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On the discontinuity of the Shannon information measures and typical sequences 论Shannon信息测度的不连续性及典型序列
Siu-Wai Ho
It is well known that the Shannon information measures are continuous functions of the probability distribution when the support is finite. This, however, does not hold when the support is countably infinite. In this paper, we investigate the continuity of the Shannon information measures for countably infinite support. With respect to a distance based on the Kullback-Liebler divergence, we use two different approaches to show that all the Shannon information measures are in fact discontinuous at all probability distributions with countably infinite support
众所周知,当支持度有限时,香农信息测度是概率分布的连续函数。然而,当支持是可数无限时,这就不成立了。本文研究了可数无限支持下香农信息测度的连续性问题。对于基于Kullback-Liebler散度的距离,我们使用两种不同的方法来证明所有香农信息度量实际上在具有无限支持的所有概率分布下都是不连续的
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引用次数: 2
On optimal quasi-orthogonal space-time block codes with minimum decoding complexity 最小译码复杂度的最优拟正交空时分组码
Haiquan Wang, Dong Wang, X. Xia
In this paper, we first present a necessary and sufficient condition on linear transformations for an QOSTBC to possess the minimum ML decoding complexity, i.e., real symbol pair-wise decoding. We then present optimal linear transformations of information symbols for quasi-orthogonal space-time block codes (QOSTBC) with minimum ML decoding complexity. The optimality is in the sense that the diversity product (or product distance) is maximized when the mean transmission power is fixed
本文首先给出了QOSTBC线性变换具有最小ML解码复杂度的充要条件,即真正的符号对解码。然后,我们提出了具有最小ML解码复杂度的准正交空时分组码(QOSTBC)信息符号的最优线性变换。最优性是指当平均传输功率一定时,分集积(或产品距离)最大
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引用次数: 47
Neyman-Pearson Detection of Gauss-Markov Signals in Noise: Closed-Form Error Exponent and Properties 噪声中高斯-马尔可夫信号的内曼-皮尔逊检测:封闭误差指数及其性质
Y. Sung, L. Tong, H. Poor
The performance of Neyman-Pearson detection of correlated stochastic signals using noisy observations is investigated via the error exponent for the miss probability with a fixed level. Using the state-space structure of the signal and observation model, a closed-form expression for the error exponent is derived, and the connection between the asymptotic behavior of the optimal detector and that of the Kalman filter is established. The properties of the error exponent are investigated for the scalar case. It is shown that the error exponent has distinct characteristics with respect to correlation strength: for signal-to-noise ratio (SNR) > 1 the error exponent decreases monotonically as the correlation becomes stronger, whereas for SNR < 1 there is an optimal correlation that maximizes the error exponent for a given SNR
研究了利用噪声观测对相关随机信号进行内曼-皮尔逊检测的性能,方法是利用固定水平的缺失概率的误差指数。利用信号和观测模型的状态空间结构,导出了误差指数的封闭表达式,并建立了最优检测器的渐近行为与卡尔曼滤波器的渐近行为之间的联系。研究了标量情况下误差指数的性质。结果表明,误差指数在相关强度方面具有明显的特征:对于信噪比(SNR) bbbb1,误差指数随着相关性的增强而单调减小,而对于信噪比< 1,存在一个最优相关性,使给定信噪比的误差指数最大化
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引用次数: 72
On the throughput, capacity and stability regions of random multiple access over standard multi-packet reception channels 标准多包接收信道上随机多址的吞吐量、容量和稳定区域
Jie Luo, A. Ephremides
This paper studies finite-terminal random multiple access over a standard multi-packet reception (MPR) channel. In the first part of the paper, we show that if the MPR channel is standard, the throughput region of random multiple access is co-ordinate convex. We then study the information capacity region of multiple access without code synchronization and feedback. We show that the asymptotic capacity region is identical to the throughput region. In the second part of the paper, we study the stability region of ALOHA multiple access. For a class of packet arrival distributions, we show that the stationary distribution of the queues possesses the positive and strong positive correlation properties; and this consequently gives an outer bound to the stability region. We also show that if a conjectured "sensitivity monotonicity" property can be shown for the stationary distribution of the queues, then the equivalence between the closure of the stability region and the throughput region follows as a direct consequence, irrespective of the packet arrival distributions
