N. Cai

Publications (19)15.53 Total impact

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  Available from: mathematik.uni-bielefeld.de

  Chapter: Search with Noisy and Delayed Responses

  R. Ahlswede, N. Cai
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  ABSTRACT: It is well–known that search problems with a stochastic response matrix acting independently for the questions can be equivalently formulated as transmission problems for a discrete memoryless channel (DMC) with feedback. This is explained in Chapter 3 of the book Search Problems by R. Ahlswede and I. Wegener (Wiley 1987, translation of Suchprobleme, Teubner 1979). There also Ahlswede’s coding scheme for the DMC and also for the arbitrarily varying channel (AVC) achieving the capacities are described. The latter can be viewed as a robust model for search. In this paper we analyse this robust model with a time delay for the noiseless feedback. In the terminology of search this means that the answers are given with delay. We determine the (asymptotically) optimal performances, that is, find the capacities, for the cases where the delay is constant and linear in the blocklength. Finally we also give the corresponding results for the DMC with zero–error probability. KeywordsSearch-noisy responses-liers-delay-feedback-list codes-0–error capacity
  12/2006: pages 695-703;
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  Available from: mathematik.uni-bielefeld.de

  Chapter: A Strong Converse Theorem for Quantum Multiple Access Channels

  R. Ahlswede, N. Cai
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  ABSTRACT: With the wringing technique developed by the first author for classical multiple access channels we show that the strong converse theorem holds also for quantum multiple access channels, if classical messages are transmitted. Keywordsclassical quantum multiple access channel-strong converse-wringing technique-non–stationary memoryless classical quantum channel
  12/2006: pages 460-485;
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  Available from: math.uni-bielefeld.de

  Chapter: Codes with the Identifiable Parent Property and the Multiple-Access Channel

  R. Ahlswede, N. Cai
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  ABSTRACT: We begin with I. The identifiable parent property and some first results about it If C{\mathcal C} is a q–ary code of length n and a n and b n are two codewords, then c n is called a descendant of a n and b n if c t ∈{a t , b t } for t=1,...,n. We are interested in codes C{\mathcal C} with the property that, given any descendant c n , one can always identify at least one of the ‘parent’ codewords in C{\mathcal C}. We study bounds on F(n,q), the maximal cardinality of a code C{\mathcal C} with this property, which we call the identifiable parent property. Such codes play a role in schemes that protect against piracy of software.
  12/2006: pages 249-257;
• Source

  Available from: uni-bielefeld.de

  Chapter: Watermarking Identification Codes with Related Topics on Common Randomness

  R. Ahlswede, N. Cai
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  ABSTRACT: Watermarking identification codes were introduced by Y. Steinberg and N. Merhav. In their model they assumed that (1) the attacker uses a single channel to attack the watermark and both,the information hider and the decoder, know the attack channel; (2) the decoder either completely he knows the covertext or knows nothing about it. Then instead of the first assumption they suggested to study more robust models and instead of the second assumption they suggested to consider the case where the information hider is allowed to send a secret key to the decoder according to the covertext. In response to the first suggestion in this paper we assume that the attacker chooses an unknown (for both information hider and decoder) channel from a set of channels or a compound channel, to attack the watermark. In response to the second suggestion we present two models. In the first model according to the output sequence of covertext the information hider generates side information componentwise as the secret key. In the second model the only constraint to the key space is an upper bound for its rate. We present lower bounds for the identification capacities in the above models, which include the Steinberg and Merhav results on lower bounds. To obtain our lower bounds we introduce the corresponding models of common randomness. For the models with a single channel, we obtain the capacities of common randomness. For the models with a compound channel, we have lower and upper bounds and the differences of lower and upper bounds are due to the exchange and different orders of the max–min operations. KeywordsWatermarking-identification-compound channel-common randomness
  12/2006: pages 107-153;
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  Available from: mathematik.uni-bielefeld.de

  Chapter: Secrecy Systems for Identification Via Channels with Additive-Like Instantaneous Block Encipherer

  R. Ahlswede, N. Cai, Z. Zhang
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  ABSTRACT: In this paper we propose a model of secrecy systems for identification via channels with ALIB encipherers and find the smallest asymptotic key rate of the ALIB encipherers needed for the requirement of security.
  08/2006: pages 285-292;
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  Available from: citeseerx.ist.psu.edu

