Ning Cai

Xidian University, Ch’ang-an, Shaanxi, China

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Publications (115)84.97 Total impact

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    Binyue Liu, Ning Cai
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    Binyue Liu, Ning Cai
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    ABSTRACT: We study a two-hop multiple access channel (MAC), where two source nodes communicate with the destination node via a set of amplify-and-forward (AF) relays. To characterize the optimal rate region, we focus on deriving the boundary points of it, which is formulated as a weighted sum rate maximization problem. In the first part, we are concerned with the scenario that all relays are under a sum power constraint. Although the optimal AF rate region for the case has been obtained, we revisit the results by an alternative method. The first step is to investigate the algebraic structures of the three SNR functions in the rate set of the two-hop MAC with a specific AF scheme. Then an equivalent optimization problem is established for deriving each boundary point of the optimal rate region. From the geometric perspective, the problem has a simple solution by optimizing a one-dimensional problem without constraint. In the second part, the optimal rate region of a two-hop MAC under the individual power constraints is discussed, which is still an open problem. An algorithm is proposed to compute the maximum individual and sum rates along with the corresponding AF schemes.
    Lecture Notes in Computer Science 03/2013; 7777:44-70.
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    ABSTRACT: We determine the secrecy capacity of the compound channel with quantum wiretapper and channel state information at the transmitter. Moreover, we derive a lower bound on the secrecy capacity of this channel without channel state information and determine the secrecy capacity of the compound classical-quantum wiretap channel with channel state information at the transmitter. We use this result to derive a new proof for a lower bound on the entanglement generating capacity of compound quantum channel. We also derive a new proof for the entanglement generating capacity of compound quantum channel with channel state information at the encoder.
    02/2013;
  • Binyue Liu, Ye Yang, Ning Cai
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    ABSTRACT: This paper investigates amplify-and-forward (AF) schemes for both one and two-way relay channels. Unlike most existing works assuming independent noise at the relays, we consider a more general scenario with correlated relay noise. We first propose an approach to efficiently solve a class of quadratically constrained fractional problems via second-order cone programming (SOCP). Then it is shown that the AF relay optimization problems studied in this paper can be incorporated into such quadratically constrained fractional problems. As a consequence, the proposed approach can be used as a unified framework to solve the optimal AF rate for the one-way relay channel and the optimal AF rate region for the two-way relay channel under both sum and individual relay power constraints. In particular, for one-way relay channel under individual relay power constraints, we propose two suboptimal AF schemes in closed-form. It is shown that they are approximately optimal in certain conditions of interest. Furthermore, we find an interesting result that, on average, noise correlation is beneficial no matter the relays know the noise covariance matrix or not for such scenario. Overall, the obtained results recover and generalize several existing results for the uncorrelated counterpart. (unsubmitted)
    01/2013;
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    Binyue Liu, Ning Cai
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    ABSTRACT: In this paper, we study the performance of an amplify-and-forward (AF) based analog network coding (ANC) relay scheme in a multi-hop wireless network under individual power constraints. In the first part, a unicast scenario is considered. The problem of finding the maximum achievable rate is formulated as an optimization problem. Rather than solving this non-concave maximization problem, we derive upper and lower bounds for the optimal rate. A cut-set like upper bound is obtained in a closed form for a layered relay network. A pseudo-optimal AF scheme is developed for a two-hop parallel network, which is different from the conventional scheme with all amplification gains chosen as the maximum possible values. The conditions under which either the novel scheme or the conventional one achieves a rate within half a bit of the upper bound are found. Then we provide an AF-based multi-hop ANC scheme with the two schemes for a layered relay network. It is demonstrated that the lower bound of the optimal rate can asymptotically achieve the upper bound when the network is in the generalized high-SNR regime. In the second part, the optimal rate region for a two-hop multiple access channel (MAC) via AF relays is investigated. In a similar manner, we first derive an outer bound for it and then focus on designing low complexity AF-based ANC schemes for different scenarios. Several examples are given and the numerical results indicate that the achievable rate region of the ANC schemes can perform close to the outer bound.
    03/2012;
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    ABSTRACT: We determine the capacity of the classical compound quantum wiretapper channel with channel state information at the transmitter. Moreover we derive a lower bound on the capacity of this channel without channel state information and determine the capacity of the classical quantum compound wiretap channel with channel state information at the transmitter.
