协作中继系统容量界及其无速率网络编码
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摘要
在过去的几十年里,高速发展的无线通信技术对人们的日常生活产生了深远的影响。现今的无线网络需要面对爆炸式增长的用户终端数量以及其数据传输需求。协作中继技术是一个潜在的解决方案,其可以有效地增强链路可靠性,增加系统吞吐量并扩大系统覆盖范围。作为下一代无线通信标准(例如LTE-A)中的关键增强型技术,协作通信在通信理论界获得了热切的关注。然而,协作通信技术仍然存在大量理论以及实际问题有待解决。首先,在信息论框架下,协作中继网络的理论性能界仍旧是开放的问题。其次,为了充分获得协作中继技术期望的性能增益,相应的编码设计还需要深入挖掘和研究。作为一种最初针对无噪网络提出的技术,网络编码能够进一步提升协作中继网络的性能。然而为了对抗无线中继网络中存在的衰落、干扰以及噪声,网络编码需要与信道编码相结合以正常工作。作为一类具有较高信道自适应性的信道编码,无速率码被认为非常适用于协作中继网络。将网络编码与无速率码相结合,我们提出了一类具有灵活性、鲁棒性以及较佳性能的联合网络信道编码。
在本学位论文中,我们在多用户信息论理论以及编码理论的指导下,研究了协作中继网络中的容量界以及联合网络信道编码设计问题。现将研究内容概述如下：
在本论文的第一部分,我们考虑了非受限半双工高斯放大转发双向中继信道(AF-TWRC)。通过计算相应的双向信道香农内外界,我们给出了该信道容量的一组内界和外界。对于高斯双向信道,其香农内外界是重合的,并以此确定了其容量区。然而对于放大转发双向中继信道,我们得出了相反的结论,即其香农内界和外界除了两个源节点都无噪的情况以外都是不重和的。这是由于放大转发双向中继信道中的中继节点带来了额外的功率限制条件,而该限制条件与两个源节点信道输入间的相关性有关,这是该信道与高斯双向信道的本质区别。虽然放大转发双向中继信道的容量区之前被认为已经是确立了,但本文推翻了该结论,其容量区应该仍旧是一个开放问题。最后我们在中继无噪的情况下研究了该信道的容量。通过依据相关平衡思想推得的新外界,我们确立了该情况下放大转发双向中继信道的容量区。
在第二部分,我们针对半双工时分双向中继系统提出了一个基于无速率码的三时隙网络编码传输协议,其中两个源节点通过一个中继节点的协助互相传输信息。在该协议中,每个源节点分别在前两个时隙中将其信息采用无速率编码后在系统中广播,直到中继节点正确译码并反馈ACK。在第三时隙,中继将两个源节点的消息利用基于无速率网络编码合并并编码,然后将其在系统中广播。两个源节点将该时隙以及前两个时隙收到的编码包进行迭代译码来恢复出对方源节点的消息。我们采用无速率码的一种,Raptor码,来实现我们的无速率网络编码方案。对于高斯噪声信道以及块衰落信道这两种情况,我们都能通过求解一组线性规划问题来联合优化系统中各节点采用的无速率码度数分布。仿真结果表明,采用优化度数分布的无速率网络编码方案要优于二元除删信道最优度数分布以及传统的联合网络信道编码方案,即能达到更高的系统吞吐量,并有着更低的系统误比特率。
在第三部分,我们考虑一个非对称时分多接入中继系统,其中包含了两个源节点,一个中继节点以及一个目的节点。所谓非对称,是指两个源节点到中继节点或目的节点的信道增益可能不同,或者两个源节点的消息长度可能不同。为了增强链路鲁棒性以及系统吞吐量,我们采用一种基于特殊无速率码的联合网络信道编码,该无速率码同时扮演了网络编码以及信道编码的角色。具体来说,源节点将各自的消息采用无速率码编码后广播给中继节点以及目的节点。而在中继节点,我们提出了一种新型的二维LT码(2D-LT),其可以将两个源节点消息的预编码比特利用二维度数分布联合编码同时内在地完成了网络编码。非常有趣的是,我们提出的编码方法可以退化成几种已知的基于无速率码的联合网络信道编码方法。为了得到趋近于理论上限的性能,我们利用外信息传递分析优化了两个源节点以及中继节点采用的无速率码的度数分布。仿真说明了我们提出的无速率网络编码在采用优化度数分布下,相较于采用传统度数分布的其他联合网络信道编码,可以达到更低的误码率以及更高的系统吞吐量。
In the past decades, the rapid development of wireless communication has a profound effect on our daily life. Today's wireless networks have to face the explosive growth of popularity of user equipments and their demands for data transmission. One potential solution is cooperative communication, which can effectively enhance the link reliability as well as increase the sys-tem throughput and coverage. Being a key role in the next generation communication standards (e.g., Long Term Evolution-Advanced), cooperative communication has received tremendous in-terests in the research community. However, there remains quite many theoretic and practical issues to be addressed for cooperative communication. The fundamental limits of cooperative relay networks, under the framework of information theory, are still open problems. Moreover, the practical coding schemes to achieve the promised gains of cooperative relaying are far from fully investigated. Network coding, originally proposed for noiseless networks, has shown its significant advantage when applied to the cooperative relay networks. Nevertheless, in order to combat the fading, interference and noise, which are inevitable in wireless cooperative relay networks, network coding should be incorporated with channel coding to work properly. As a highly compatible channel code, rateless code, has been found synergistic matching in coopera-tive relay networks. By merging the two, we propose a class of flexible and robust joint network and channel coding schemes with good performances.
