558,2022,2911,3740,3645,3483,3321,2997,3912,2807,2025,3532,3437,3970,2012,3875,3808,1917,3495,3048,3862,3781,3754,1975,3700,3538,3021,3443,2940,3727,3646,3512,3865,3322,2998,3675,3485,2026,3295,3027,3438,3761,1999,1918,3001,3972,2811,3877,3782,3687,3553,3022,3920,2927,3756,2033,3540,3499,3445,3866,3785,1979,3704,3486,3391,3324,3056,3677,3762,2028,3029,3002,3735,3878,2975,3554,2813,3907,2034,3527,3976,3446,3881,3786,2007,3691,3501,3868,3311,3043,1981,3678,3544,1791,3449,3030,2935,3764,3507,3004,3793,2814,3936,3033,3556,3739,3909,3882,2036,3502,3855,3788,1982,3693,3531,3450,3045,2011,3751,3423,3984,2991,3889,3794,3699,3509,3034,3319,2939,3768,3910,2559,2023,3741,3884,3694,3560,3913,3046,2040,3533,3452,3971,2013,3890,3809,3510,3049,3863,3796,3755,3701,3539,3036,2941,3742,3647,3513,3323,2999,3914,2027,3534,3439,4000,2014,3810,1919,3973,3050,3892,3783,3702,3568,3023,3921,2942,3757,3541,3514,3867,3800,3705,3487,3325,3057,3916,3763,2029,3003,3974,3879,3812,3555,3052,3922,3758,2035,3542,3977,3447,3896,3787,3706,3516,3869,3326,3058,3679,3545,2030,3031,3765,3005,4032,2815,3937,3557,3978,3924,3883,3816,2037,3503,3870,3789,1983,3708,3546,3451,3060,3766,3985,3006,3795,3938,3035,3558,3769,3911,2038,3980,3885,3790,3695,3561,3928,3047,2041,3548,3453,3986,3891,3824,3511,3064,3797,3770,3940,3037,3743,3886,3562,3915,2042,3535,3454,4001,2015,3811,3988,3051,3893,3798,3703,3569,3038,2943,3772,3515,3801,3944,3564,3917,4002,2044,3975,3894,3813,3570,3053,3923,3759,3543,3992,3897,3802,3707,3517,3327,3059,3918,2031,4004,3814,4033,3054,3952,3572,3979,3925,3898,3817,3518,3871,3804,3709,3547,3061,3767,3007,4034,3939,3559,4008,3926,3818,2039,3981,3900,3791,3710,3576,3929,3062,3549,3987,3825,3065,4036,3771,3941,3982,3887,3820,3563,3930,2043,3550,3455,4016,3826,3989,3066,3799,3942,3039,3773,4040,3945,3565,3932,4003,2045,3990,3895,3828,3571,3068,3774,3993,3803,3946,3566,3919,2046,4005,3815,4048,3055,3953,3573,3994,3899,3832,3519,3805,3948,4006,4035,3954,3574,4009,3927,3819,3996,3901,3806,3711,3577,3063,4064,4037,4010,3956,3983,3902,3821,3578,3931,3551,4017,3827,3067,4038,3943,4012,3822,4041,3960,3580,3933,4018,3991,3829,3069,3775,4042,3947,3567,3934,2047,4020,3830,4049,3070,3995,3833,4044,3949,4007,4050,3955,3575,4024,3834,3997,3807,3950,4065,4052,4011,3957,3998,3903,3836,3579,4066,4039,3958,4013,3823,4056,3961,3581,4019,4068,4014,4043,3962,3582,3935,4021,3831,3071,4072,4045,3964,4022,4051,4025,3835,4046,3951,4080,4053,4026,3999,3837,4067,4054,3959,4028,3838,4057,4069,4015,4058,3963,3583,4070,4073,4060,3965,4023,4074,4047,3966,4081,4027,4076,4082,4055,4029,3839,4084,4030,4059,4071,4088,4061,4075,4062,3967,4077,4083,4078,4085,4031,4086,4089,4090,4063,4092,4079,4087,4091,4093,4094,4095,]。
