多用户信息论中的差错指数分析与传输策略研究
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摘要
随着社会生活水平的提高,要求无线通信系统能够支持高速率和满足不同的服务质量(Quality of Service, QoS),具有高速率高链路可靠性特征的无线通信系统成为了演进目标。面向多用户架构的宽带无线通信网络的最根本理论基础是多用户信息论,其能够刻画和体现信息流在无线通信网络多点传输过程中的实际网络特征(多源、多信宿、多址接入、广播、干扰、协作、反馈等)。多用户信息论是研究多个相互影响制约的信源信宿对所组成网络的信息传输极限并给予具体实现方案指导的理论。因此,近年来多用户信息论受到了理论研究者的格外关注。
本论文主要针对认知无线电信道(也称为认知干扰信道)和多源中继广播信道开展研究,其主要贡献在于分别提出了这两类信道模型下的系统传输策略以及推导给出了在该传输策略下的可达速率域。此外,还从差错指数的角度揭示了系统可靠性、传输速率与编码码长之间的关系。
第一,本论文给出了四个用户离散无记忆认知无线电信道的可达速率域,并指出该可达速率域由速率拆分、叠加编码、Gel'fand-Pinkser编码以及同时译码等传输策略得到。对于四个用户离散无记忆认知无线电信道中的所有接收机能够对公有消息进行译码情形,认知用户发射机在进行Gel'fand-Pinkser编码的时候仅仅预删除被认知用户的私有消息。对于认知用户的公有消息不能由被认知用户接收机译码,同时被认知用户的公有消息不能由认知用户接收机译码的情形,认知用户发射机在进行Gel'fand-Pinkser编码时将预删除被认知用户的所有消息(公有消息与私有消息)。同时,在公有消息能够被所有接收机译码的四个用户离散无记忆认知无线电信道中,如果固定某些辅助随机变量,所给出的可达速率域等价于前人得到的结果。
第二,本论文运用不等式引理和Gallager界,给出了离散无记忆认知无线电信道的差错指数域。该差错指数域是基于叠加编码、Gel'fand-Pinkser编码以及最大似然译码等系统传输策略得到。同时,考虑高斯信道情况,根据所提的离散无记忆认知无线电信道的差错指数域,得到了固定参数下高斯认知无线电信道的差错指数域。
第三,本论文针对退化高斯多源中继广播信道,提出了一种基于分组马尔科夫规则编码以及滑动窗译码的系统传输策略,并在该策略下通过推导得出了相应的可达速率域。同时,通过Fano不等式、网络最大流最小割定理以及条件熵引理本论文还给出了该信道模型的一个外界。
第四,本论文分别提出了在速率拆分策略下基于放大转发(Amplify and Forward, AF)和译码转发(Decode and Forward, DF)的适用于两跳高斯多源中继广播信道的系统传输策略,并给出了相应的系统差错概率界。其中,AF中继策略下,其差错概率界可以通过综合指数函数得到。而在DF中继策略下,由于中继译码阶段和广播阶段的传输速率存在一个最小割集界,其差错概率界是一个分段函数,其中,差错指数的表达式在不同的传输速率区间不一样。同时,由于系统差错概率界不能刻画出各个源节点链路的可靠性,论文还给出了两跳高斯多源中继广播信道的可达差错指数域。
With the development of society, the demand for high data rates and different quality-of-service is growing rapidly. Improving the throughput and reliability have been the evolutional directions of wireless communication systems. As the theoretical foundation of broadband wireless communication networks, multi-user information theory can capture the aspects of information flow in real-world multipoint-to-multipoint communication networks (Multiple sources, multiple destinations, multi-access, broadcasting, interference, cooperation, feedback, etc.). Multi-user information theory is devoted to investigate the information theoretic capacity limits in networks where multiple sources and destinations interactive with each other. Therefore, the multi-user information theory has become an important research topic in recent years.
This dissertation mainly focuses on cognitive radio channels (also called cognitive interference channels) and multi-source relay broadcast channels. The main contribution of our work lies in deriving several achieve rate regions under the corresponding transmission strategies, and showing the relationship among the communication reliability, transmission rate and the code length from an error exponent perspective.