In this dissertation, resorting to multiuser information theory and coding theory, we investi-gate the capacity bounds as well as joint network and channel coding design in cooperative relay networks. The contents of this dissertation are listed as follows.
In the first part of this dissertation, we revisit the non-restricted half-duplex Gaussian amplify-and-forward two-way relay channel (AF-TWRC). The inner and outer bounds of its capacity region are derived by evaluating Shannon's inner and outer bounds for general two-way channels. We prove that, in contrast to the case of Gaussian two-way channel (GTWC) where the two bounds coincide thus establishing its capacity region, the two bounds of AF-TWRC do not coincide unless both terminals are noise-free, due to that the intermediate relay node introduces additional power constraint relating to the correlation of channel inputs from both terminals. This indicates that the capacity region of non-restricted Gaussian AF-TWRC, which was previously believed to be already established in a way similar to that of GTWC, still remains open. We further investigate a special case of non-restricted AF-TWRC where the relay is noise-free, and obtain its capacity region based on the tighter dependence balance bound.
In the second part, we propose a three-stage rateless coded protocol for a half-duplex time-division two-way relay system, where two terminals send messages to each other through a relay between them. In the protocol, each terminal takes one of the first two stages respectively to encode its message using rateless code and broadcast the result until the relay acknowledges successful decoding. During the third stage, the relay combines and re-encodes both messages with a joint network-channel coding scheme based on rateless coding which provides incremen-tal redundancy. Together with the packets received directly in previous stages, each terminal then retrieves the desired message using an iterative decoder. The degree profiles of the specific rateless codes, i.e., Raptor codes, implemented at both terminals and the relay, are jointly opti-mized for both the AWGN channel and the Rayleigh block fading channel through solving a set of linear programming problems. Simulation results show that, the system throughput as well as the error rate achieved by the optimized degree profiles always outperforms those achieved by the conventional degree profile optimized for Binary Erasure Channel (BEC) and the previous network coding scheme with rateless codes.
