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Information Theory, IEEE Transactions on

Issue 5 • Date May 2012

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Displaying Results 1 - 25 of 54
  • Table of contents

    Publication Year: 2012 , Page(s): C1 - C4
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  • IEEE Transactions on Information Theory publication information

    Publication Year: 2012 , Page(s): C2
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  • Least Squares Superposition Codes of Moderate Dictionary Size Are Reliable at Rates up to Capacity

    Publication Year: 2012 , Page(s): 2541 - 2557
    Cited by:  Papers (9)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (629 KB) |  | HTML iconHTML  

    For the additive white Gaussian noise channel with average codeword power constraint, coding methods are analyzed in which the codewords are sparse superpositions, that is, linear combinations of subsets of vectors from a given design, with the possible messages indexed by the choice of subset. Decoding is by least squares (maximum likelihood), tailored to the assumed form of codewords being linear combinations of elements of the design. Communication is shown to be reliable with error probability exponentially small for all rates up to the Shannon capacity. View full abstract»

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  • Analysis of the Second Moment of the LT Decoder

    Publication Year: 2012 , Page(s): 2558 - 2569
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (353 KB) |  | HTML iconHTML  

    In this paper, the second moment of the ripple size during the Luby transform (LT) decoding process is analyzed. Combined with a result by Karp et al. (2004) stating that the expectation of the ripple size is of the order of k , our study gives bounds on the error probability of the LT decoder. Furthermore, an analytic expression for the variance of the ripple size up to terms of constant order is given, and the expression of Karp et al. for the expectation of the ripple size is refined up to terms of the order of 1/k. This provides a first step toward an analytic finite-length analysis of LT decoding. View full abstract»

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  • The Performance of Serial Turbo Codes Does Not Concentrate

    Publication Year: 2012 , Page(s): 2570 - 2588
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (526 KB) |  | HTML iconHTML  

    Minimum distances and maximum likelihood error probabilities of serial turbo codes with uniform interleaver are analyzed. It is shown that, for a fraction of interleavers approaching one as the block-length grows large, the minimum distance of serial turbo codes grows as a positive power of their block-length, while their error probability decreases exponentially fast in some positive power of their block-length, on sufficiently good memoryless channels. Such a typical code behavior contrasts the performance of the average serial turbo code, whose error probability is dominated by an asymptotically negligible fraction of poorly performing interleavers, and decays only as a negative power of the block-length. The analysis proposed in this paper relies on precise bounds of the minimum distance of the typical serial turbo code, whose scaling law is shown to depend both on the free distance of its outer constituent encoder, which determines the exponent of its sub-linear growth in the block-length, and on the effective free distance of its inner constituent encoder. The latter is defined as the smallest weight of codewords obtained when the input word of the inner encoder has weight two, and appears as a linear scaling factor for the minimum distance of the typical serial turbo code. Hence, despite the lack of concentration of the maximum likelihood error probability around its expected value, the main design parameters suggested by the average-code analysis turn out to characterize also the performance of the typical serial turbo code. By showing for the first time that the typical serial turbo code's minimum distance scales linearly in the effective free distance of the inner constituent encoder, the presented results generalize, and improve upon, the probabilistic bounds of Kahale and Urbanke, as well as the deterministic upper bound of Bazzi, Mahdian, and Spielman, where only the dependence on the outer encoder's free distance was proved. View full abstract»

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  • Bases for Riemann–Roch Spaces of One-Point Divisors on an Optimal Tower of Function Fields

    Publication Year: 2012 , Page(s): 2589 - 2598
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (267 KB) |  | HTML iconHTML  

    For applications in algebraic geometric codes, an explicit description of bases of Riemann-Roch spaces of divisors on function fields over finite fields is needed. We give an algorithm to compute such bases for one-point divisors, and Weierstrass semigroups over an optimal tower of function fields. We also explicitly compute Weierstrass semigroups till level eight. View full abstract»

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  • Subspace Properties of Network Coding and Their Applications

    Publication Year: 2012 , Page(s): 2599 - 2619
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (649 KB) |  | HTML iconHTML  

