吳 一，劉宏展，郝 源，劉麗媛

無線光通信中噴泉碼的發(fā)展現(xiàn)狀與展望

吳 一，劉宏展*，郝 源，劉麗媛

華南師范大學(xué)信息光電子科技學(xué)院，廣東省微納光子功能材料與器件重點(diǎn)實(shí)驗(yàn)室，廣東 廣州 510006

無線光通信信道復(fù)雜多變，噴泉碼作為一種新興的無速率編碼無需信道的先驗(yàn)信息即可實(shí)現(xiàn)不同信道環(huán)境下的自適應(yīng)傳輸，與傳統(tǒng)編碼相比更能提升無線傳輸?shù)馁|(zhì)量。本文首先總結(jié)了噴泉碼應(yīng)用于無線光通信的優(yōu)勢(shì)以及國(guó)內(nèi)外噴泉碼的發(fā)展現(xiàn)狀，然后深入研究了兩類噴泉碼編碼方案的設(shè)計(jì)以及對(duì)噴泉碼性能影響重大的度分布函數(shù)的設(shè)計(jì)，總結(jié)了一種噴泉碼即(LT)碼的譯碼方法以及近些年不斷提出優(yōu)化的方案，同時(shí)指出了噴泉碼設(shè)計(jì)中亟需解決的關(guān)鍵難點(diǎn)，最后提出了噴泉碼應(yīng)用于無線光通信的必要技術(shù)和探索方向。

無線光通信；噴泉碼；無速率編碼；度分布函數(shù)

1 引 言

無線光通信(Optical wireless communication，OWC)是一種新興的視距傳輸技術(shù)，與傳統(tǒng)射頻(radio frequency，RF)通信相比，具有保密性好、帶寬高、信道容量大以及無需頻率請(qǐng)求等優(yōu)點(diǎn)。但是，由于激光信號(hào)在大氣中傳輸易受到大氣湍流等效應(yīng)的影響，易產(chǎn)生光束漂移，強(qiáng)度起伏等問題，使得無線光通信中光束傳輸質(zhì)量降低，嚴(yán)重影響了OWC系統(tǒng)的性能[1]。

無線光通信信道復(fù)雜多變，受天氣、海拔等條件影響較大，傳統(tǒng)的線性分組碼、卷積碼、極化碼等編碼方法往往采用事先確定好的碼率傳輸，在受到信道條件不規(guī)律變化的影響時(shí)，會(huì)使得譯碼端復(fù)雜度高，并造成較高的誤碼率和通信時(shí)延；并且，在大氣條件較好時(shí)，若采用較低的發(fā)射功率與較低碼率編碼方案，又會(huì)影響通信效率，使其無法充分利用無線光通信中豐富的信道資源[2]，考慮到噴泉碼的諸多特性，將其應(yīng)用于無線光通信具有一定的研究意義。

噴泉碼最初在解決大規(guī)模數(shù)據(jù)可靠性傳輸和廣播或者多播快速傳輸?shù)膯栴}中被提出。與傳統(tǒng)信道編碼相比，噴泉碼由于其碼率不固定的特性更加適合無線光通信[3]，其本身可以利用信道估計(jì)和譯碼端信噪比估計(jì)等算法，估計(jì)大氣信道的衰落特性，然后利用噴泉碼的譯碼累積分布函數(shù)動(dòng)態(tài)調(diào)整碼率和發(fā)射機(jī)發(fā)射功率，根據(jù)信道的變化自動(dòng)改變編碼方式，用來提高無線光通信的有效性，甚至在信道反饋或者信道估計(jì)不準(zhǔn)確時(shí)也能一定程度上保證通信質(zhì)量。噴泉碼具有廣闊的應(yīng)用前景，目前已被DVB-H和3GPP TS等國(guó)際標(biāo)準(zhǔn)采用[4]。

本文介紹了噴泉碼的優(yōu)勢(shì)以及目前國(guó)內(nèi)外發(fā)展現(xiàn)狀，綜述了已經(jīng)提出的兩類實(shí)用噴泉碼的度分布函數(shù)的設(shè)計(jì)以及不同的譯碼方案，歸納了前人對(duì)噴泉碼性能不斷優(yōu)化的方案，同時(shí)指出了噴泉碼應(yīng)用于無線光通信中需要解決的一些關(guān)鍵問題，最后對(duì)噴泉碼在無線光通信領(lǐng)域的發(fā)展前景和研究方向進(jìn)行了展望。