第一序列Q2通过均衡考虑待编码比特长度K为235,470,940,1880,2820,3760下码的性能得到,序列长度为8192(出于篇幅以及实际使用考虑,当前Q2显示的实际序列的长度为3760,在母码长度为8192的情况下,该场景最大的信息比特数量为3760,所以只需要关注8192个序号中需要的3760个序号),Q2=[6309,5445,6419,5391,6298,6203,5667,5287,6414,5654,6252,5425,5330,5235,6310,6663,5446,5657,6339,5277,3623,6258,5420,4819,6421,5230,6313,6231,5449,3381,3721,6300,4935,6205,5669,5507,5004,5426,5345,4909,4814,3613,3289,5399,5332,5291,6692,5237,5658,6435,5278,3405,5010,5183,4915,6422,6341,6314,3681,6260,3463,6667,5450,4821,3382,3301,4794,3722,6287,4964,3668,3627,6206,5670,3411,4767,6425,3247,2979,5346,4910,3614,6235,3480,5699,5509,4586,3385,3290,5428,2966,5319,4939,5768,3195,5238,6321,5673,4559,7180,5457,4478,5293,3406,5025,6722,3729,6532,5660,4835,6437,6342,5403,2969,5336,5012,3682,6247,3492,6696,5241,2779,4917,4822,3845,6480,3302,2922,6316,4727,4593,3655,7186,3521,6669,5452,5299,3440,4796,2895,6426,3724,6345,4539,3629,6264,3467,5728,5510,3413,4825,3386,3305,5415,2981,5348,4968,1947,3672,6237,5701,2791,6322,5674,4588,3359,3292,6675,5458,4941,5294,3197,5026,2929,3730,6295,5647,5513,3635,6438,2549,1901,5432,2970,5323,4999,6724,3255,2875,5242,4918,4837,3846,6467,5405,2495,1959,4594,3684,7201,3522,6670,5215,2781,6536,4947,5776,3427,4783,2924,6441,6346,5681,2002,4567,7188,5016,3630,6251,3496,1907,5301,3414,4921,4826,3849,6428,3306,5892,2982,1527,4731,1976,4541,3659,6238,3469,5702,6785,5568,1786,4351,3388,3279,6704,5473,3011,4942,1949,3198,2930,3745,6324,5676,1759,5514,3417,6677,5460,2550,1902,5419,2985,5352,5028,2903,3732,6353,5705,2795,4838,3637,6496,3475,5406,2972,5325,5057,7202,3313,2877,5244,2782,6299,4976,5763,6469,2687,6442,2553,5682,2017,4596,7175,3524,5003,6728,3259,4949,5302,3429,4922,4841,3850,6415,6348,5655,2004,5521,1963,4542,3688,6253,3470,1909,6786,5331,4895,4828,3375,3308,6691,5474,3040,4733,1950,4571,3661,7192,3746,6311,1855,1788,5305,3418,6678,5447,3013,6544,5896,2986,1531,4791,2932,6449,3719,6354,5706,5516,3638,6259,3504,5421,2959,5326,5058,3857,3314,2878,5231,2797,6328,4963,5792,3667,6470,3477,6681,5464,2554,2018,4583,7204,3287,5032,2907,3736,6301,4950,5765,3430,4842,3641,6444,2527,5684,1991,5522,7233,5005,6254,3261,1910,5427,2993,5360,4924,4815,3852,6473,5713,2803,4734,1965,4600,3662,7179,3528,6788,5333,4953,1775,5306,3433,6693,5476,3014,6531,5659,2008,4573,2919,6450,3748,6369,1913,5279,3420,5011,6736,3491,5422,2988,1533,4849,3858,6423,3777,6356,5708,2798,6315,1971,3696,6261,3478,6682,5451,3017,5060,3383,3316,4795,2936,3723,6302,4965,5766,3669,3642,6207,2556,5671,2020,5537,7234,5006,2909,3262,5904,2994,5347,4911,4844,3615,6474,3481,5714,5524,1966,4587,7208,3291,5429,2967,5334,4954,5769,3434,6694,5239,2805,6560,5688,1995,4574,7181,6913,6370,1914,4479,5308,3407,5040,6723,3968,6533,5661,2751,1534,4850,3873,6452,3778,6343,1887,6792,5337,5013,3683,6262,3493,6697,5480,3018,4823,3860,6481,3303,2923,3752,6317,4966,1973,3670,7187,3536,6684,5453,2543,1783,5538,3441,4797,2910,6427,3725,6360,5891,5824,1023,3644,6265,3482,5729,5511,7236,5064,3387,3320,5430,2996,5349,4969,5770,3673,6476,5716,2806,6323,5675,2024,4589,7182,3293,6914,5459,3025,4956,5295,3436,5027,6752,3731,6534,5662,1997,5528,3874,6439,6372,1916,5433,2971,5338,5014,6725,3494,6698,5243,2809,4919,4852,3847,6482,3780,7297,6318,1974,4595,3685,7216,3523,6671,5454,3020,6537,5777,3442,4798,2925,6456,3726,6347,5920,2003,7189,5017,3631,6266,3497,5730,5540,3415,4827,3864,6429,3307,5893,2983,5350,4970,1977,3674,6239,3484,5703,6800,5569,1787,4590,3389,3294,6705,5488,3026,4943,5772,3199,2931,3760,6325,5677,1998,5515,7240,6916,5461,2551,1903,5434,3000,5353,5029,6726,3733,6592,5720,2810,4839,3876,6497,7298,5407,2973,5340,5072,3686,7203,3552,6700,5245,2783,6538,4977,5778,3905,6484,