    Systems that employ network coding for content distribution convey to the receivers linear combinations of the source packets. If we assume randomized network coding, during this process, the network nodes collect random subspaces of the space spanned by the source packets. We establish several fundamental properties of the random subspaces induced in such a system and show that these subspaces implicitly carry topological information about the network and its state that can be passively collected and inferred. We leverage this information toward a number of applications that are interesting in their own right, such as topology inference, bottleneck discovery in peer-to-peer systems, and locating Byzantine attackers. We thus argue that randomized network coding, apart from its better known properties for improving information delivery rate, can additionally facilitate network management and control. View full abstract»

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  • Performance Analysis of Differential Space–Time Modulation

    Publication Year: 2012 , Page(s): 2620 - 2632
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2529 KB) |  | HTML iconHTML  

    In this paper, we analyze the performance of the differential space-time modulation (DSTM) in Rayleigh fading channels. By using the moment-generating function (MGF)-based approach, we derive a number of closed-form expressions for the pairwise error probability (PEP) of the DSTM in various fading environments. For spatially independent channels, we derive a closed-form expression for the exact PEP of the DSTM for both slow- and fast-fading cases. In the case of fast-fading channels, we show that an irreducible error floor exists in the PEP and in the block error rate of the DSTM, and derive a closed-form expression for the PEP error floor in terms of the fading rate. For spatially correlated channels, we derive a new closed-form expression for the PEP at asymptotically high signal-to-noise ratios and show that an existing asymptotic PEP expression derived by the residue method can also be obtained by using the MGF-based approach. Finally, we use computer simulations to verify the theoretical results. View full abstract»

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  • Low-Delay, High-Rate Nonsquare Complex Orthogonal Designs

    Publication Year: 2012 , Page(s): 2633 - 2647
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (394 KB) |  | HTML iconHTML  

    The maximal rate of a nonsquare complex orthogonal design for n transmit antennas is [1/2]+[1/(n)] if n is even and [1/2]+[1/(n+1)] if n is odd and the codes have been constructed for all n by Liang (2003) and Lu (2005) to achieve this rate. A lower bound on the decoding delay of maximal-rate complex orthogonal designs has been obtained by Adams (2007) and it is observed that Liang's construction achieves the bound on delay for n equal to 1 and 3 modulo 4 while Lu et al.'s construction achieves the bound for n=0 , 1, 3 mod 4. For n=2 mod 4, Adams (2010) have shown that the minimal decoding delay is twice the lower bound, in which case, both Liang's and Lu et al.'s construction achieve the minimum decoding delay. For large value of n , it is observed that the rate is close to half and the decoding delay is very large. A class of rate-[1/2] codes with low decoding delay for all n has been constructed by Tarokh (1999). In this paper, another class of rate-[1/2] codes is constructed for all n in which case the decoding delay is half the decoding delay of the rate-[1/2] codes given by Tarokh This is achieved by giving first a general construction of square real orthogonal designs which includes as special cases the well-known constructions of Adams, Lax, and Phillips and the construction of Geramita and Pullman, and then making use of it to obtain the desired rate-[1/2] codes. For the case of nine transmit antennas, the proposed rate-[1/2] code is shown to be of minimal delay. The proposed construction results in designs with zero entries which may have high peak-to-average power ratio and it is shown that by appropriate postmultiplication, a design with no zero entry can be obtained with no change in the code parameters. View full abstract»

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  • Cyclic and Quasi-Cyclic LDPC Codes on Constrained Parity-Check Matrices and Their Trapping Sets

    Publication Year: 2012 , Page(s): 2648 - 2671
    Cited by:  Papers (23)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (5822 KB) |  | HTML iconHTML  

    This paper is concerned with construction and structural analysis of both cyclic and quasi-cyclic codes, particularly low-density parity-check (LDPC) codes. It consists of three parts. The first part shows that a cyclic code given by a parity-check matrix in circulant form can be decomposed into descendant cyclic and quasi-cyclic codes of various lengths and rates. Some fundamental structural properties of these descendant codes are developed, including the characterization of the roots of the generator polynomial of a cyclic descendant code. The second part of the paper shows that cyclic and quasi-cyclic descendant LDPC codes can be derived from cyclic finite-geometry LDPC codes using the results developed in the first part of the paper. This enlarges the repertoire of cyclic LDPC codes. The third part of the paper analyzes the trapping set structure of regular LDPC codes whose parity-check matrices satisfy a certain constraint on their rows and columns. Several classes of finite-geometry and finite-field cyclic and quasi-cyclic LDPC codes with large minimum distances are shown to have no harmful trapping sets of size smaller than their minimum distances. Consequently, their error-floor performances are dominated by their minimum distances. View full abstract»