In the third part of this dissertation, we consider an asymmetric time-division multiple ac-cess relay system consisting of two sources, one relay and one destination, where the channel conditions and message lengths of the two sources are allowed to be different. To enhance the link robustness and the system throughput, joint network-channel coding (JNCC) is employed with a specially designed rateless code which conducts both the channel coding and network coding simultaneously. In particular, at the sources, messages are rateless coded and then broad-casted to the relay and destination. While at the relay, a novel two-dimensional (2-D) LT code is proposed, which jointly encodes the precoded message bits of the two sources using a2-D degree profile and at the meantime completes the network coding inherently. Interestingly, the proposed scheme can be degraded to several conventional JNCC schemes based on rateless cod-ing. To further approach the theoretical limit, the corresponding degree profiles implemented at both sources and the relay are jointly designed based on the extrinsic information transfer (EXIT) function analysis. Simulations show that our proposed JNCC scheme with the optimized degree profiles outperforms other JNCC schemes with the conventional profiles both on the BER and throughput performances.
在本学位论文中,我们在多用户信息论理论以及编码理论的指导下,研究了协作中继网络中的容量界以及联合网络信道编码设计问题。现将研究内容概述如下：
在本论文的第一部分,我们考虑了非受限半双工高斯放大转发双向中继信道(AF-TWRC)。通过计算相应的双向信道香农内外界,我们给出了该信道容量的一组内界和外界。对于高斯双向信道,其香农内外界是重合的,并以此确定了其容量区。然而对于放大转发双向中继信道,我们得出了相反的结论,即其香农内界和外界除了两个源节点都无噪的情况以外都是不重和的。这是由于放大转发双向中继信道中的中继节点带来了额外的功率限制条件,而该限制条件与两个源节点信道输入间的相关性有关,这是该信道与高斯双向信道的本质区别。虽然放大转发双向中继信道的容量区之前被认为已经是确立了,但本文推翻了该结论,其容量区应该仍旧是一个开放问题。最后我们在中继无噪的情况下研究了该信道的容量。通过依据相关平衡思想推得的新外界,我们确立了该情况下放大转发双向中继信道的容量区。
在第二部分,我们针对半双工时分双向中继系统提出了一个基于无速率码的三时隙网络编码传输协议,其中两个源节点通过一个中继节点的协助互相传输信息。在该协议中,每个源节点分别在前两个时隙中将其信息采用无速率编码后在系统中广播,直到中继节点正确译码并反馈ACK。在第三时隙,中继将两个源节点的消息利用基于无速率网络编码合并并编码,然后将其在系统中广播。两个源节点将该时隙以及前两个时隙收到的编码包进行迭代译码来恢复出对方源节点的消息。我们采用无速率码的一种,Raptor码,来实现我们的无速率网络编码方案。对于高斯噪声信道以及块衰落信道这两种情况,我们都能通过求解一组线性规划问题来联合优化系统中各节点采用的无速率码度数分布。仿真结果表明,采用优化度数分布的无速率网络编码方案要优于二元除删信道最优度数分布以及传统的联合网络信道编码方案,即能达到更高的系统吞吐量,并有着更低的系统误比特率。
在第三部分,我们考虑一个非对称时分多接入中继系统,其中包含了两个源节点,一个中继节点以及一个目的节点。所谓非对称,是指两个源节点到中继节点或目的节点的信道增益可能不同,或者两个源节点的消息长度可能不同。为了增强链路鲁棒性以及系统吞吐量,我们采用一种基于特殊无速率码的联合网络信道编码,该无速率码同时扮演了网络编码以及信道编码的角色。具体来说,源节点将各自的消息采用无速率码编码后广播给中继节点以及目的节点。而在中继节点,我们提出了一种新型的二维LT码(2D-LT),其可以将两个源节点消息的预编码比特利用二维度数分布联合编码同时内在地完成了网络编码。非常有趣的是,我们提出的编码方法可以退化成几种已知的基于无速率码的联合网络信道编码方法。为了得到趋近于理论上限的性能,我们利用外信息传递分析优化了两个源节点以及中继节点采用的无速率码的度数分布。仿真说明了我们提出的无速率网络编码在采用优化度数分布下,相较于采用传统度数分布的其他联合网络信道编码,可以达到更低的误码率以及更高的系统吞吐量。
In the past decades, the rapid development of wireless communication has a profound effect on our daily life. Today's wireless networks have to face the explosive growth of popularity of user equipments and their demands for data transmission. One potential solution is cooperative communication, which can effectively enhance the link reliability as well as increase the sys-tem throughput and coverage. Being a key role in the next generation communication standards (e.g., Long Term Evolution-Advanced), cooperative communication has received tremendous in-terests in the research community. However, there remains quite many theoretic and practical issues to be addressed for cooperative communication. The fundamental limits of cooperative relay networks, under the framework of information theory, are still open problems. Moreover, the practical coding schemes to achieve the promised gains of cooperative relaying are far from fully investigated. Network coding, originally proposed for noiseless networks, has shown its significant advantage when applied to the cooperative relay networks. Nevertheless, in order to combat the fading, interference and noise, which are inevitable in wireless cooperative relay networks, network coding should be incorporated with channel coding to work properly. As a highly compatible channel code, rateless code, has been found synergistic matching in coopera-tive relay networks. By merging the two, we propose a class of flexible and robust joint network and channel coding schemes with good performances.
