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Information Theory, IEEE Transactions on

Issue 10 • Date Oct. 2011

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Displaying Results 1 - 25 of 64
  • Table of contents

    Publication Year: 2011 , Page(s): C1 - C4
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    Freely Available from IEEE
  • IEEE Transactions on Information Theory publication information

    Publication Year: 2011 , Page(s): C2
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  • When Is a Function Securely Computable?

    Publication Year: 2011 , Page(s): 6337 - 6350
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (4308 KB) |  | HTML iconHTML  

    A subset of a set of terminals that observe correlated signals seek to compute a function of the signals using public communication. It is required that the value of the function be concealed from an eavesdropper with access to the communication. We show that the function is securely computable if and only if its entropy is less than the capacity of a new secrecy generation model, for which a single-letter characterization is provided. View full abstract»

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  • On Extracting Common Random Bits From Correlated Sources

    Publication Year: 2011 , Page(s): 6351 - 6355
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1444 KB) |  | HTML iconHTML  

    Suppose Alice and Bob receive strings of unbiased independent but noisy bits from some random source. They wish to use their respective strings to extract a common sequence of random bits with high probability but without communicating. How many such bits can they extract? The trivial strategy of outputting the first k bits yields an agreement probability of (1-ε)k <; 2-1.44kε, where ε is the amount of noise. We show that no strategy can achieve agreement probability better than 2-kε/(1-ε). On the other hand, we show that when k ≥ 10 + 2(1 - ε)/ε, there exists a strategy which achieves an agreement probability of 0.003(kε)-1/2 · 2-kε/(1-ε). View full abstract»

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  • A Recursive Construction of the Set of Binary Entropy Vectors and Related Algorithmic Inner Bounds for the Entropy Region

    Publication Year: 2011 , Page(s): 6356 - 6363
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1890 KB) |  | HTML iconHTML  

    A method for checking membership in the region of entropic vectors generated from N bits is presented. A general technique for utilizing this method to create inner bounds for regions of entropic vectors as a function of outer bounds is then presented. These two algorithms are then used to provide new insights regarding relationships among well known bounds for the region of entropic vectors.. View full abstract»

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  • Truncation Technique for Characterizing Linear Polymatroids

    Publication Year: 2011 , Page(s): 6364 - 6378
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3635 KB) |  | HTML iconHTML  

    Linear polymatroids have a strong connection to network coding. The problem of finding the linear network coding capacity region is equivalent to the characterization of all linear polymatroids. It is well known that linear polymatroids must satisfy the inequalities of Ingleton (Combin. Math. Appln., 1971). However, it has been an open question for years as to whether these inequalities are sufficient. It was until recently that new subspace rank inequalities have been discovered (independently by Kinser and Dougherty, ). In this paper, we propose a new approach to investigate properties of linear polymatroids. Specifically, we demonstrate how to construct a new polymatroid that satisfies not only the Ingleton and DFZ inequalities, but also lies outside the minimal closed and convex cone containing all linear polymatroids. Using this polymatroid, we prove that all truncation-preserving inequalities (including Ingleton inequalities and DFZ inequalities) are insufficient to characterize linear polymatroids. View full abstract»

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  • Message and State Cooperation in Multiple Access Channels

    Publication Year: 2011 , Page(s): 6379 - 6396
    Cited by:  Papers (14)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (4936 KB) |  | HTML iconHTML  

    We investigate the capacity of a multiple access channel with cooperating encoders where partial state information is known to each encoder and full state information is known to the decoder. The cooperation between the encoders has a two-fold purpose: to generate empirical state coordination between the encoders, and to share information about the private messages that each encoder has. For two-way cooperation, this two-fold purpose is achieved by double-binning, where the first layer of binning is used to generate the state coordination similarly to the two-way source coding, and the second layer of binning is used to transmit information about the private messages. The complete result provides the framework and perspective for addressing a complex level of cooperation that mixes states and messages in an optimal way. View full abstract»

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  • The Capacity of Several New Classes of Semi-Deterministic Relay Channels