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  • SISO APP Searches in Lattices With Tanner Graphs

    Publication Year: 2012 , Page(s): 2672 - 2688
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (742 KB) |  | HTML iconHTML  

    An efficient, low-complexity, soft-output detector for general lattices is presented, based on their Tanner graph (TG) representations. Closest-point searches in lattices can be performed as nonbinary belief propagation on associated TGs; soft-information output is naturally generated in the process; the algorithm requires no backtrack (cf. classic sphere decoding), and extracts extrinsic information. A lattice's coding gain enables equivalence relations between lattice points, which can be thereby partitioned in cosets. Total and extrinsic a posteriori probabilities at the detector's output further enable the use of soft detection information in iterative schemes. The algorithm is illustrated via two scenarios that transmit a 32-point, uncoded super-orthogonal (SO) constellation for multiple-input multiple-output (MIMO) channels, carved from an 8-dimensional nonorthogonal lattice D4D4: it achieves maximum likelihood performance in quasistatic fading; and, performs close to interference-free transmission, and identically to list sphere decoding, in independent fading with coordinate interleaving and iterative equalization and detection. Latter scenario outperforms former despite absence of forward error correction coding-because the inherent lattice coding gain allows for the refining of extrinsic information. The lattice constellation is the same as the one employed in the SO space-time trellis codes first introduced for 2 × 2 MIMO by Ionescu et al., then independently by Jafarkhani and Seshadri. Algorithmic complexity is log-linear in lattice dimensionality versus cubic in classic sphere decoders. View full abstract»

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  • Weight Distribution and List-Decoding Size of Reed–Muller Codes

    Publication Year: 2012 , Page(s): 2689 - 2696
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (227 KB) |  | HTML iconHTML  

    The weight distribution and list-decoding size of Reed-Muller codes are studied in this work. Given a weight parameter, we are interested in bounding the number of Reed-Muller codewords with weight up to the given parameter; and given a received word and a distance parameter, we are interested in bounding the size of the list of Reed-Muller codewords that are within that distance from the received word. Obtaining tight bounds for the weight distribution of Reed-Muller codes has been a long standing open problem in coding theory, dating back to 1976. In this work, we make a new connection between computer science techniques used to study low-degree polynomials and these coding theory questions. This allows us to resolve the weight distribution and list-decoding size of Reed-Muller codes for all distances. Previous results could only handle bounded distances: Azumi, Kasami, and Tokura gave bounds on the weight distribution which hold up to 2.5 times the minimal distance of the code; and Gopalan, Klivans, and Zuckerman gave bounds on the list-decoding size which hold up to the Johnson bound. View full abstract»

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  • Semidefinite Code Bounds Based on Quadruple Distances

    Publication Year: 2012 , Page(s): 2697 - 2705
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (412 KB) |  | HTML iconHTML  

    Let A(n,d) be the maximum number of 0, 1 words of length n , any two having Hamming distance at least d. It is proved that A(20,8)=256, which implies that the quadruply shortened Golay code is optimal. Moreover, it is shown that A(18,6) ≤ 673, A(19,6) ≤ 1237, A(20,6) ≤ 2279, A(23,6) ≤ 13674, A(19,8) ≤ 135, A(25,8) ≤ 5421, A(26,8) ≤ 9275, A(27,8) ≤ 17099, A(21,10) ≤ 47, A(22,10) ≤ 84, A(24,10) ≤ 268, A(25,10) ≤ 466, A(26,10) ≤ 836, A(27,10) ≤ 1585, A(28,10) ≤ 2817, A(25,12) ≤ 55, and A(26,12) ≤ 96. The method is based on the positive semidefiniteness of matrices derived from quadruples of words. This can be put as constraint in a semidefinite program, whose optimum value is an upper bound for A(n,d). The order of the matrices involved is huge. However, the semidefinite program is highly symmetric, by which its feasible region can be restricted to the algebra of matrices invariant under this symmetry. By block diagonalizing this algebra, the order of the matrices will be reduced so as to make the program solvable with semidefinite programming software in the above range of values of n and d. View full abstract»

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  • Optimal Ternary Constant-Weight Codes With Weight 4 and Distance 5

    Publication Year: 2012 , Page(s): 2706 - 2718
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (869 KB) |  | HTML iconHTML  