  Chapter: Appendix: On Edge–Isoperimetric Theorems for Uniform Hypergraphs

  R. Ahlswede, N. Cai
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  ABSTRACT: Denote by Ω={1,...,n} an n–element set. For all A,B Î \binomWkA,B\in\binom{\Omega}k, the k–element subsets of Ω, define the relation ~ as follows: A~B iff A and B have a common shadow, i.e. there is a C Î \binomWk-1C\in\binom{\Omega}{k-1} with C ⊂A and C ⊂B. For fixed integer α, our goal is to find a family A{\mathcal A} of k–subsets with size α, having as many as possible ~–relations for all pairs of its elements. For k=2 this was achieved by Ahlswede and Katona [2] many years ago.
  08/2006: pages 979-1005;
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  Available from: mathematik.uni-bielefeld.de

  Chapter: Transmission, Identification and Common Randomness Capacities for Wire-Tape Channels with Secure Feedback from the Decoder

  R. Ahlswede, N. Cai
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  ABSTRACT: We analyze wire-tape channels with secure feedback from the legitimate receiver. We present a lower bound on the transmission capacity (Theorem 1), which we conjecture to be tight and which is proved to be tight (Corollary 1) for Wyner’s original (degraded) wire-tape channel and also for the reversely degraded wire-tape channel for which the legitimate receiver gets a degraded version from the enemy (Corollary 2). Somewhat surprisingly we completely determine the capacities of secure common randomness (Theorem 2) and secure identification (Theorem 3 and Corollary 3). Unlike for the DMC, these quantities are different here, because identification is linked to non-secure common randomness.
  08/2006: pages 258-275;
• Article: Introduction to the Special Issue on Networking and Information Theory

  N. Cai, M. Chiang, M. Effros, R. Koetter, M. Medard, B. Prabhakar, R. Srikant, D. Towsley, R.W. Yeung
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  ABSTRACT: Not Available
  IEEE Transactions on Information Theory 07/2006; 52(6):2285-2288. · 3.01 Impact Factor
• Article: A separation theorem for single-source network coding

  L. Song, R.W. Yeung, N. Cai
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  ABSTRACT: In this paper, we consider a point-to-point communication network of discrete memoryless channels. In the network, there are a source node and possibly more than one sink node. Information is generated at the source node and is multicast to each sink node. We allow a node to encode its received information before loading it onto an outgoing channel, where the channels are independent of each other. We also allow the nodes to pass along messages asynchronously. In this paper, we characterize the admissibility of single-source multi-sink communication networks. Our result can be regarded as a network generalization of Shannon's result that feedback does not increase the capacity of a discrete memoryless channels (DMCs), and it implies a separation theorem for network coding and channel coding in such a communication network.
  IEEE Transactions on Information Theory 06/2006; · 3.01 Impact Factor
• Book: Network Coding Theory

  R ~W Yeung, S-Y ~R Li, N Cai, Z Zhang
  01/2005; now Publishers.
• Article: Quantum privacy and quantum wiretap channels

  N. Cai, A. Winter, R. W. Yeung
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  ABSTRACT: Following Schumacher and Westmoreland, we address the problem of the capacity of a quantum wiretap channel. We first argue that, in the definition of the so-called quantum privacy, Holevo quantities should be used instead of classical mutual informations. The argument actually shows that the security condition in the definition of a code should limit the wiretappers Holevo quantity. Then we show that this modified quantum privacy is the optimum achievable rate of secure transmission.
  Problems of Information Transmission 09/2004; 40(4):318-336. · 0.48 Impact Factor
• Conference Proceeding: Secure Network Coding

  N Cai, R ~W Yeung
  Proceedings of IEEE International Symposium on Information Theory; 01/2002
• Article: A counterexample in rate-distortion theory for correlated sources

  R. Ahlswede, N. Cai
  Applied Mathematics Letters 01/1999; 12(7):1-3. · 1.37 Impact Factor
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  Available from: psu.edu

  Article: Higher Level Extremal Problems

  R. Ahlswede, N. Cai
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  ABSTRACT: this paper are exact and asymptotic results for the restricted and the unrestricted case for the relations "comparable", "disjoint" and "intersecting". Key tools are results on related graph coloring problems (Theorem 1 in Section 2 and Theorem 2 in Section 3). Our results on families of "comparable" clouds, of clouds with the "disjoint" relation and of clouds with the "intersecting" relation appear in Sections 4, 5, and 6. The following chart is for the orientation of the reader about the present state of our knowledge about the various problems. Here we make the Conventions:
  08/1998;
• Article: Zero-error capacity for models with memory and the enlightened dictator channel