    Publication Year: 2011 , Page(s): 6397 - 6404
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    The relay channel consists of a transmitter input x1, a relay input x2, a relay output y2 , and a receiver output y3. In this paper, we establish the capacity of three new classes of semi-deterministic relay channels: 1) a class of degraded semi-deterministic relay channels, 2) a class of semi-deterministic orthogonal relay channels, and 3) a class of semi-deterministic relay channels with relay-transmitter feedback. For the first class of relay channels, the output of the relay y2 depends on a deterministic function of the transmitter's input x1, i.e., on s=f1(x1), rather than on x1 directly. In addition, the relay channels satisfy the condition that S → (X2,Y2) → Y3 forms a Markov chain for all input probability distributions p(x1,x2). Hence, the first class of relay channels includes, but is strictly not limited to, the class of degraded relay channels previously considered by Cover and El Gamal. The partial decode-and-forward strategy achieves the capacity of the class of degraded semi-deterministic relay channels. Next, we consider the class of semi-deterministic orthogonal relay channels where there are orthogonal channels from the relay to the receiver and from the transmitter to the receiver. In addition, the output of the relay y2 is a deterministic function of x1, x2 and y3 , i.e., y2=f4(x1,x2,y3). The class of semi-deterministic orthogonal relay channels is a generalization of the class of deterministic relay channels considered by Kim. The compress-and-forward strategy achieves the capacity of the class of semi- - -deterministic orthogonal relay channels. For the third class of relay channels, there is a causal and noiseless feedback from the relay to the transmitter. In addition, similar to the second class of relay channels, the output of the relay y2 is a deterministic function of x1, x2, and y3 . Both the generalized strategy of Gabbai and Bross and the hash-and-forward strategy of Kim achieve the capacity of the class of semi-deterministic relay channels with relay-transmitter feedback. View full abstract»

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  • Achievable Rate Regions and Performance Comparison of Half Duplex Bi-Directional Relaying Protocols

    Publication Year: 2011 , Page(s): 6405 - 6418
    Cited by:  Papers (40)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3995 KB) |  | HTML iconHTML  

    In a bi-directional relay channel, two nodes wish to exchange independent messages over a shared wireless half-duplex channel with the help of a relay. In this paper, we derive achievable rate regions for four new half-duplex protocols and compare these to four existing half-duplex protocols and outer bounds. In time, our protocols consist of either two or three phases. In the two phase protocols, both users simultaneously transmit during the first phase and the relay alone transmits during the second phase, while in the three phase protocol the two users sequentially transmit followed by a transmission from the relay. The relay may forward information in one of four manners; we outline existing amplify and forward (AF), decode and forward (DF), lattice based, and compress and forward (CF) relaying schemes and introduce the novel mixed forward scheme. The latter is a combination of CF in one direction and DF in the other. We derive achievable rate regions for the CF and Mixed relaying schemes for the two and three phase protocols. We provide a comprehensive treatment of eight possible half-duplex bi-directional relaying protocols in Gaussian noise, obtaining their relative performance under different SNR and relay geometries. View full abstract»

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  • The Achievable Distortion Region of Sending a Bivariate Gaussian Source on the Gaussian Broadcast Channel

    Publication Year: 2011 , Page(s): 6419 - 6427
    Cited by:  Papers (13)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (519 KB) |  | HTML iconHTML  

    We provide a complete characterization of the achievable distortion region for the problem of sending a bivariate Gaussian source over bandwidth-matched Gaussian broadcast channels, where each receiver is interested in only one component of the source. This setting naturally generalizes the simple single Gaussian source bandwidth-matched broadcast problem for which the uncoded scheme is known to be optimal. We show that a hybrid scheme can achieve the optimum for the bivariate case, but neither an uncoded scheme alone nor a separation-based scheme alone is sufficient. We further show that in this joint source channel coding setting, the Gaussian scenario is the worst scenario among the sources and channel noises with the same covariances. View full abstract»

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  • Achieving the Secrecy Capacity of Wiretap Channels Using Polar Codes

    Publication Year: 2011 , Page(s): 6428 - 6443
    Cited by:  Papers (35)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (392 KB) |  | HTML iconHTML  

    Suppose that Alice wishes to send messages to Bob through a communication channel C1, but her transmissions also reach an eavesdropper Eve through another channel C2. This is the wiretap channel model introduced by Wyner in 1975. The goal is to design a coding scheme that makes it possible for Alice to communicate both reliably and securely. Reliability is measured in terms of Bob's probability of error in recovering the message, while security is measured in terms of the mutual information between the message and Eve's observations. Wyner showed that the situation is characterized by a single constant Cs, called the secrecy capacity, which has the following meaning: for all ε >; 0, there exist coding schemes of rate R ≥ Cs-ε that asymptotically achieve the reliability and security objectives. However, his proof of this result is based upon a random-coding argument. To date, despite consider able research effort, the only case where we know how to construct coding schemes that achieve secrecy capacity is when Eve's channel C2 is an erasure channel, or a combinatorial variation thereof. Polar codes were recently invented by Arikan; they approach the capacity of symmetric binary-input discrete memoryless channels with low encoding and decoding complexity. In this paper, we use polar codes to construct a coding scheme that achieves the secrecy capacity for a wide range of wiretap channels. Our construction works for any instantiation of the wiretap channel model, as long as both C1 and C2 are symmetric and binary-input, and C2 is degraded with respect to C1. Moreover, we show how to modify our construction in order to provide strong security, in the sense defined by Maurer, while still operating at a rate that approaches the secrecy capacity. In this case, we cannot guarantee that the reliability condition will also be satisfied unless the m- - ain channel C1 is noiseless, although we believe it can be always satisfied in practice. View full abstract»