    Constant-weight codes (CWCs) play an important role in coding theory. The problem of determining the sizes for optimal ternary CWCs with length n, weight 4, and minimum Hamming distance 5 ((n,5,4)3 code) has been settled for all positive integers n ≤ 10 or n >; 10 and n ≡ 1 mod 3 with n ∈ {13,52,58} undetermined. In this paper, we investigate the problem of constructing optimal (n,5,4)3 codes for all lengths n with the tool of group divisible codes. We determine the size of an optimal (n,5,4)3 code for each integer n ≥ 4 leaving the lengths n ∈ {12,13,21,27,33,39,45,52} unsolved. View full abstract»

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  • Entropy of the Mixture of Sources and Entropy Dimension

    Publication Year: 2012 , Page(s): 2719 - 2728
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (236 KB) |  | HTML iconHTML  

    Suppose that we are given two sources S1, S2 which both send us information from the data space X . We assume that we lossy-code information coming from S1 and S2 with the same maximal error but with different alphabets P1 and P2, respectively. Consider a new source S which sends a signal produced by source S1 with probability a1 and by source S2 with probability a2=1-a1 . We provide a simple greedy algorithm which constructs a coding alphabet P which encodes data from S with the same value of maximal error as single sources, such that the entropy h(S;P) satisfies: h(S;P) ≤ a1h(S1;P1)+a2h(S2;P2) +1. In the proof of the aforementioned formula, the basic role is played by a new equivalent definition of entropy based on measures instead of partitions. As a consequence, we decompose the entropy dimension of the mixture of sources in terms of the convex combination of the entropy dimensions of the single sources. In the case of probability measures in BBRN, this allows us to link the upper local dimension at point with the upper entropy dimension of a measure by an improved version of Young estimation. View full abstract»

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  • Complex-Valued Random Vectors and Channels: Entropy, Divergence, and Capacity

    Publication Year: 2012 , Page(s): 2729 - 2744
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (438 KB) |  | HTML iconHTML  

    Recent research has demonstrated significant achievable performance gains by exploiting circularity/noncircularity or properness/improperness of complex-valued signals. In this paper, we investigate the influence of these properties on important information theoretic quantities such as entropy, divergence, and capacity. We prove two maximum entropy theorems that strengthen previously known results. The proof of the first maximum entropy theorem is based on the so-called circular analog of a given complex-valued random vector. The introduction of the circular analog is additionally supported by a characterization theorem that employs a minimum Kullback-Leibler divergence criterion. In the proof of the second maximum entropy theorem, results about the second-order structure of complex-valued random vectors are exploited. Furthermore, we address the capacity of multiple-input multiple-output (MIMO) channels. Regardless of the specific distribution of the channel parameters (noise vector and channel matrix, if modeled as random), we show that the capacity-achieving input vector is circular for a broad range of MIMO channels (including coherent and noncoherent scenarios). Finally, we investigate the situation of an improper and Gaussian distributed noise vector. We compute both capacity and capacity-achieving input vector and show that improperness increases capacity, provided that the complementary covariance matrix is exploited. Otherwise, a capacity loss occurs, for which we derive an explicit expression. View full abstract»

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  • A Normal Law for the Plug-in Estimator of Entropy

    Publication Year: 2012 , Page(s): 2745 - 2747
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (115 KB) |  | HTML iconHTML  

    This paper establishes a sufficient condition for the asymptotic normality of the plug-in estimator of Shannon's entropy defined on a countable alphabet. The sufficient condition covers a range of cases with countably infinite alphabets, for which no normality results were previously known. View full abstract»

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  • Three-Receiver Broadcast Channels With Common and Confidential Messages

    Publication Year: 2012 , Page(s): 2748 - 2765
    Cited by:  Papers (14)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (452 KB) |  | HTML iconHTML  

    This paper establishes inner bounds on the secrecy capacity regions for the general three-receiver broadcast channel with one common and one confidential message sets. We consider two setups. The first is when the confidential message is to be sent to two receivers and kept secret from the third receiver. Achievability is established using indirect decoding, Wyner wiretap channel coding, and the new idea of generating secrecy from a publicly available superposition codebook. The inner bound is shown to be tight for a class of reversely degraded broadcast channels and when both legitimate receivers are less noisy than the third receiver. The second setup investigated in this paper is when the confidential message is to be sent to one receiver and kept secret from the other two receivers. Achievability in this case follows from Wyner wiretap channel coding and indirect decoding. This inner bound is also shown to be tight for several special cases. View full abstract»