  R. Ahlswede, N. Cai, Z. Zhang
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  ABSTRACT: We present a general class of zero-error capacity problems with memory covering known cases such as coding for error correction and many new cases. This class can be incorporated into a model of channels with memory, which thus are shown to give a unification of a multitude of seemingly very different coding problems. We analyze a seemingly basic channel in this class
  IEEE Transactions on Information Theory 06/1998; · 3.01 Impact Factor
• Article: On interactive communication

  R. Ahlswede, N. Cai, Z. Zhang
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  ABSTRACT: Ahlswede has previously introduced an abstract correlated source (𝒱×𝒲,S) with outputs (υ, ω)∈S⊂𝒱×𝒲, where persons P_𝒱 and P_𝒲 observe υ and ω, respectively. More recently, Orlitsky considered the minimal number C _m of bits to be transmitted in m rounds to “inform P _𝒲 about υ over one channel.” He showed that C ₂⩽4C_∞+3 and that in general C₂NOT~C_∞. We give a simple example for C₃NOT~C_∞. However, for the new model “inform P_𝒲 over two channels”, four rounds are optimal for this example-a result we conjecture in general. If both P_𝒱 and P_𝒲 are to be informed over two channels about the other outcome, we determine asymptotically the complexities for all sources. In our last model “inform P_𝒱 and P_𝒲 over one channel” for all sources the total number T₂ of required bits is known asymptotically and T_∞ is bounded from below in terms of average degrees. There are exact results for several classes of regular sources. An attempt is made to discuss the methods of the subject systematically
  IEEE Transactions on Information Theory 02/1997; · 3.01 Impact Factor
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  Available from: uni-bielefeld.de

  Article: Two proofs of Pinsker's conjecture concerning arbitrarily varying channels

  R. Ahlswede, N. Cai
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  ABSTRACT: M.S. Pinsker (1990) conjectured the following theorem: for an arbitrary varying channel (AVC), every rate below the random code capacity is achievable with deterministic list codes of constant list size, if the average error criterion is used. Two proofs of this theorem are given
  IEEE Transactions on Information Theory 12/1991; · 3.01 Impact Factor
• Conference Proceeding: Arbitrarily varying multiple-access channels. II. Correlatedsender's side information, correlated messages, and ambiguoustransmission

  R. Ahlswede, N. Cai
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  ABSTRACT: For pt.I see ibid., p.22 (1997). We have shown previously how a memoryless correlated source (MCS) helps the transmission over an arbitrarily varying channel (AVC). For an arbitrarily varying multiple access channel (AMAC), defined by a set of stochastic matrices, the effect of the MCS is investigated. It is well-known that the dependency structure of a MCS may enlarge the achievable region of a MAC. The the question of whether we can transmit the outputs of a MCS at positive rates via some AVMAC satisfying the symmetrizability conditions is also addressed
  Information Theory. 1997. Proceedings., 1997 IEEE International Symposium on;
• Conference Proceeding: Arbitrarily varying multiple-access channels. I. Ericson'ssymmetrizability is adequate, Gubner's conjecture is true

  R. Ahlswede, N. Cai
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  ABSTRACT: Ericson's conjecture has been established by Csiszar and Narayan (1988). In the theory of identification the cycle closes: both, the non-single letter separability by random words and symmetrizability are used and needed. Gubner extends the decoding rule of Csiszar and Narayan to the multiple-access situation by following “conditional decoding”. This is a suboptimal decoding rule, but was suited for the discovery of the capacity theorem for the multiple-access channel (MAC). Its drawback for systems of channels was soon realized by Ahlswede (1974), where for the derivation of the capacity theorem for the compound MAC maximum likelihood decoding could be analysed. For the arbitrarily varying MAC (AVMAC) suboptimality of the conditional decoding rule becomes even more significant. The authors examine if Gubner's conjecture is true
  Information Theory. 1997. Proceedings., 1997 IEEE International Symposium on;
• Conference Proceeding: Network error correction

  N. Cai, R.W. Yeung
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  ABSTRACT: This paper discusses the error correction in all existing communication networks which is done on a link-by-link approach. We define a network coding and a distributed error correction in a network is considered when a source message is transmitted to a set of receiving nodes on a network. Network generalizations of the Hamming bound and Gilbert-Varshamov bound are obtained.
  Information Theory, 2003. Proceedings. IEEE International Symposium on;