In this dissertation, resorting to multiuser information theory and coding theory, we investi-gate the capacity bounds as well as joint network and channel coding design in cooperative relay networks. The contents of this dissertation are listed as follows.
In the first part of this dissertation, we revisit the non-restricted half-duplex Gaussian amplify-and-forward two-way relay channel (AF-TWRC). The inner and outer bounds of its capacity region are derived by evaluating Shannon's inner and outer bounds for general two-way channels. We prove that, in contrast to the case of Gaussian two-way channel (GTWC) where the two bounds coincide thus establishing its capacity region, the two bounds of AF-TWRC do not coincide unless both terminals are noise-free, due to that the intermediate relay node introduces additional power constraint relating to the correlation of channel inputs from both terminals. This indicates that the capacity region of non-restricted Gaussian AF-TWRC, which was previously believed to be already established in a way similar to that of GTWC, still remains open. We further investigate a special case of non-restricted AF-TWRC where the relay is noise-free, and obtain its capacity region based on the tighter dependence balance bound.
In the second part, we propose a three-stage rateless coded protocol for a half-duplex time-division two-way relay system, where two terminals send messages to each other through a relay between them. In the protocol, each terminal takes one of the first two stages respectively to encode its message using rateless code and broadcast the result until the relay acknowledges successful decoding. During the third stage, the relay combines and re-encodes both messages with a joint network-channel coding scheme based on rateless coding which provides incremen-tal redundancy. Together with the packets received directly in previous stages, each terminal then retrieves the desired message using an iterative decoder. The degree profiles of the specific rateless codes, i.e., Raptor codes, implemented at both terminals and the relay, are jointly opti-mized for both the AWGN channel and the Rayleigh block fading channel through solving a set of linear programming problems. Simulation results show that, the system throughput as well as the error rate achieved by the optimized degree profiles always outperforms those achieved by the conventional degree profile optimized for Binary Erasure Channel (BEC) and the previous network coding scheme with rateless codes.
In the third part of this dissertation, we consider an asymmetric time-division multiple ac-cess relay system consisting of two sources, one relay and one destination, where the channel conditions and message lengths of the two sources are allowed to be different. To enhance the link robustness and the system throughput, joint network-channel coding (JNCC) is employed with a specially designed rateless code which conducts both the channel coding and network coding simultaneously. In particular, at the sources, messages are rateless coded and then broad-casted to the relay and destination. While at the relay, a novel two-dimensional (2-D) LT code is proposed, which jointly encodes the precoded message bits of the two sources using a2-D degree profile and at the meantime completes the network coding inherently. Interestingly, the proposed scheme can be degraded to several conventional JNCC schemes based on rateless cod-ing. To further approach the theoretical limit, the corresponding degree profiles implemented at both sources and the relay are jointly designed based on the extrinsic information transfer (EXIT) function analysis. Simulations show that our proposed JNCC scheme with the optimized degree profiles outperforms other JNCC schemes with the conventional profiles both on the BER and throughput performances.
引文
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