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  • On the Multicast Capacity of the Wireless Broadcast Channel

    Publication Year: 2012 , Page(s): 2766 - 2780
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (623 KB) |  | HTML iconHTML  

    For a multicast network, in which a common source is transmitted to N users, the problem of maximizing the average rate subject to a coverage constraint (minimum quality of service) is studied. Considering such a network with single-antenna nodes and assuming that the channel state information is available only at the receiver side, the highest expected rate achievable by a random user in the network, called the expected typical rate, is derived in two scenarios: hard coverage constraint and soft coverage constraint. In the first case, the coverage is expressed in terms of the outage probability, while in the second case, the expected rate should satisfy a certain minimum requirement. It is shown that the optimum solution (achieving the highest expected typical rate for given coverage requirements) in both cases is achieved by an infinite layer superposition code for which the optimal power allocation among different layers is derived. The analysis is extended to a scenario with multiple transmit antennas. For the MISO case, a suboptimal coding scheme is proposed, which is shown to be asymptotically optimal, when the number of transmit antennas grows at least logarithmically with the number of users in the network. View full abstract»

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  • Approximate Capacity of the Dirty Multiple-Access Channel With Partial State Information at the Encoders

    Publication Year: 2012 , Page(s): 2781 - 2787
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1888 KB) |  | HTML iconHTML  

    In this paper, we consider the K -user Gaussian multiple-access channel with multiple independent additive white Gaussian interferences. Each interference is known to exactly one transmitter non-causally. The capacity region is characterized to within a bounded gap regardless of channel parameters. These results are based on a layered modulo-lattice scheme which realizes distributed interference cancellation. View full abstract»

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  • Interference Channels With Rate-Limited Feedback

    Publication Year: 2012 , Page(s): 2788 - 2812
    Cited by:  Papers (23)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (896 KB) |  | HTML iconHTML  

    We consider the two-user interference channel with rate-limited feedback. Related prior works focus on the case where feedback links have infinite capacity, while no research has been done for the rate-limited feedback problem. Several new challenges arise due to the capacity limitations of the feedback links, both in deriving inner bounds and outer bounds. We study this problem under three different interference models: the El Gamal-Costa deterministic model, the linear deterministic model, and the Gaussian model. For the first two models, we develop an achievable scheme that employs three techniques: Han-Kobayashi message splitting, quantize-and-binning, and decode-and-forward. We also derive new outer bounds for all three models and we show the optimality of our scheme under the linear deterministic model. In the Gaussian case, we propose a transmission strategy that incorporates lattice codes, inspired by the ideas developed in the first two models. For symmetric channel gains, we prove that the gap between the achievable sum rate of the proposed scheme and our new outer bounds is bounded by a constant number of bits, independent of the channel gains. View full abstract»

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  • On the Capacity of Interference Channel With Causal and Noncausal Generalized Feedback at the Cognitive Transmitter

    Publication Year: 2012 , Page(s): 2813 - 2837
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1111 KB) |  | HTML iconHTML  

    In this paper, taking into account the effect of link delays, we investigate the capacity region of the cognitive interference channel (C-IFC), where cognition can be obtained from either causal or noncausal generalized feedback. For this purpose, we introduce the causal C-IFC with delay (CC-IFC-WD) in which the cognitive user's transmission can depend on L future received symbols as well as the past ones. We show that the CC-IFC-WD model is equivalent to a classical causal C-IFC (CC-IFC) with link delays. Moreover, CC-IFC-WD extends both genie-aided and causal cognitive radio channels and bridges the gap between them. First, we derive an outer bound on the capacity region for the arbitrary value of L and specialize this general outer bound to the strong interference case. Then, under strong interference conditions, we tighten the outer bound. To derive the achievable rate regions, we concentrate on three special cases: 1) classical CC-IFC (L=0); 2) CC-IFC without delay (L=1) ; and 3) CC-IFC with unlimited look ahead in which the cognitive user noncausally knows its entire received sequence. In each case, we obtain a new inner bound on the capacity region. The derived achievable rate regions under special conditions reduce to several previously known results. Moreover, we show that the coding strategy which we use to derive an achievable rate region for the classical CC-IFC achieves the capacity for the classes of degraded and semideterministic classical CC-IFC under strong interference conditions. Furthermore, we extend our achievable rate regions to the Gaussian case. Providing some numerical examples for Gaussian CC-IFC-WD, we compare the performances of the different strategies and investigate the rate gain of the cognitive link for different delay values. We show that one can achieve larger rate regions in the “without delay” and “unlimited look-ahead” cases than in the classical CC-IFC; this improve- ent is likely due to the fact that, in the former two cases, the cognitive user can cooperate more effectively with the primary user by knowing the current and future received symbols. View full abstract»