2926,6443,6376,5683,2032,4597,7190,3525,5018,6729,3498,5303,3444,4923,4856,3851,6430,3784,6349,5894,2005,1978,4543,3689,6268,3471,5732,6787,5570,4829,3390,3309,6706,5475,3041,4972,1951,3676,7193,3747,6326,5678,1789,5544,3419,6679,5462,3028,6545,5897,2987,5354,5030,2933,3734,6355,5707,5517,3639,6498,3505,5436,2974,5327,5059,3315,2879,5246,2812,6329,4978,5793,3906,6471,7300,6920,5465,2555,2019,4598,7205,3526,5033,6730,3737,6540,4951,5780,3431,4843,3880,6350,5685,2006,5523,7248,5020,3690,6255,3500,1911,6816,5361,4925,4830,3853,6488,3310,5952,3042,4735,1980,4601,3663,7194,3529,6789,5572,1790,5307,3448,6708,5477,3015,6546,5898,2009,2934,3749,6384,5736,5518,3421,3506,5423,2989,5356,5088,3859,3792,2799,5794,3697,6500,3479,5466,3032,5061,3317,5034,2937,3738,4980,3908,7425,3643,2557,2021,5552,5007,3263,5905,2995,5362,4926,4845,3854,7304,1967,4602,3692,3530,5335,4955,5784,3435,3044,2010,4575,6928,3750,1915,5309,3422,5041,3969,5900,2990,1535,4851,3888,3779,5576,3698,3508,3019,5062,3318,2938,4967,7426,3537,2558,2022,7264,5036,2911,3740,4846,3645,3483,5744,3321,2997,4984,3912,2807,2025,4604,3532,6848,3437,3970,2012,3808,1917,3048,7312,1975,3021,6016,2940,7428,3512,2998,2026,6944,1918,3972,3920,3056,7681,6445,6451,6737,6357,5709,6330,6683,7206,6303,5767,6446,5686,7235,6732,6475,5715,5525,7209,6790,6695,5478,6561,5689,7196,6371,6738,6548,6453,6358,5710,6793,6263,6712,5481,3861,3753,6332,5796,3671,6685,5468,5539,6361,5906,5825,6504,5526,7237,5065,7210,5431,5364,5771,6477,5717,6562,5690,7183,6915,4957,5310,5042,6753,6535,5663,5529,3875,6454,6373,6794,5339,5015,6740,3495,6699,5482,4853,3862,6483,3781,3754,6319,3700,7217,3538,6686,5455,6552,3443,4799,6457,3727,6362,5921,5826,3646,6267,5731,5541,7238,5066,3865,3322,5908,5351,4971,5800,3675,6478,3485,5718,6801,5584,4591,7212,3295,5489,3027,4958,5773,3438,6754,3761,6564,5692,1999,5530,7241,6917,6374,5435,3001,5368,5044,6727,6593,5721,2811,4854,3877,6512,3782,7299,6796,5341,5073,3687,7218,3553,6701,5484,3022,6539,5779,6485,2927,6458,3756,6377,5922,2033,7191,3540,5019,6744,3499,5542,3445,4857,3866,6431,3785,6364,5895,5828,1979,3704,6269,3486,5733,6802,5571,5068,3391,3324,6707,5490,4973,5774,3677,7432,3762,6327,5679,2028,5545,7242,6918,5463,3029,5912,3002,5355,5031,6756,3735,6594,5722,5532,3878,6499,7328,5437,2975,5342,5074,3554,6702,5247,2813,6568,4979,5808,3907,6486,7301,6921,6378,2034,4599,7220,3527,5048,6731,3976,6541,5781,3446,4858,3881,6460,3786,6351,5924,2007,7249,5021,3691,6270,3501,5734,6817,5600,4831,3868,6489,3311,5953,3043,4974,1981,3678,7195,3544,6804,5573,1791,5546,3449,6709,5492,3030,6547,5899,5832,2935,3764,6385,5737,5519,7244,6976,3507,5438,3004,5357,5089,7682,3793,6596,5724,2814,6331,5795,3936,6501,7302,6922,5467,3033,5076,7207,3556,5035,6760,3739,6542,4981,5782,3909,7440,3882,6447,6380,5687,2036,5553,7250,5022,6733,3502,6818,5363,4927,4860,3855,6490,3788,7305,5954,1982,4603,3693,7224,3531,6791,5574,5785,3450,6710,5479,3045,6576,5928,2011,7197,6929,3751,6386,5738,5548,3423,6739,3984,6549,5901,2991,5358,5090,3889,3794,6359,5711,6808,5577,3699,6502,3509,6713,5496,3034,5063,7684,3319,2939,3768,6333,4982,5797,3910,7427,7360,6924,5469,2559,2023,5554,7265,5037,6734,3741,6600,5907,5840