研究了基于标准多包接收(MPR)信道的有限终端随机多址接入。在本文的第一部分,我们证明了当MPR信道是标准信道时,随机多址的吞吐量区域是坐标凸的。然后研究了无码同步与反馈的多址信息容量区域。我们证明了渐近容量区域与吞吐量区域是相同的。在论文的第二部分,我们研究了ALOHA多址的稳定区域。对于一类数据包到达分布,我们证明了队列的平稳分布具有正相关和强正相关性质;这就给出了稳定区域的外边界。我们还表明,如果对于队列的平稳分布可以显示推测的“敏感单调性”性质,那么无论数据包到达分布如何,稳定区域和吞吐量区域的闭包之间的等价性都是直接的结果
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引用次数: 1
Achieving the DMD tradeoff of the MIMO-ARQ channel 实现MIMO-ARQ信道的DMD折衷
S. Pawar, K. R. Kumar, P. V. Kumar, P. Elia, B. Sethuraman
For the quasi-static, Rayleigh-fading MIMO channel with nt transmit and nr receive antennas, Zheng and Tse showed that there exists a fundamental tradeoff between diversity and multiplexing gains, referred to as the diversity-multiplexing gain (D-MG) tradeoff. Explicit constructions for D-MG optimal ST codes are now available. In a subsequent paper, El Gamal, Caire and Damen considered signaling across the quasi-static ST channel using an L-round ARQ protocol that assumes the presence of a noiseless feedback channel capable of conveying one bit of information (ACK or NACK) per use of the feedback channel. They showed that given a fixed number of ARQ rounds L, there is a tradeoff between diversity and multiplexing gains under which the optimum diversity gain of the ARQ channel transmitting R = r log(SNR) bits per channel use, is that of the quasi-static channel without feedback investigated by Zheng and Tse, transmitting at (1/L)th the information rate. This tradeoff, which now is a function of the number L of ARQ rounds, is termed the diversity-multiplexing gain-delay (DMD) tradeoff. In the current paper, a sufficient condition under which a ST code will achieve the DMD tradeoff is presented for the case nr ges nt. The cyclic-division-algebra-based constructions of DMG optimal ST codes by Elia et. al. are then modified to yield codes which meet this sufficient criterion and are thereby DMD-optimal. This modification requires that either nt|L or L|nt
对于具有nt发射天线和nr接收天线的准静态瑞利衰落MIMO信道,Zheng和Tse表明在分集和复用增益之间存在基本的权衡,称为分集-复用增益(D-MG)权衡。D-MG最优ST规范的显式结构现在是可用的。在随后的一篇论文中,El Gamal, Caire和Damen考虑了使用l轮ARQ协议跨准静态ST信道的信令,该协议假设存在一个能够在每次使用反馈信道时传输1位信息(ACK或NACK)的无噪声反馈信道。他们表明,给定固定数量的ARQ轮数L,在分集增益和复用增益之间存在权衡,在这种情况下,每通道使用R = R log(SNR)比特的ARQ信道的最佳分集增益是Zheng和Tse研究的无反馈的准静态信道的分集增益,以(1/L)的信息速率传输。这种权衡现在是ARQ轮数L的函数,称为分集复用增益延迟(DMD)权衡。在本文中,本文给出了一个充分条件,在此条件下,ST码将实现DMD权衡。然后修改Elia等人基于循环除法代数的DMG最优ST码结构,以产生满足该充分准则的码,从而实现DMD最优。这个修改要求nt|L或L|nt
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引用次数: 4
STBC-schemes with non-vanishing determinant for certain number of transmit antennas 对于一定数量的发射天线,具有不消失行列式的stbc方案
K. Gowda, B. Rajan
This paper presents a systematic technique for constructing STBC-schemes (space-time block code schemes) with non-vanishing determinant, based on cyclic division algebras. Prior constructions of STBC-schemes with non-vanishing determinant are available only for 2,3,4 and 6 transmit antennas. In this paper, by using an appropriate representation of a cyclic division algebra over a maximal subfield, we construct STBC-schemes with non-vanishing determinant for the number of transmit antennas of the form 2k or 3middot2k or 2middot3k or qk(q - 1)/2, where q is a prime of the form 4s + 3 and s is any arbitrary integer. In a recent work, Elia et. al. have proved that non-vanishing determinant is a sufficient condition for STBC-schemes from cyclic division algebra to achieve the optimal diversity-multiplexing gain (D-MG) tradeoff; thus proving that the STBC-schemes constructed in this paper achieve the optimal D-MG tradeoff
本文提出了一种基于循环除法代数的非消失行列式空时分组码格式的系统构造技术。现有的非消失行列式stbc方案仅适用于2、3、4和6发射天线。本文利用极大子域上循环除法代数的适当表示,构造了形式为2k或3middot2k或2middot3k或qk(q - 1)/2的发射天线数具有非消失行列式的stbc -格式,其中q是4s + 3形式的素数,s是任意整数。在最近的一项工作中,Elia等人证明了非消失行列式是循环除法代数的stbc -方案实现最优分集-复用增益(D-MG)权衡的充分条件;从而证明本文构造的stbc -方案实现了最优的D-MG权衡
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引用次数: 71
Capacity approaching turbo coding for half duplex relaying 容量接近半双工中继的涡轮编码
Zheng Zhang, T. Duman