2 噴泉碼的優(yōu)勢(shì)和發(fā)展現(xiàn)狀

傳統(tǒng)的前向糾錯(cuò)(forward error correction，F(xiàn)EC)方式需要預(yù)先估計(jì)信道狀態(tài)信息，并根據(jù)實(shí)際情況選擇合適的編碼長(zhǎng)度及碼字，通常在OWC系統(tǒng)中，信道質(zhì)量因?yàn)樘鞖獾淖兓瘏^(qū)別較大，故需要多次重復(fù)設(shè)計(jì)編碼方案，這樣大大增加了系統(tǒng)的復(fù)雜度[5]。

除此之外，無線通信下大規(guī)模MIMO(multiple input multiple output)系統(tǒng)可以引入噴泉碼，不同的接收端可以根據(jù)處理能力和信道條件自主選擇接收合適數(shù)量的編碼包，一旦完全恢復(fù)了原始信息就停止接收，不同接收端不會(huì)相互影響，有效地降低了MIMO系統(tǒng)的復(fù)雜度。噴泉編碼器產(chǎn)生的不同編碼數(shù)據(jù)包之間相互獨(dú)立且完全等價(jià)，能否譯碼成功僅僅取決于接收到編碼包的數(shù)量，與接收到編碼包種類和順序無關(guān)[6]。由于無線光通信系統(tǒng)在惡劣天氣條件下通常會(huì)通信中斷，利用噴泉碼的特性，在接收端疊加累積譯碼，可以在高中斷概率的條件下得到比較好的效果，也可以有效解決斷點(diǎn)續(xù)傳和異步接入帶來的復(fù)雜度問題。而且一旦成功譯碼，接收端只需給發(fā)送端一個(gè)反饋信號(hào)，從而避免了傳統(tǒng)線性分組碼的復(fù)雜反饋過程帶來的“反饋風(fēng)暴”問題[7]。

基于以上優(yōu)勢(shì)，噴泉碼在被提出后的二十多年來受到了廣泛的關(guān)注[8]。目前的研究主要集中于編碼方式的選擇[9]、度分布的設(shè)計(jì)與優(yōu)化、譯碼算法的設(shè)計(jì)、與具有高糾錯(cuò)能力的編碼級(jí)聯(lián)[10-12]、利用不等差錯(cuò)理論[13]實(shí)現(xiàn)高質(zhì)量傳輸以及噴泉碼理論在數(shù)據(jù)傳輸，深空通信和云存儲(chǔ)等場(chǎng)景的實(shí)際應(yīng)用拓展[14]。

表1介紹了噴泉碼的研究現(xiàn)狀。在國(guó)內(nèi)的研究中，2017年，重慶理工大學(xué)的張勛課題組研究了在2′2的MIMO_FSO系統(tǒng)中，用Gamma-Gamma模型模擬大氣湍流信道下基于修正轉(zhuǎn)移魯棒孤子度分布(ISRSD)[15]的LT碼與傳統(tǒng)LDPC碼的性能比較。使用改進(jìn)的LT碼能夠在強(qiáng)湍流條件下，誤碼率為10-6時(shí)獲得2.2 dB的編碼增益，同樣誤碼率情況下，在弱湍流條件下獲得0.9 dB的編碼增益。隨后，又研究了魯棒泊松度分布(PRSD)下的LT碼在3′3 MIMO-FSO的性能。在強(qiáng)湍流條件下，誤碼率為10-6時(shí)，采用PRSD度分布的LT碼比RSD獲得了1 dB的編碼增益；弱湍流條件下，同樣誤碼率下，采用PRSD的LT碼比RSD獲得了0.4 dB的編碼增益。以上成果研究了噴泉碼及其改進(jìn)方案，對(duì)優(yōu)化無線光通信質(zhì)量大有裨益[15]。