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  • Exact Random Coding Exponents for Erasure Decoding

    Publication Year: 2011 , Page(s): 6444 - 6454
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (286 KB) |  | HTML iconHTML  

    Random coding of channel decoding with an erasure option is studied. By analyzing the large deviations behavior of the code ensemble, we obtain exact single-letter formulas for the error exponents in lieu of Forney's lower bounds. The analysis technique we use is based on an enhancement and specialization of tools for assessing the statistical properties of certain distance enumerators. We specialize our results to the setup of the binary symmetric channel case with uniform random coding distribution and derive an explicit expression for the error exponent which, unlike Forney's bounds, does not involve optimization over two parameters. We also establish the fact that for this setup, the difference between the exact error exponent corresponding to the probability of undetected decoding error and the exponent corresponding to the erasure event is equal to the threshold parameter. Numerical calculations indicate that for this setup, as well as for a Z-channel, Forney's bound coincides with the exact random coding exponent. View full abstract»

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  • Simultaneous Communication in Noisy Channels

    Publication Year: 2011 , Page(s): 6455 - 6462
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2100 KB) |  | HTML iconHTML  

    A sender wishes to broadcast a message of length n over an alphabet to r users, where each user i, 1 ≤ i ≤ r, should be able to receive one m, possible messages. The broadcast channel has noise for each of the users (possibly different noise for different users), who cannot distinguish between some pairs of letters. The vector (m1, m2,...,mr)(n) is said to be feasible if length n encoding and decoding schemes exist enabling every user to decode his message. A rate vector (R1, R2...,Rr) is feasible if there exists a sequence of feasible vectors (m1, m2...,mr)(n) such that Ri = limn→∞ Log2 mi/n for all i. We determine the feasible rate vectors for several different scenarios and investigate some of their properties. An interesting case discussed is when one user can only distinguish between all the letters in a subset of the alphabet. Tight restrictions on the feasible rate vectors for some specific noise types for the other users are provided. The simplest nontrivial cases of two users and alphabet of size three are fully characterized. To this end a more general previously known result, to which we sketch an alternative proof, is used. This problem generalizes the study of the Shannon capacity of a graph, by considering more than a single user. View full abstract»

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  • Compute-and-Forward: Harnessing Interference Through Structured Codes

    Publication Year: 2011 , Page(s): 6463 - 6486
    Cited by:  Papers (163)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (674 KB) |  | HTML iconHTML  

    Interference is usually viewed as an obstacle to communication in wireless networks. This paper proposes a new strategy, compute-and-forward, that exploits interference to obtain significantly higher rates between users in a network. The key idea is that relays should decode linear functions of transmitted messages according to their observed channel coefficients rather than ignoring the interference as noise. After decoding these linear equations, the relays simply send them towards the destinations, which given enough equations, can recover their desired messages. The underlying codes are based on nested lattices whose algebraic structure ensures that integer combinations of codewords can be decoded reliably. Encoders map messages from a finite field to a lattice and decoders recover equations of lattice points which are then mapped back to equations over the finite field. This scheme is applicable even if the transmitters lack channel state information. View full abstract»

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  • Outage Analysis of Block-Fading Gaussian Interference Channels

    Publication Year: 2011 , Page(s): 6487 - 6501
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (552 KB) |  | HTML iconHTML  

    This paper considers the asymptotic behavior of the outage probability of a two-source block-fading single-antenna Gaussian interference channel in the high-SNR regime by means of the diversity-multiplexing tradeoff. A general setting where the user rates and the average channel gains are not restricted to be symmetric is investigated. This asymmetric scenario allows to analyze networks with “mixed” interference, i.e., when different sources are at different distance from their intended destination, that are not possible under the commonly used symmetric assumption. Inner and outer bounds for the diversity are derived. The outer bound is based on the recent “to within one bit” capacity result of Etkin for the unfaded Gaussian channel and is a re-derivation of a known bound for which an error is pointed out. The inner bound is based on the Han and Kobayashi achievable region both without rate splitting and with a rate spitting inspired by the “to within one bit” capacity result. An analytical comparison of the diversity upper and lower bounds for a general channel seems difficult; by numerical evaluations, the two bounds are shown to coincide for a fairly large set of channel parameters. View full abstract»

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  • A Lower Bound on the Capacity of Wireless Erasure Networks

    Publication Year: 2011 , Page(s): 6502 - 6513
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1898 KB) |  | HTML iconHTML  