,4847,3884,6505,7306,5745,5527,7252,5080,3694,7211,3560,6820,5365,4985,5786,3913,6492,5956,3046,6563,5691,2040,4605,7198,3533,6930,6849,5311,3452,5043,6768,3971,6550,5902,2013,3890,6455,3809,6388,5740,6795,5578,6741,3510,6714,5483,3049,5092,3863,3796,7313,3755,6334,5798,3701,7456,3539,6687,5470,3036,6553,6017,7266,5038,2941,3742,6363,5936,5827,7429,3647,6506,3513,5746,5556,7239,5067,7688,3323,5909,2999,5366,4986,5801,3914,6479,7308,5719,7040,5585,2027,4606,7213,3534,6945,6850,4959,5788,3439,6755,4000,6565,5693,2014,5531,7256,6932,3810,6375,1919,6824,5369,5045,6742,3973,6608,5960,3050,4855,3892,6513,3783,7314,6797,5580,3702,7219,3568,6716,5485,3023,6554,6018,3921,2942,6459,3757,6392,5923,5856,7430,3541,6745,3514,5543,7268,5096,3867,3800,6365,5910,5829,5802,3705,6508,3487,5748,6803,5586,5069,7214,3325,6946,5491,3057,4988,5775,3916,7433,3763,6566,5694,2029,5560,7243,6919,6852,5913,3003,5370,5046,6757,3974,6595,5723,5533,3879,6514,3812,7329,6798,5343,5075,7696,3555,6703,5486,3052,6569,5809,3922,6487,7316,6936,3758,6379,2035,7221,3542,5049,6746,3977,6556,6020,3447,4859,3896,6461,3787,6366,5925,5830,7488,3706,6271,3516,5735,6832,5601,5070,3869,3326,5968,3058,4975,5804,3679,7434,3545,6805,5588,2030,5547,7272,6948,5493,3031,5914,5833,6758,3765,6624,5752,5534,7245,6977,7330,5439,3005,5372,5104,7683,4032,6597,5725,2815,6570,5810,3937,6516,7303,6923,6856,5077,7222,3557,5050,6761,3978,6543,5783,3924,7441,3883,6462,3816,6381,5926,2037,7251,5023,6748,3503,6819,5602,4861,3870,6491,3789,7320,5955,1983,3708,7225,3546,6806,5575,6024,3451,6711,5494,3060,6577,5929,5834,7436,3766,6387,5739,5549,7246,6978,3985,5916,3006,5359,5091,7712,3795,6598,5726,6809,5592,3938,6503,7332,6952,5497,3035,5078,7685,3558,6762,3769,6572,4983,5812,3911,7442,7361,6925,6382,2038,5555,7280,5052,6735,3980,6601,5841,4862,3885,6520,3790,7307,5984,7253,5081,3695,7226,3561,6821,5604,5787,3928,6493,5957,3047,6578,5930,2041,7199,3548,6931,6864,5550,3453,6769,3986,6551,5903,5836,3891,3824,6389,5741,6810,5579,6980,3511,6715,5498,3064,5093,7686,3797,7552,3770,6335,5799,3940,7457,7362,6926,5471,3037,6032,7267,5039,6764,3743,6602,5937,5842,7444,3886,6507,7336,5747,5557,7254,5082,7689,3562,6822,5367,4987,5816,3915,6494,7309,5958,7041,2042,4607,7228,3535,6960,6851,5789,3454,6770,4001,6580,5932,2015,7257,6933,3811,6390,5742,6825,5608,6743,3988,6609,5961,3051,5094,3893,3798,7315,6812,5581,3703,7458,3569,6717,5500,3038,6555,6019,7744,2943,3772,6393,5938,5857,7431,7364,6984,3515,5558,7269,5097,7690,3801,6604,5911,5844,5803,3944,6509,7310,5749,7042,5587,5084,7215,3564,6947,6880,4989,5790,3917,7448,4002,6567,5695,2044,5561,7258,6934,6853,6826,5371,5047,6772,3975,6610,5962,3894,6515,3813,7344,6799,5582,7697,3570,6718,5487,3053,6584,6048,3923,7317,6937,3759,6394,5858,7460,3543,6747,3992,6557,6021,7270,5098,3897,3802,6367,5940,5831,7489,3707,6510,3517,5750,6833,5616,5071,7692,3327,5969,3059,4990,5805,3918,7435,7368,7044,5589,2031,5562,7273,6949,6854,5915,5848,6759,4004,6625,5753,5535,7260,6992,3814,7331,6828,5373,5105,7698,4033,6612,5964,3054,6571,5811,3952,6517,7318,6938,6857,7223,3572,5051,6776,3979,6558,6022,3925,3898,6463,3817,6396,5927,5860,7490,6749,3518,6834,5603,5100,3871,3804