3 噴泉碼的原理與分類

噴泉碼可以形象地表示為圖1，這里編碼器為一個(gè)噴泉源，噴泉源向外面隨機(jī)地噴灑水珠(編碼包)，接收水桶即為譯碼器，目的是接到足夠的水(完成譯碼)?！八啊辈魂P(guān)心水從哪里來，如果某次檢查發(fā)現(xiàn)水不夠(譯碼失敗)，則繼續(xù)接水珠(編碼包)，直到解渴(完成譯碼)[25-27]。

圖2介紹了上述噴泉碼編碼器和譯碼器的原理，首先編碼器對(duì)數(shù)據(jù)進(jìn)行分割，進(jìn)行異或操作得到源源不斷的數(shù)據(jù)包；然后譯碼器接收到編碼器產(chǎn)生的源源不斷的數(shù)據(jù)包，對(duì)數(shù)據(jù)包進(jìn)行處理恢復(fù)出原始數(shù)據(jù)[28]。

表1 國(guó)內(nèi)外噴泉碼的研究進(jìn)展

圖1 噴泉碼原理示意圖

圖2 (a) 噴泉碼的編碼器原理；(b) 噴泉碼的譯碼器原理

從理論上來看，噴泉碼的編碼器和譯碼器仍有一些細(xì)節(jié)需要考慮：

編碼器：1) 需要預(yù)先設(shè)定相應(yīng)的函數(shù)來保證所有的數(shù)據(jù)包都能被選擇，而不會(huì)有遺漏導(dǎo)致譯碼失??；2) 在保證噴泉碼譯碼端能譯碼成功條件下，譯碼端所需要的編碼分組盡可能小，編碼數(shù)據(jù)包應(yīng)該盡可能簡(jiǎn)單，減少譯碼器的工作負(fù)擔(dān)[29]。

譯碼器：譯碼器選擇的譯碼算法應(yīng)該能從任意一組(>)個(gè)編碼數(shù)據(jù)包中恢復(fù)個(gè)原始數(shù)據(jù)。接近即意味著譯碼開銷很低，而且譯碼器的復(fù)雜度能夠與個(gè)原始數(shù)據(jù)有線性關(guān)系，這就是比較優(yōu)良的譯碼器。

根據(jù)以上討論，目前有兩類受到廣泛研究的噴泉碼，即LT碼和Raptor碼。

3.1 LT碼

如圖3，LT碼的編碼過程：1) 根據(jù)預(yù)先選定的度分布函數(shù)隨機(jī)選擇一個(gè)度值；2) 從個(gè)原始信息符號(hào)中隨機(jī)選擇個(gè)符號(hào)進(jìn)行異或得到一個(gè)編碼符號(hào)；3) 不斷根據(jù)上述方法源源不斷地產(chǎn)生編碼符號(hào)。

式(2)的編碼矩陣取決于度分布函數(shù)，度分布函數(shù)對(duì)LT碼的編譯碼復(fù)雜度、錯(cuò)誤平層和譯碼開銷等有重要影響[31]。早期提出的線性噴泉碼由于采用了均勻分布的度函數(shù)，編碼符號(hào)的平均度值很高使其有較高的編譯碼復(fù)雜度，故這類噴泉碼并不實(shí)用。所以設(shè)計(jì)出的一個(gè)好的度函數(shù)既要保證較低的編譯碼復(fù)雜度，還要實(shí)現(xiàn)在接收到比較少的編碼符號(hào)時(shí)就可以開始譯碼，而且在譯碼迭代的過程可以持續(xù)進(jìn)行，不至于找不到度值為1的編碼符號(hào)而譯碼中斷[32-33]。

為了在譯碼迭代過程中能源源不斷找到度值為1的編碼數(shù)據(jù)包，同時(shí)平均度值不會(huì)明顯增加。Luby在理想孤波分布基礎(chǔ)上進(jìn)行了一定的修正，提出了魯棒孤子分布(robust soliton distribution，RSD)：