    02/2012;
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    ABSTRACT: In this paper, a time-variant decoding model of a convolutional network code (CNC) is proposed. New necessary and sufficient conditions are established for the decodability of a CNC at a node r with delay L. They only involve the first L+1 terms in the power series expansion of the global encoding kernel matrix at r. Concomitantly, a time-variant decoding algorithm is proposed with a decoding matrix over the base symbol field. The present time-variant decoding model only deals with partial information of the global encoding kernel matrix, and hence potentially makes CNCs applicable in a decentralized manner.
    IEEE Communications Letters 01/2012; 16(10):1656-1659. · 1.16 Impact Factor
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    ABSTRACT: In this paper, convolutional network coding is formulated by means of matrix power series representation of the local encoding kernel (LEK) matrices and global encoding kernel (GEK) matrices to establish its theoretical fundamentals for practical implementations. From the encoding perspective, the GEKs of a convolutional network code (CNC) are shown to be uniquely determined by its LEK matrix $K(z)$ if $K_0$, the constant coefficient matrix of $K(z)$, is nilpotent. This will simplify the CNC design because a nilpotent $K_0$ suffices to guarantee a unique set of GEKs. Besides, the relation between coding topology and $K(z)$ is also discussed. From the decoding perspective, the main theme is to justify that the first $L+1$ terms of the GEK matrix $F(z)$ at a sink $r$ suffice to check whether the code is decodable at $r$ with delay $L$ and to start decoding if so. The concomitant decoding scheme avoids dealing with $F(z)$, which may contain infinite terms, as a whole and hence reduces the complexity of decodability check. It potentially makes CNCs applicable to wireless networks.
    09/2011;
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    Binyue Liu, Ning Cai
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    ABSTRACT: In a recent paper [4], Mari\'c et al. analyzed the performance of the analog network coding (ANC) in a layered relay network for the high-SNR regime. They have proved that under the ANC scheme, if each relay transmits the received signals at the upper bound of the power constraint, the transmission rate will approach the network capacity. In this paper, we consider a more general scenario defined as the generalized high-SNR regime, where the relays at layer $l$ in a layered relay network with $L$ layers do not satisfy the high-SNR conditions, and then determine an ANC relay scheme in such network. By relating the received SNR at the nodes with the propagated noise, we derive the rate achievable by the ANC scheme proposed in this paper. The result shows that the achievable ANC rate approaches the upper bound of the ANC capacity as the received powers at relays in high SNR increase. A comparison of the two ANC schemes implies that the scheme proposed in [4] may not always be the optimal one in the generalized high-SNR regime. The result also demonstrates that the upper and lower bounds of the ANC rate coincide in the limit as the number of relays at layer L-1 dissatisfying the high-SNR conditions tends to infinity, yielding an asymptotic capacity result.
    06/2011;
  • Ning Cai, T. Chan
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    ABSTRACT: In this tutorial paper, we focus on the basic theory of linear secure network coding. Our goal is to present fundamental results and provide preliminary knowledge for anyone interested in the area. We first present a model for secure network coding and then a necessary and sufficient condition for a linear network code to be secure. Optimal methods to construct linear secure network codes are also provided. For further investigation of the secure properties of linear network codes, we illuminate different secure criteria and requirements, with a few alternative models.
    Proceedings of the IEEE 04/2011; · 6.91 Impact Factor
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    ABSTRACT: We propose an efficient Adaptive Random Convolutional Network Coding (ARCNC) algorithm to address the issue of field size in random network coding. ARCNC operates as a convolutional code, with the coefficients of local encoding kernels chosen randomly over a small finite field. The lengths of local encoding kernels increase with time until the global encoding kernel matrices at related sink nodes all have full rank. Instead of estimating the necessary field size a priori, ARCNC operates in a small finite field. It adapts to unknown network topologies without prior knowledge, by locally incrementing the dimensionality of the convolutional code. Because convolutional codes of different constraint lengths can coexist in different portions of the network, reductions in decoding delay and memory overheads can be achieved with ARCNC. We show through analysis that this method performs no worse than random linear network codes in general networks, and can provide significant gains in terms of average decoding delay in combination networks.