,7321,5970,5806,3709,7464,3547,6807,5590,6025,7274,6950,5495,3061,5944,5835,7437,3767,6626,5754,5564,7247,6979,7808,5917,3007,5374,5106,7713,4034,6599,5727,7048,5593,3939,6518,7333,6953,6858,5079,7700,3559,6763,4008,6573,5813,3926,7443,7376,6940,3818,6383,2039,7281,5053,6750,3981,6616,6080,4863,3900,6521,3791,7322,5985,7492,3710,7227,3576,6836,5605,6026,3929,5972,3062,6579,5931,5864,7438,3549,6865,5551,7276,7008,3987,5918,5837,7714,3825,6628,5756,6811,5594,6981,7334,6954,5499,3065,5108,7687,4036,7553,3771,6574,5814,3941,7472,7363,6927,6860,6033,7282,5054,6765,3982,6603,5843,7445,3887,6522,3820,7337,5986,7255,5083,7704,3563,6823,5606,5817,3930,6495,7324,5959,7056,2043,7229,3550,6961,6866,6028,3455,6771,4016,6581,5933,5838,7496,3826,6391,5743,6840,5609,6982,3989,5976,3066,5095,7716,3799,7554,6813,5596,3942,7459,7392,6956,5501,3039,6034,7745,6766,3773,6632,5939,5872,7446,7365,6985,7338,5559,7284,5112,7691,4040,6605,5845,5818,3945,6524,7311,5988,7043,5085,7230,3565,6962,6881,5791,3932,7449,4003,6582,5934,2045,7259,6935,6868,6827,5610,6773,3990,6611,5963,3895,3828,7345,6814,5583,7936,3571,6719,5502,3068,6585,6049,7746,7556,3774,6395,5859,7461,7366,6986,3993,6036,7271,5099,7720,3803,6606,5941,5846,7504,3946,6511,7340,5751,7072,5617,5086,7693,3566,6882,4991,5820,3919,7450,7369,7045,2046,5563,7288,6964,6855,5849,6774,4005,6640,5992,7261,6993,3815,7346,6829,5612,7699,4048,6613,5965,3055,6586,6050,3953,7319,6939,6872,7462,3573,6777,3994,6559,6023,7748,3899,3832,6397,5942,5861,7491,6988,3519,6835,5618,5101,7694,3805,7560,5971,5807,3948,7465,7370,7046,5591,6040,7275,6951,6884,5945,5850,7452,4006,6627,5755,5565,7262,6994,7809,6830,5375,5107,7728,4035,6614,5966,7049,3954,6519,7348,6968,6859,7701,3574,6778,4009,6588,6052,3927,7377,6941,3819,6398,5862,7520,6751,3996,6617,6081,5102,3901,3806,7323,6000,7493,3711,7466,3577,6837,5620,6027,7752,5973,3063,5946,5865,7439,7372,7104,5566,7277,7009,7810,5919,5852,7715,4064,6629,5757,7050,5595,6996,7335,6955,6888,5109,7702,4037,7568,4010,6575,5815,3956,7473,7378,6942,6861,7283,5055,6780,3983,6618,6082,3902,6523,3821,7352,5987,7494,7705,3578,6838,5607,6056,3931,7325,5974,7057,5866,7468,3551,6867,6029,7278,7010,4017,5948,5839,7497,3827,6630,5758,6841,5624,6983,7812,5977,3067,5110,7717,4038,7555,7052,5597,3943,7474,7393,6957,6862,6035,7760,6767,4012,6633,5873,7447,7380,7000,3822,7339,7285,5113,7706,4041,6620,6084,5819,3960,6525,7326,5989,7058,7231,3580,6963,6896,6030,3933,4018,6583,5935,5868,7498,6869,6842,5611,7012,3991,5978,7718,3829,7584,6815,5598,7937,7394,6958,5503,3069,6064,7747,7557,3775,6634,5874,7476,7367,6987,7816,6037,7286,5114,7721,4042,6607,5847,7505,3947,6526,7341,5990,7073,5087,7708,3567,6883,5821,3934,7451,7384,7060,2047,7289,6965,6870,6088,6775,4020,6641,5993,7500,3830,7347,6844,5613,7938,4049,5980,3070,6587,6051,7776,7558,6873,7463,7396,7016,3995,6038,7749,7722,3833,6636,5943,5876,7506,6989,7342,7074,5619,5116,7695,4044,7561,5822,3949,7480,7371,7047,6041,7290,6966,6885,5851,7453,4007,6642,5994,7263,6995,7824,6831,5614,7729,4050,6615,5967,7064,3955,7349,6969,6874,7940,3575,6779,4024,6589,6053,7750,7616,3834,6399,5863,7521,6990,3997,6096,5103,7724,3807,7562,6001,7508,3950,7467,7400,7