圖4 K=10000，δ=0.05，c=0.2，0.3，0.4，0.5，0.6時(shí)RSD的概率密度分布

表2比較了優(yōu)化的PRSD和RSD的性能。

3.2 Raptor碼

編碼過程：1) LDPC碼編碼：將個(gè)原始符號(hào)進(jìn)行LDPC碼編碼，編為碼長(zhǎng)為的LDPC碼碼字，即預(yù)編碼過程；2) LT碼編碼：將上述過程產(chǎn)生的LDPC碼編碼碼字作為L(zhǎng)T碼的輸入符號(hào)進(jìn)行LT碼編碼，產(chǎn)生的LT編碼輸出符號(hào)即為Raptor碼的編碼符號(hào)。

表2 PRSD和RSD的性能對(duì)比

圖 5 Raptor的編碼過程

Shokrollahi結(jié)合了碼長(zhǎng)來考慮了度分布的設(shè)計(jì)，得到了Raptor碼在有限碼長(zhǎng)下的度分布設(shè)計(jì)準(zhǔn)則，如表3所示。

其中以碼長(zhǎng)=65536為例：

Raptor碼與LT碼相比擁有線性時(shí)間復(fù)雜度，并且其錯(cuò)誤平層很低可以對(duì)信息進(jìn)行較好的保護(hù)非常適合于在復(fù)雜差錯(cuò)環(huán)境下傳輸數(shù)據(jù)。目前，有兩類Raptor碼被廣泛應(yīng)用和研究，即R10(Raptor10)碼和RQ(RaptorQ)碼。R10碼已經(jīng)被多個(gè)國(guó)際化標(biāo)準(zhǔn)組織使用，如3GPP(3rdGeneration Partnership Project)，DVB-H(Digital Video Broadcasting-Handheld)和IETF(Internet Engineering Task Force)。作為FEC的傳輸方案，R10碼適合于中等長(zhǎng)度數(shù)據(jù)塊，應(yīng)用于移動(dòng)廣播等對(duì)數(shù)據(jù)保護(hù)要求不高的場(chǎng)合，RQ碼適合于目前無線光通信等復(fù)雜環(huán)境的大規(guī)模數(shù)據(jù)傳輸且需要較高精確度的場(chǎng)合。

3.3 噴泉碼的譯碼

3.2中介紹的Raptor碼是LDPC碼和LT碼級(jí)聯(lián)得到的，故譯碼過程為先對(duì)LT碼進(jìn)行譯碼再進(jìn)行LDPC碼譯碼。故這里著重介紹LT碼在BEC信道和AWGN信道下的譯碼方法[35]。

3.3.1 LT碼在二進(jìn)制刪除信道下的BP譯碼

1) 在編碼符號(hào)集中尋找一個(gè)度為1的編碼符號(hào)y，假設(shè)在二分圖上編碼符號(hào)y與原始符號(hào)s相連；

2) 直接令s=y，并在二分圖上一出s與y相連的邊；

4) 重復(fù)上述步驟，直到原始符號(hào)被全部譯出，或者在迭代的過程中找不到度為1的編碼符號(hào)。

表3 不同碼長(zhǎng)下優(yōu)化出Raptor碼的度分布

圖6 LT碼的BP譯碼方法

2012年Chong等人提出了一種設(shè)計(jì)簡(jiǎn)單的短消息噴泉碼(short message fountain codes)，能夠在理想的信道下，到刪除率為0.5的刪除信道下以較低的效率成功譯碼。Huang等人研究了帶有消息傳遞(message passing，MP)和最大似然(maximum likelihood，ML)解碼算法的噴泉碼在刪除信道下的性能，證明了MP算法能夠在中長(zhǎng)碼長(zhǎng)下有較高的譯碼效率，對(duì)于短碼長(zhǎng)MP算法會(huì)帶來較大的譯碼開銷，在此基礎(chǔ)上提出了針對(duì)于短碼長(zhǎng)消息的混合消息傳遞和快速最大似然譯碼方法。