Firstly, the achievable rate regions of the four-user discrete memoryless cognitive radio channel are obtianed by rate splitting, superposition coding, Gel' fand-Pinsker coding and simultaneous decoding strategies. According to the different encoding and decoding strategies, the Gel'fand-Pinsker coding is only applied to cancel the private messages of the non-cognitive users at the cognitive transmitters in the case that public messages can be decoded by all the receivers, and the Gel' and-Pinsker coding is applied to cancel all the messages of the non-cognitive users at the cognitive transmitters in the case that public messages can not be decoded between cognitive receivers and non-cognitive receivers. Also, we show that the region is identical to the existing results via fixing some auxiliary random variables for the the four-user discrete memoryless cognitive radio channel in which the public messages can be decoded by all the receivers.
Secondly, the error exponent for the cognitive radio channels is investigated, in which the superposition coding, Gel' fand-Pinsker coding and maximum likelihood decoding are considered. Under this model, we derive the error exponent region for the discrete memoryless cognitive radio channel with the inequality lemma and Gallager's bounding technique. Also, the error exponent region for the Gaussian cognitive radio channels under choosing the special parameter case is analyzed.
Thirdly, this dissertation investigates the capacity of the degraded multi-source relay broadcast channels, where each source wants to communicate individual messages with its intended destination via both direct and relay links. An achievable rate region of this channel is obtained, in which the block Markov regular encoding and the sliding-window decoding transmission strategies are exploited. Also, the outer bound is derived via using the Fano's inequality, the max-flow min-cut theorem and condition entropy lemma.
Finally, the error exponents of the two-hop multiple source-destination relay channels are obtained. Two relay modes are mentioned:amplified and forward (AF) and decode and forward (DF). An achievable rate region can be obtained by the rate splitting strategies which each source can split its message into private and public parts. We determine the system error probability via integrated exponent function under AF relay strategies. The most significant difference between AF and DF system error probability evaluations lies in a minimized cut-set bound of transmission rate under the DF strategy. There are many cases among transmission rate intervals for different system parameters (e.g. transmit power) and we derive the system error probability for the DF strategy. Moreover, in order to draw deep insight into the reliability requirement of each source node in this network, we provide the error exponent region for different source nodes to show the trade-off of error probability among source nodes.
本论文主要针对认知无线电信道(也称为认知干扰信道)和多源中继广播信道开展研究,其主要贡献在于分别提出了这两类信道模型下的系统传输策略以及推导给出了在该传输策略下的可达速率域。此外,还从差错指数的角度揭示了系统可靠性、传输速率与编码码长之间的关系。
第一,本论文给出了四个用户离散无记忆认知无线电信道的可达速率域,并指出该可达速率域由速率拆分、叠加编码、Gel'fand-Pinkser编码以及同时译码等传输策略得到。对于四个用户离散无记忆认知无线电信道中的所有接收机能够对公有消息进行译码情形,认知用户发射机在进行Gel'fand-Pinkser编码的时候仅仅预删除被认知用户的私有消息。对于认知用户的公有消息不能由被认知用户接收机译码,同时被认知用户的公有消息不能由认知用户接收机译码的情形,认知用户发射机在进行Gel'fand-Pinkser编码时将预删除被认知用户的所有消息(公有消息与私有消息)。同时,在公有消息能够被所有接收机译码的四个用户离散无记忆认知无线电信道中,如果固定某些辅助随机变量,所给出的可达速率域等价于前人得到的结果。
第二,本论文运用不等式引理和Gallager界,给出了离散无记忆认知无线电信道的差错指数域。该差错指数域是基于叠加编码、Gel'fand-Pinkser编码以及最大似然译码等系统传输策略得到。同时,考虑高斯信道情况,根据所提的离散无记忆认知无线电信道的差错指数域,得到了固定参数下高斯认知无线电信道的差错指数域。
第三,本论文针对退化高斯多源中继广播信道,提出了一种基于分组马尔科夫规则编码以及滑动窗译码的系统传输策略,并在该策略下通过推导得出了相应的可达速率域。同时,通过Fano不等式、网络最大流最小割定理以及条件熵引理本论文还给出了该信道模型的一个外界。
第四,本论文分别提出了在速率拆分策略下基于放大转发(Amplify and Forward, AF)和译码转发(Decode and Forward, DF)的适用于两跳高斯多源中继广播信道的系统传输策略,并给出了相应的系统差错概率界。其中,AF中继策略下,其差错概率界可以通过综合指数函数得到。而在DF中继策略下,由于中继译码阶段和广播阶段的传输速率存在一个最小割集界,其差错概率界是一个分段函数,其中,差错指数的表达式在不同的传输速率区间不一样。同时,由于系统差错概率界不能刻画出各个源节点链路的可靠性,论文还给出了两跳高斯多源中继广播信道的可达差错指数域。