076,5621,6042,7753,6886,5947,5880,7454,7373,7105,5567,7292,7024,7811,5853,7730,4065,6644,5996,7051,6997,7350,6970,6889,7703,4052,7569,4011,6590,6054,3957,7379,6943,6876,7522,6781,3998,6619,6083,3903,3836,7353,6002,7495,7944,3579,6839,5622,6057,7754,7564,5975,5867,7469,7374,7106,6044,7279,7011,7840,5949,5854,7512,4066,6631,5759,7080,5625,6998,7813,6890,5111,7732,4039,7570,7053,3958,7475,7408,6972,6863,7761,6782,4013,6648,6112,7381,7001,3823,7354,7524,7707,4056,6621,6085,6058,3961,7327,6004,7059,7470,3581,6897,6031,7756,4019,5950,5869,7499,7108,6843,5626,7013,7814,5979,7719,4068,7585,7054,5599,7952,7395,6959,6892,6065,7762,7572,4014,6635,5875,7477,7382,7002,7817,7287,5115,7736,4043,6622,6086,3962,6527,7356,5991,7088,7709,3582,6898,6060,3935,7385,7061,5870,7528,6871,6089,7014,4021,6008,7501,3831,7586,6845,5628,7939,7872,5981,3071,6066,7777,7559,7112,7478,7397,7017,7818,6039,7764,7723,4072,6637,5877,7507,7004,7343,7075,5117,7710,4045,7576,5823,3964,7481,7386,7062,7291,6967,6900,6090,4022,6643,5995,7502,7825,6846,5615,7968,4051,5982,7065,7778,7588,6875,7941,7398,7018,4025,6068,7751,7617,3835,6638,5878,7536,6991,7820,6097,5118,7725,4046,7563,7509,3951,7482,7401,7077,6043,7768,6887,5881,7455,7388,7120,7293,7025,7826,6092,7731,4080,6645,5997,7066,7351,6971,6904,7942,4053,4026,6591,6055,7780,7618,6877,7523,7020,3999,6098,7726,3837,7592,6003,7510,7945,7402,7078,5623,6072,7755,7565,5882,7484,7375,7107,6045,7294,7026,7841,5855,7513,4067,6646,5998,7081,6999,7828,6891,7733,4054,7571,7068,3959,7409,6973,6878,8000,6783,4028,6649,6113,7620,3838,7355,7525,7946,4057,6100,6059,7784,7566,6005,7471,7404,7136,6046,7757,7842,5951,5884,7514,7109,7082,5627,7028,7815,7734,4069,7600,7055,7953,7410,6974,6893,7763,7573,4015,6650,6114,7383,7003,7832,7526,7737,4058,6623,6087,3963,7357,6006,7089,7948,3583,6899,6061,7758,7624,5871,7529,7110,6104,7015,7844,6009,7516,4070,7587,7084,5629,7954,7873,6894,6067,7792,7574,7113,7479,7412,7032,7819,7765,7738,4073,6652,6116,7005,7358,7090,7711,4060,7577,6062,3965,7387,7063,7530,6901,6091,4023,6010,7503,8064,6847,5630,7969,7874,5983,7779,7589,7114,7956,7399,7019,7848,6069,7766,7632,4074,6639,5879,7537,7006,7821,5119,7740,4047,7578,3966,7483,7416,7092,7769,6902,6120,7389,7121,7532,7827,6093,7970,4081,6012,7067,7590,6905,7943,7876,4027,6070,7781,7619,7116,7538,7021,7822,6099,7727,4076,7593,7511,7960,7403,7079,6073,7770,7580,5883,7485,7390,7122,7295,7027,7856,6094,4082,6647,5999,7096,7829,6906,7972,4055,7069,7782,7648,6879,8001,7022,4029,6128,7621,3839,7594,7540,7947,7880,6101,6074,7785,7567,7486,7405,7137,6047,7772,7843,5885,7515,7124,7083,7029,7830,7735,4084,7601,7070,7411,6975,6908,8002,4030,6651,6115,7622,7833,7527,7976,4059,6102,7786,7596,6007,7949,7406,7138,6076,7759,7625,5886,7544,7111,6105,7030,7845,7517,4071,7602,7085,7955,7888,6895,7793,7575,7128,7413,7033,7834,8004,7739,4088,6653,6117,7359,7091,7950,4061,6063,7788,7626,7531,7140,6106,7846,6011,7518,8065,7086,5631,7984,7875,7794,7604,7115,7957,7414,7034,7849,7767,7633,4075,6654,6118,7007,7836,7741,4062,7579,3967,7417,7093,8008,6903,6121,7628,7533,8066,6108,7971,7904,6013,7591,7144,7958,7877,7850,6071,7796,7634,7117,7539,7036,7823,7742,4077,7608,7961,7418,7094