3.3.2 高斯消元法譯碼

圖7 LT碼的BP譯碼和GE譯碼在不同碼長(zhǎng)K下的性能

3.3.3 LT碼在有噪信道下的譯碼

最初噴泉碼的提出是基于刪除信道下的，所以在有噪信道下LT碼的BP譯碼和GE譯碼會(huì)更復(fù)雜。2006年Etesami和Shokrollahi等人在一般噪聲二進(jìn)制輸入無記憶對(duì)稱(binary input has no memory symmetric，BIMS)信道下利用BP譯碼更新的算法研究了噴泉碼的性能[38]。Palanki論述了在有噪信道中考慮到譯碼速率和復(fù)雜性，在接收到一定數(shù)量編碼符號(hào)后應(yīng)當(dāng)繼續(xù)接收還是譯碼的問題[39]。Jenkac提出了在譯碼端設(shè)計(jì)一個(gè)度量使得有足夠的編碼數(shù)據(jù)被接收到時(shí)再開始譯碼。論證了噴泉碼采用增量解碼方案時(shí)，若小于最大譯碼迭代次數(shù)，譯碼器在譯碼嘗試時(shí)進(jìn)行等待操作，接收到一定編碼數(shù)據(jù)才進(jìn)行譯碼[40]。Castura等人研究了在塊衰落信道中，噴泉碼解碼時(shí)間的分布[41]。比較流行的算法是Jenkac和Palanki等人給出了LT碼在AWGN信道下的軟判決譯碼算法先驗(yàn)似然對(duì)數(shù)比算法：

4 總結(jié)和展望

目前噴泉碼的研究已經(jīng)取得不小的成功，但目前噴泉碼的研究大部分停留在理論研究和實(shí)驗(yàn)仿真上。噴泉碼靈活多變的特性在未來的無線光通信領(lǐng)域有重大的應(yīng)用前景，目前噴泉碼亟需解決的問題有：

1) 需要借助概率論等工具從理論上分析LT碼中RSD的本質(zhì)原因。在源數(shù)據(jù)較大時(shí)，選用RSD的LT碼有良好的性能，目前需要設(shè)計(jì)出在短碼長(zhǎng)條件下LT碼性能優(yōu)良的度分布。5G通信要求的高速、低時(shí)延，使得短碼長(zhǎng)在日后有重大的應(yīng)用前景，所以短碼長(zhǎng)的Raptor碼的性能也是亟需改善的。

2) 噴泉碼本身的誤碼平層高于普通的線性分組碼，在應(yīng)用于信噪比較低的無線光通信下時(shí)會(huì)帶來非常大的誤差，所以優(yōu)化噴泉碼的誤碼平層構(gòu)造性能更加優(yōu)良的Raptor碼也是未來的研究重點(diǎn)。

研究噴泉碼與其它信道編碼(如Turbo碼，卷積碼等)級(jí)聯(lián)時(shí)的性能，以及特點(diǎn)級(jí)聯(lián)方案優(yōu)化的譯碼方法。將噴泉碼的研究拓展到更多的信道，并對(duì)不同的信道應(yīng)當(dāng)由新的譯碼方案被提出。

3) 噴泉碼在無線光通信領(lǐng)域的應(yīng)用受到了廣泛的研究。在OWC領(lǐng)域，將自適應(yīng)技術(shù)與噴泉碼相結(jié)合可以大大提高OWC系統(tǒng)的傳輸效率，充分利用頻帶資源；目前噴泉碼應(yīng)用于OWC系統(tǒng)的重點(diǎn)在于信道估計(jì)，經(jīng)典的無線通信信道估計(jì)策略并不完全適合于光通信場(chǎng)景，所以需要設(shè)計(jì)出借助光信號(hào)對(duì)大氣信道時(shí)刻變化的大氣湍流、大氣衰減等效應(yīng)以及在深空通信中對(duì)太陽(yáng)光閃爍等效應(yīng)進(jìn)行估計(jì)。在實(shí)際工程應(yīng)用中，如何利用自適應(yīng)技術(shù)來動(dòng)態(tài)調(diào)整發(fā)射接收設(shè)備的相關(guān)設(shè)置，在實(shí)際信道中提升OWC系統(tǒng)的性能，都是發(fā)展?jié)摿^大的領(lǐng)域。

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Development and prospect of fountain codes in optical wireless communication

Wu Yi, Liu Hongzhan*, Hao Yuan, Liu Liyuan

Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices, School of Information and Optoelectronics, South China Normal University, Guangzhou, Guangdong 510006, China