With the development of society, the demand for high data rates and different quality-of-service is growing rapidly. Improving the throughput and reliability have been the evolutional directions of wireless communication systems. As the theoretical foundation of broadband wireless communication networks, multi-user information theory can capture the aspects of information flow in real-world multipoint-to-multipoint communication networks (Multiple sources, multiple destinations, multi-access, broadcasting, interference, cooperation, feedback, etc.). Multi-user information theory is devoted to investigate the information theoretic capacity limits in networks where multiple sources and destinations interactive with each other. Therefore, the multi-user information theory has become an important research topic in recent years.
This dissertation mainly focuses on cognitive radio channels (also called cognitive interference channels) and multi-source relay broadcast channels. The main contribution of our work lies in deriving several achieve rate regions under the corresponding transmission strategies, and showing the relationship among the communication reliability, transmission rate and the code length from an error exponent perspective.
Firstly, the achievable rate regions of the four-user discrete memoryless cognitive radio channel are obtianed by rate splitting, superposition coding, Gel' fand-Pinsker coding and simultaneous decoding strategies. According to the different encoding and decoding strategies, the Gel'fand-Pinsker coding is only applied to cancel the private messages of the non-cognitive users at the cognitive transmitters in the case that public messages can be decoded by all the receivers, and the Gel' and-Pinsker coding is applied to cancel all the messages of the non-cognitive users at the cognitive transmitters in the case that public messages can not be decoded between cognitive receivers and non-cognitive receivers. Also, we show that the region is identical to the existing results via fixing some auxiliary random variables for the the four-user discrete memoryless cognitive radio channel in which the public messages can be decoded by all the receivers.
Secondly, the error exponent for the cognitive radio channels is investigated, in which the superposition coding, Gel' fand-Pinsker coding and maximum likelihood decoding are considered. Under this model, we derive the error exponent region for the discrete memoryless cognitive radio channel with the inequality lemma and Gallager's bounding technique. Also, the error exponent region for the Gaussian cognitive radio channels under choosing the special parameter case is analyzed.
Thirdly, this dissertation investigates the capacity of the degraded multi-source relay broadcast channels, where each source wants to communicate individual messages with its intended destination via both direct and relay links. An achievable rate region of this channel is obtained, in which the block Markov regular encoding and the sliding-window decoding transmission strategies are exploited. Also, the outer bound is derived via using the Fano's inequality, the max-flow min-cut theorem and condition entropy lemma.
Finally, the error exponents of the two-hop multiple source-destination relay channels are obtained. Two relay modes are mentioned:amplified and forward (AF) and decode and forward (DF). An achievable rate region can be obtained by the rate splitting strategies which each source can split its message into private and public parts. We determine the system error probability via integrated exponent function under AF relay strategies. The most significant difference between AF and DF system error probability evaluations lies in a minimized cut-set bound of transmission rate under the DF strategy. There are many cases among transmission rate intervals for different system parameters (e.g. transmit power) and we derive the system error probability for the DF strategy. Moreover, in order to draw deep insight into the reliability requirement of each source node in this network, we provide the error exponent region for different source nodes to show the trade-off of error probability among source nodes.
引文
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