In this paper, we develop capacity approaching turbo coding schemes for half-duplex relay systems as an extension of our previous work on the full-duplex relay systems. We design the codes to be used at the source and the relay nodes, and develop an information combining technique at the destination node. In addition, by utilizing information theoretical results, we compute the optimal fraction of time during which the relay node should listen, and use it in the design of capacity approaching coding/decoding schemes. We observe that the performance of the practical coding schemes proposed is about 1.2 dB away from the theoretical limits (for a variety of channel models)
在本文中,我们开发了半双工中继系统的容量逼近turbo编码方案,作为我们之前对全双工中继系统工作的扩展。我们设计了用于源节点和中继节点的码,并开发了用于目的节点的信息组合技术。此外,利用信息论的结果,我们计算了中继节点应该侦听的最佳时间分数,并将其用于容量逼近编码/解码方案的设计。我们观察到,所提出的实际编码方案的性能与理论极限(对于各种信道模型)相差约1.2 dB。
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引用次数: 8
Space-time constellation design for partial CSI at the receiver 接收机部分CSI的时空星座设计
J. Giese, M. Skoglund
We consider the design of space-time constellations when the channel state information that is available at the receiver is an estimate of the channel coefficients with known error covariance. This setup encompasses the well-studied scenarios of perfect and no channel knowledge and allows a smooth transition between these two cases. We perform an asymptotic pairwise error probability analysis and derive a criterion to design constellations matched to the level of channel knowledge available at the receiver. Moreover, we use the criterion to assess the power tradeoff between data transmission and channel coefficient acquisition for any given specific set of constellations. Simulation results illustrate the benefit of the proposed criterion
当接收端可用的信道状态信息是已知误差协方差的信道系数估计时,我们考虑了时空星座的设计。这种设置包含了经过充分研究的完美和没有渠道知识的场景,并允许在这两种情况之间顺利过渡。我们执行渐近成对误差概率分析,并推导出一个标准来设计与接收机可用信道知识水平相匹配的星座。此外,我们使用该准则来评估任何给定特定星座集的数据传输和信道系数采集之间的功率权衡。仿真结果表明了该准则的有效性
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引用次数: 1
Achievable diversity-multiplexing-delay tradeoff in half-duplex ARQ relay channels 半双工ARQ中继信道中可实现的分集-复用-延迟权衡
T. Tabet, S. Dusad, R. Knopp
In this paper, we present an efficient protocol for the delay-limited fading automatic retransmission request single relay channel. The source is using an ARQ retransmission protocol to send data to the relay and the destination. When the relay is able to decode, both the relay and the source send the same data to the destination providing additional gains. The proposed protocol exploits two kinds of diversity: (i) space diversity available through the cooperative (relay) terminal, which retransmits the source's signals, (ii) ARQ diversity obtained by leveraging the retransmission delay to enhance the reliability. The performance characterization is in terms of the achievable diversity, multiplexing gain and delay tradeoff for a high signal-to-noise ratio (snr) regime
本文提出了一种有效的单中继信道时延限制衰落自动重传协议。源端使用ARQ重传协议向中继端和目的端发送数据。当中继能够解码时,中继和源都将相同的数据发送到目的地,从而提供额外的增益。提出的协议利用了两种分集:(1)通过合作(中继)终端获得的空间分集,它可以重传源的信号;(2)利用重传延迟获得的ARQ分集来提高可靠性。性能表征是根据可实现的分集,多路复用增益和高信噪比(snr)制度的延迟权衡
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引用次数: 24
Martingales and information divergence 鞅和信息散度
P. Harremoës
A new maximal inequality for non-negative martingales is proved. It strengthens a well-known maximal inequality by Doob, and it is demonstrated that the stated inequality is tight. The inequality emphasizes the relation between martingales and information divergence. It implies pointwise convergence of X log X bounded martingales. A similar inequality holds for ergodic sequences. Relations to the Shannon-McMillan-Breiman theorem and Markov chains are mentioned
证明了非负鞅的一个新的极大不等式。它加强了Doob的一个著名的极大不等式,并证明了所述不等式是紧的。不等式强调了鞅与信息发散之间的关系。它暗示了X log X有界鞅的逐点收敛。一个类似的不等式也适用于遍历序列。给出了与Shannon-McMillan-Breiman定理和Markov链的关系
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引用次数: 2
期刊
International Symposium on Information Theory and its Applications. International Symposium on Information Theory and its Applications
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