The principle of fountain codes

Overview:Fountain codes is a typical rateless coding scheme, which can also provide reliable guarantee for data transmission without channel feedback or channel estimation, and exhibit excellent adaptability to complex and variable optical wireless communication (OWC) channels. This paper reviews the development of fountain codes proposed nearly three decades ago. In 1998, Luby and other scholars proposed the concept of digital fountain in the context of solving large-scale data reliability transmission and broadcasting or multicast. Until 2002, Luby and his team designed the first practical fountain codes which be called Luby transform (LT) codes. In the theory of LT codes, robust soliton distribution (RSD) is innovatively proposed to regularize the choice of source symbols. In 2004, in order to solve the disadvantages of LT codes such as the high complexity and disability of realizing linear-time encoding or decoding, Shokrollahi et al. proposed a novel encoding scheme named Raptor (rapid tornado) codes that creatively concatenates linear block codes and LT codes together. They also optimized the fixed distribution function of Raptor codes for different information lengths. After that, some new digital fountain codes such as system fountain codes, incremental codes, spinal codes and Kite codes were successively proposed these years. Although the fountain codes was originally proposed for erasure channels, since it has great adaptivity in various channel conditions, the research of fountain code has been extended to the wireless channel in 2006, and the soft decision decoding algorithm for the fountain codes under wireless channels was obtained. At present, the fountain codes has been widely applied in wireless communication relay, space diversity, wireless cooperative transmission, etc. Thanks to its rateless characteristics, any number of coded packets can be adaptively generated according to channel conditions, producing excellent performance under erasure channel. However, when fountain codes are used in wireless channels, the design of the coding and degree distribution need to be reconsidered, which often causes the problem of high complexity and error floor. Therefore, the research hotspot of the fountain code under optical wireless communication is to cascade it with the channel coding schemes with capability of error detection, so that the fountain code can also exert its advantages under the noise channel. In short, the application prospects of fountain codes in OWC will be promising. This review focuses on the principle of fountain code and the fountain code with excellent performance, and it sheds some light on the future application of fountain code in scenario of OWC.

Citation: Wu Y, Liu H Z, Hao Y,Development and prospect of fountain codes in optical wireless communication[J]., 2020, 47(3): 190623

Development and prospect of fountain codes in optical wireless communication

Wu Yi, Liu Hongzhan*, Hao Yuan, Liu Liyuan

Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices, School of Information and Optoelectronics, South China Normal University, Guangzhou, Guangdong 510006, China

The optical wireless communication channel is complex and changeable. Fountain codes as an emerging rateless coding can achieve adaptive transmission in different channel environments without a priori information of the channel. Compared with traditional coding, it can improve the quality of wireless transmission. In this paper, we first summarize the advantages of fountain codes applied to optical wireless communication and the domestic and foreign researches on the development status of fountain codes. Then we deeply study the design of two kinds of fountain codes coding schemes, as well as the degree distribution function which has significant influence on the performance of fountain code. Soon we put forward one kind of fountain codes, namely Luby transform (LT) codes, and introduce the optimization schemes in recent years. Meanwhile, the key difficulties that need to be solved in the fountain codes design are pointed out. Finally, the necessary technologies and explorations direction of fountain codes for wireless optical communication are proposed.

optical wireless communication; fountain codes; rateless coding; degree distribution functionC

TN929.1

A

10.12086/oee.2020.190623

: Wu Y, Liu H Z, Hao Y,. Development and prospect of fountain codes in optical wireless communication[J]., 2020,47(3): 190623

2019-10-16；

2019-12-25基金項(xiàng)目：國(guó)家自然科學(xué)基金資助項(xiàng)目(61875057，61475049)

吳一(1995-)，男，碩士研究生，主要從事自由空間光通信技術(shù)的研究。E-mail：1121377742@qq.com

劉宏展(1975-)，男，博士，教授，博士生導(dǎo)師，從事空間光通信、圖像處理及光傳感技術(shù)方面的教學(xué)和研究工作。 E-mail: lhzscnu@163.com

吳一，劉宏展，郝源，等. 無線光通信中噴泉碼的發(fā)展現(xiàn)狀與展望[J]. 光電工程，2020，47(3): 190623

Supported by National Natural Science Foundation of China (61875057, 61475049)

* E-mail: lhzscnu@163.com