    03/2011;
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    Ning Cai, R.W. Yeung
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    ABSTRACT: In the paradigm of network coding, the nodes in a network are allowed to encode the information received from the input links. With network coding, the full capacity of the network can be utilized. In this paper, we propose a model, call the wiretap network, that incorporates information security with network coding. In this model, a collection of subsets of the channels in the network is given, and a wiretapper is allowed to access any one (but not more than one) of these subsets without being able to obtain any information about the message transmitted. Our model includes secret sharing in classical cryptography as a special case. We present a construction of secure linear network codes that can be used provided a certain graph-theoretic condition is satisfied. We also prove the necessity of this condition for the special case that the wiretapper may choose to access any subset of channels of a fixed size. The optimality of our code construction is established for this special case. Finally, we extend our results to the scenario when the wiretapper is allowed to obtain a controlled amount of information about the message.
    IEEE Transactions on Information Theory 02/2011; · 2.62 Impact Factor
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    ABSTRACT: A condition governing the possibility and impossibility of linear independence among the global encoding kernels of a linear network code is found. Based on this condition, we propose several alternative definitions of generic network codes, which give interpretations of such codes from different perspectives. We also present a unified framework for specifying and constructing different classes of linear network codes. Finally, using the insight obtained from the unified framework, we show that the proofs of some existing results regarding generic network codes can be greatly simplified.
    IEEE Transactions on Information Theory 02/2011; · 2.62 Impact Factor
  • IEEE Transactions on Information Theory. 01/2011; 57:416-423.
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    Ning Cai, Raymond W. Yeung
    IEEE Transactions on Information Theory 01/2011; 57:424-435. · 2.62 Impact Factor
  • Ning Cai
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    ABSTRACT: In this work we extend localized error correction codes introduced by L. A. Bassalygo et al from point-to-point coding to non-coherent network coding. We have a lower bound and an upper bound of the capacity, which are tight when the sum of two times of the dimension of the codewords and the dimension of error configurations does not exceed the dimension of the ground space.
    01/2011;
  • Ning Cai, T. Chan, A. Grant
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    ABSTRACT: The arbitrarily varying channel can be modeled as communication in the presence of a jammer. In this paper we propose a new model: a jammer who knows the channel input, and where the transmitter and receiver share a secret random key. Shared randomness differentiates this scenario from the case where the jammer knows the message. For sufficiently large key rate, we determine the capacity of this channel (which may be strictly smaller than the case where the jammer knows only the message). We also provide an upper bound on the minimum key rate required to achieve capacity. We prove that additionally revealing the message to the jammer does not change the capacity, provided the key rate is sufficiently large. This new capacity result differs from existing results for the AVC, and in fact coincides with a well-known upper bound on the deterministic coding capacity of the AVC with maximum error. Without secret keys, our problem degenerates to deterministic coding for the AVC with maximum probability of error, a well-known hard problem. Our results demonstrate that knowledge of the channel input is better than knowledge of the message for the jammer.
    Information Theory Proceedings (ISIT), 2010 IEEE International Symposium on; 07/2010
  • Wangmei Guo, Ning Cai
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    ABSTRACT: In this paper, we derive a lower bound on the minimum decoding delay for convolutional network codes, which provides us with a guide line in the performance of decoding delay for convolutional network code decoders. The lower bound can be achievable by the sequential decoder introduced by E. Erez and F. Feder. Then we discuss the relationship between the network topology and the minimum decoding delay. Finally, we illustrate our results by an example.
    IEICE Transactions. 01/2010; 93-A:1518-1523.
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    T. Chan, Ning Cai, A. Grant
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    ABSTRACT: This paper considers a key agreement problem in which two parties aim to agree on a key by exchanging messages in the presence of adversarial tampering. The aim of the adversary is to disrupt the key agreement process, but there are no secrecy constraints (i.e. we do not insist that the key is kept secret from the adversary). The main results of the paper are coding schemes and bounds on maximum key generation rates for this problem.
    Information Theory, 2009. ISIT 2009. IEEE International Symposium on; 08/2009
  • Ning Cai
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    ABSTRACT: Motivated by the fact that the most problems on network coding can be represented as how much information about a given subset of network inputs can be obtained by legal or illegal users from the channels accessed by them, in this paper we investigate the relation between a subset of random network inputs and the outputs of an arbitrarily given set of channels in networks. We focus on linear network codes because they are widely studied and applied. We begin with the algebraic structure of cosets of linear subspaces and derive bounds on their mutual information and the conditions for their tightness. To apply the results to random linear network coding we introduce strongly generic linear network codes such that for sufficiently large coding fields a random linear network code is strongly generic with high probability. Our results show that random linear network coding is good for error correction and security but not efficient for multiple source network coding.
    Information Theory, 2009. ISIT 2009. IEEE International Symposium on; 08/2009