,7771,7581,6122,7391,7123,7534,7857,6095,4083,6014,7097,8068,6907,7973,7878,7783,7649,7118,8016,7023,7852,6129,7636,4078,7595,7541,7962,7881,6075,7800,7582,7487,7420,7152,7773,7858,6124,7125,7098,7831,7974,4085,7071,7650,6909,8003,4031,6130,7623,8072,7542,7977,7882,6103,7787,7597,7964,7407,7139,6077,7774,7640,5887,7545,7126,7031,7860,4086,7603,7100,7889,6910,8032,7129,7652,7835,8005,7978,4089,6132,7598,7951,7884,6078,7789,7627,7546,7141,6107,7847,7519,8080,7087,7985,7890,7795,7605,7130,7415,7035,7864,8006,4090,6655,6119,7837,7980,4063,7790,7656,8009,7142,6136,7629,7548,8067,6109,7986,7905,7606,7145,7959,7892,7851,7797,7635,7132,7037,7838,7743,4092,7609,7419,7095,8010,6123,7630,7535,8096,6110,7906,6015,8069,7146,7988,7879,7798,7664,7119,8017,7038,7853,7637,4079,7610,7963,7896,7801,7583,7421,7153,8012,7859,6125,7099,8070,7975,7908,7651,7148,8018,7854,6131,7638,8073,7543,7992,7883,7802,7612,7965,7422,7154,7775,7641,6126,7127,7861,4087,7101,8128,6911,8033,7653,8074,8020,7979,7912,6133,7599,7966,7885,6079,7804,7642,7547,7156,7862,8081,7102,7891,8034,7131,7654,7865,8007,4091,6134,8076,7981,7886,7791,7657,8024,7143,6137,7644,7549,8082,7987,7920,7607,7160,7893,7866,8036,7133,7839,7982,4093,7658,8011,6138,7631,7550,8097,6111,7907,8084,7147,7989,7894,7799,7665,7134,7039,7868,4094,7611,7897,8040,7660,8013,8098,6140,8071,7990,7909,7666,7149,8019,7855,7639,8088,7993,7898,7803,7613,7423,7155,8014,6127,8100,7910,8129,7150,8048,7668,8075,8021,7994,7913,7614,7967,7900,7805,7643,7157,7863,7103,8130,8035,7655,8104,8022,7914,6135,8077,7996,7887,7806,7672,8025,7158,7645,8083,7921,7161,8132,7867,8037,8078,7983,7916,7659,8026,6139,7646,7551,8112,7922,8085,7162,7895,8038,7135,7869,4095,8136,8041,7661,8028,8099,6141,8086,7991,7924,7667,7164,7870,8089,7899,8042,7662,8015,6142,8101,7911,8144,7151,8049,7669,8090,7995,7928,7615,7901,8044,8102,8131,8050,7670,8105,8023,7915,8092,7997,7902,7807,7673,7159,8160,8133,8106,8052,8079,7998,7917,7674,8027,7647,8113,7923,7163,8134,8039,8108,7918,8137,8056,7676,8029,8114,8087,7925,7165,7871,8138,8043,7663,8030,6143,8116,7926,8145,7166,8091,7929,8140,8045,8103,8146,8051,7671,8120,7930,8093,7903,8046,8161,8148,8107,8053,8094,7999,7932,7675,8162,8135,8054,8109,7919,8152,8057,7677,8115,8164,8110,8139,8058,7678,8031,8117,7927,7167,8168,8141,8060,8118,8147,8121,7931,8142,8047,8176,8149,8122,8095,7933,8163,8150,8055,8124,7934,8153,8165,8111,8154,8059,7679,8166,8169,8156,8061,8119,8170,8143,8062,8177,8123,8172,8178,8151,8125,7935,8180,8126,8155,8167,8184,8157,8171,8158,8063,8173,8179,8174,8181,8127,8182,8185,8186,8159,8188,8175,8183,8187,8189,8190,8191,]。
缩短位置集合,S1=[15,31,47,63,79,95,111,127,143,159,175,191,207,223,239,255,271,287,303,319,335,351,367,383,399,415,431,447,463,479,495,511,527,543,559,575,591,607,623,639,655,671,687,703,719,735,751,767,783,799,815,831,847,863,879,895,911,927,943,959,975,991,1007,1023,1039,1055,1071,1087,1103,1119,1135,1151,1167,1183,1199,1215,1231,1247,1263,1279,1295,1311,1327,1343,1359,1375,1391,1407,1423,1439,1455,1471,1487,1503,1519,1535,1551,1567,1583,1599,1615,1631,1647,1663,1679,1695,1711,1727,1743,1759,1775,1791,1807,1823,1839,1855,1871,1887,1903,1919,1935,1951,1967,1983,1999,2015