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  • Wiretap Channel With Causal State Information

    Publication Year: 2012 , Page(s): 2838 - 2849
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (5087 KB) |  | HTML iconHTML  

    A lower bound on the secrecy capacity of the wiretap channel with state information available causally at both the encoder and the decoder is established. The lower bound is shown to be strictly larger than that for the noncausal case by Liu and Chen. Achievability is proved using block Markov coding, Shannon strategy, and key generation from common state information. The state sequence available at the end of each block is used to generate a key to enhance the transmission rate of the confidential message in the following block. An upper bound on the secrecy capacity when the state is available noncausally at the encoder and the decoder is established and is shown to coincide with the aforementioned lower bound for several classes of wiretap channels with state. View full abstract»

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  • The Spectral Efficiency of Successive Cancellation With Linear Multiuser Detection for Randomly Spread CDMA

    Publication Year: 2012 , Page(s): 2850 - 2873
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1833 KB) |  | HTML iconHTML  

    We consider the problem of multiuser detection for randomly spread direct-sequence (DS) code-division multiple access (CDMA) over flat fading channels. The analysis focuses on the case of many users, and large spreading sequences such that their ratio, which is the system load, is kept fixed. Spectral efficiency of practical linear detectors such as match-filter and decorrelator employing successive interference cancellation (SIC) at the receiver is derived. This is used to extend the notion of strongest users detectors for SIC receivers. The strongest users detectors system design relies on an outage approach where each user transmits in a single layer (fixed rate), and only users experiencing good channel conditions may be reliably decoded, while the other users are in outage, i.e., not decoded. In this scheme, iterative SIC decoding is studied, and it is shown that for equal power users, the optimal rate allocation, for maximizing the expected spectral efficiency, is equal rates for all users. This outage approach analysis is extended for multilayer coding broadcast approach per user. The expected sum-rate, under iterative decoding with linear multiuser detectors, is optimized, and the optimal layering power distribution is obtained. For small system loads, the achievable spectral efficiency with the continuous broadcast approach and a linear matched filter detector exhibits significant gains over the single layer coding approach. View full abstract»

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  • On the Structure of Limited-Feedback Beamforming Codebooks for Amplify-and-Forward Relay Networks

    Publication Year: 2012 , Page(s): 2874 - 2895
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (615 KB) |  | HTML iconHTML  

    We determine necessary conditions on the structure of symbol error rate (SER) optimal compact quantizer codebooks for limited feedback beamforming in wireless networks with one transmitter-receiver pair and R parallel amplify-and-forward relays. We call a codebook “small” if its cardinality is less than R, and “large” otherwise. A “d-codebook” depends on the power constraints and can be optimized accordingly, while an “i-codebook” remains fixed. It was previously shown that any i-codebook that contains the single-relay selection (SRS) codebook achieves the full-diversity order, R. We prove the following: Every full-diversity i-codebook contains the SRS codebook, and thus is necessarily large. In general, as the power constraints grow to infinity, the limit of an SER-optimal large d-codebook contains an SRS codebook, provided that it exists. For small codebooks, the maximal diversity is equal to the codebook cardinality. Every diversity-optimal small i-codebook is an orthogonal multiple-relay selection (OMRS) codebook. Moreover, the limit of an SER-optimal small d-codebook is an OMRS codebook. We observe that SRS is nothing but a special case of OMRS for codebooks with cardinality equal to R. As a result, we call OMRS as "the universal necessary condition" for codebook optimality. Finally, we confirm our analytical findings through simulations. View full abstract»

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IEEE Transactions on Information Theory publishes papers concerned with the transmission, processing, and utilization of information.

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Editor-in-Chief
Frank R. Kschischang

Department of Electrical and Computer Engineering