,2031,2047,2063,2079,2095,2111,2127,2143,2159,2175,2191,2207,2223,2239,2255,2271,2287,2303,2319,2335,2351,2367,2383,2399,2415,2431,2447,2463,2479,2495,2511,2527,2543,2559,2575,2591,2607,2623,2639,2655,2671,2687,2703,2719,2735,2751,2767,2783,2799,2815,2831,2847,2863,2879,2895,2911,2927,2943,2959,2975,2991,3007,3023,3039,3055,3071,3087,3103,3119,3135,3151,3167,3183,3199,3215,3231,3247,3263,3279,3295,3311,3327,3343,3359,3375,3391,3407,3423,3439,3455,3471,3487,3503,3519,3535,3551,3567,3583,3599,3615,3631,3647,3663,3679,3695,3711,3727,3743,3759,3775,3791,3807,3823,3839,3855,3871,3887,3903,3919,3935,3951,3967,3983,3999,4015,4031,4047,4063,4079,4095]。
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Polar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。
Claims (26)
1.一种极化Polar码编码方法,其特征在于,包括:
获取K个待编码比特;
从第一序列中选择K个序号,所述K个序号对应的极化信道放置所述待编码比特,并对所述K个待编码比特进行Polar码编码,得到编码后的比特,其中,所述第一序列中包括N个极化信道的序号,所述第一序列为说明书中的序列Q1或Q2所示的序列的全部或者子序列,所述K为正整数,N为Polar码的母码长度,N=2n,n为正整数,K≤N。
2.根据权利要求1所述的方法,其特征在于,所述方法还包括:
对所述Polar码编码后的比特进行速率匹配,得到速率匹配后的比特。
3.根据权利要求1或2所述的方法,其特征在于,所述第一序列是预先存储的。
4.根据权利要求1-3中任一权利要求所述的方法,其特征在于,
当所述母码长度N为4096时,所述待编码比特的数量K为:452,536,904,1048,1808,2072,2712或3096;或者
当所述母码长度N为8192时,所述待编码比特的数量K为:235,470,940,1880,2820或3760。
5.根据权利要求1-4中任一权利要求所述的方法,其特征在于,
当所述母码长度为4096时,所述第一序列为说明书中的序列Q1;或者
当所述母码长度为8192时,所述第一序列为说明书中的序列Q2。
6.根据权利要求1-5中任一权利要求所述的方法,所述N个极化信道的序号为0~(N-1)或1~N。
7.根据权利要求1-6中任一权利要求所述的方法,所述待编码比特中包括循环冗余校验CRC比特。
8.根据权利要求1-7中任一权利要求所述的方法,所述待编码比特中包括奇偶校验PC比特。
9.一种极化Polar码译码方法,其特征在于,包括:
接收待译码的比特信息,所述待译码的比特信息包括K个信息比特的信息,所述K个信息比特承载在第一序列的K个序号对应的极化信道上,所述第一序列包括N个极化信道的序号,所述第一序列为说明书中的序列Q1或Q2所示的序列的全部或者子序列,所述K为正整数,N为Polar码的母码长度,N=2n,n为正整数,K≤N;
根据待译码的比特信息进行Polar码译码,得到所述K个信息比特。
10.如权利要求11所述的方法,其特征在于,
所述选择的K个序号对应的极化信道可靠度高于所述第一序列中剩余的(N-K)个序号对应的极化信道的可靠度。
11.根据权利要求9或10所述的方法,其特征在于,所述第一序列是预先存储的。
12.根据权利要求9-11中任一权利要求所述的方法,其特征在于,
当所述母码长度N为4096时,所述信息比特的数量K为:452,536,904,1048,1808,2072,2712或3096;或者
当所述母码长度N为8192时,所述信息比特的数量K为:235,470,940,1880,2820或3760。
13.根据权利要求9-12中任一权利要求所述的方法,其特征在于,
当所述母码长度为4096时,所述第一序列为说明书中的序列Q1;或者
当所述母码长度为8192时,所述第一序列为说明书中的序列Q2。
14.根据权利要求9-13中任一权利要求所述的方法,所述N个极化信道的序号为0~(N-1)或1~N。
15.根据权利要求9-14中任一权利要求所述的方法,所述待编码比特中包括循环冗余校验CRC比特。
16.根据权利要求9-15中任一权利要求所述的方法,所述待编码比特中包括奇偶校验PC比特。
17.一种极化Polar码编码装置,其特征在于,包括:
获取单元,用于获取K个待编码比特;
选择单元,用于从第一序列中选择K个序号,所述K个序号对应的极化信道放置所述待编码比特;
编码单元,用于对所述K个待编码比特进行Polar码编码,得到编码后的比特;
其中,所述第一序列中包括N个极化信道的序号,所述第一序列为说明书中的序列Q1或Q2所示的序列的全部或者子序列,所述K为正整数,N为Polar码的母码长度,N=2n,n为正整数,K≤N。
18.如权利要求17所述的装置,其特征在于,所述装置还包括:速率匹配单元,用于对所述Polar码编码后的比特进行速率匹配,得到速率匹配后的比特。
19.根据权利要求17或18所述的装置,其特征在于,所述第一序列是预先存储的。
20.根据权利要求17-19中任一权利要求所述的装置,其特征在于,
当所述母码长度N为4096时,所述待编码比特的数量K为:452,536,904,1048,1808,2072,2712或3096;或者
当所述母码长度N为8192时,所述待编码比特的数量K为:235,470,940,1880,2820或3760。
21.根据权利要求17-20中任一权利要求所述的装置,其特征在于,
当所述母码长度为4096时,所述第一序列为说明书中的序列Q1;或者
当所述母码长度为8192时,所述第一序列为说明书中的序列Q2。
22.根据权利要求17-21中任一权利要求所述的装置,其特征在于,所述N个极化信道的序号为0~(N-1)或1~N。
23.根据权利要求17-22中任一权利要求所述的装置,其特征在于,所述待编码比特中包括循环冗余校验CRC比特。
24.根据权利要求17-23中任一权利要求所述的装置,其特征在于,所述待编码比特中包括奇偶校验PC比特。
25.一种极化Polar码处理装置,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1-8任一项所述的方法,或者执行如权利要求9-16任一项所述的方法。
26.如权利要求25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。
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