    In this paper, a lower bound on the capacity of wireless ad hoc erasure networks is derived in closed form in the case where n nodes are uniformly and independently distributed in the unit area square. It holds almost surely and is asymptotically tight. Nodes are assumed to have fixed transmit power; hence, two nodes should be within a specified distance rn to overcome noise. With interference determining outages, each transmitter-receiver pair is modeled as an erasure channel with a broadcast constraint, i.e., each node can transmit only one signal across all its outgoing links. A lower bound of Θ(nrn) for the network capacity is derived when erasures across distinct links are independent, with constant erasure probabilities. When erasures are correlated, the lower bound Θ(1/(rn)) is proved. If the broadcast constraint is relaxed, the gain is a function of rn and the link erasure probabilities, and is at most a constant if the erasure probabilities grow sufficiently large with n. Finally, the case where the erasure probabilities are random variables, for example due to randomness in geometry or channels, is analyzed. In this setting, it is shown somewhat surprisingly that variability in erasure probabilities increases network capacity. View full abstract»

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  • Opportunistic Wireless Relay Networks: Diversity-Multiplexing Tradeoff

    Publication Year: 2011 , Page(s): 6514 - 6538
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (4399 KB) |  | HTML iconHTML  

    The performance of many opportunistic relay networks has been unknown in part because opportunistic analysis relies on independence assumptions that break down in many interesting and useful network topologies. This paper develops techniques that expand opportunistic analysis to a broader class of networks, proposes new opportunistic methods for several network geometries, and analyzes them in the high-SNR regime. For each of the geometries studied in the paper, we analyze the opportunistic DMT of several relay protocols, including amplify-and-forward, decode-and-forward, compress-and-forward, nonorthogonal amplify-forward, and dynamic decode-forward. Among the highlights of the results: In a variety of multi-user single-relay networks, simple selection strategies are developed and shown to be DMT-optimal. It is shown that compress-forward relaying achieves the DMT upper bound in the opportunistic multiple-access relay channel as well as in the opportunistic n×n user network with relay. Other protocols, e.g., dynamic decode-forward, are shown to be near optimal in several cases. Finite-precision feedback is analyzed for the opportunistic multiple-access relay channel, the opportunistic broadcast relay channel, and the opportunistic gateway channel, and is shown to be almost as good as full channel state information. View full abstract»

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  • Distributed Rate Allocation for Wireless Networks

    Publication Year: 2011 , Page(s): 6539 - 6554
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (472 KB) |  | HTML iconHTML  

    This paper develops a distributed algorithm for rate allocation in wireless networks that achieves the same throughput region as optimal centralized algorithms. This cross-layer algorithm jointly performs medium access control and physical-layer rate adaptation. The paper establishes that this algorithm is throughput-optimal for general rate regions. In contrast to on-off scheduling, rate allocation enables optimal utilization of physical-layer schemes by scheduling multiple rate levels. The algorithm is based on local queue-length information, and thus the algorithm is of significant practical value. An important application of this algorithm is in multiple-band multiple-radio throughput-optimal distributed scheduling for white-space networks. The algorithm requires that each link can determine the global feasibility of increasing its current data-rate. In many classes of networks, any one link's data-rate primarily impacts its neighbors and this impact decays with distance. Hence, local exchanges can provide the information needed to determine feasibility. Along these lines, the paper discusses the potential use of existing physical-layer control messages to determine feasibility. This can be considered as a technique analogous to carrier sensing in carrier sense multiple access (CSMA) networks. View full abstract»

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  • Cooperative Diversity With Mobile Nodes: Capacity Outage Rate and Duration

    Publication Year: 2011 , Page(s): 6555 - 6568
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3217 KB) |  | HTML iconHTML  

    The outage probability is an important performance measure for cooperative diversity schemes. However, in mobile environments, the outage probability does not completely describe the behavior of cooperative diversity schemes since the mobility of the involved nodes introduces variations in the channel gains. As a result, the capacity outage events are correlated in time and second-order statistical parameters of the achievable information-theoretic capacity such as the average capacity outage rate (AOR) and the average capacity outage duration (AOD) are required to obtain a more complete description of the properties of cooperative diversity protocols. In this paper, assuming slow Rayleigh fading, we derive exact expressions for the AOR and the AOD of three well-known cooperative diversity protocols: variable-gain amplify-and-forward, decode-and-forward, and selection decode-and-forward relaying. Furthermore, we develop asymptotically tight high signal-to-noise ratio (SNR) approximations, which offer important insights into the influence of various system and channel parameters on the AOR and the AOD. In particular, we show that on a double-logarithmic scale, similar to the outage probability, the AOR asymptotically decays with the SNR with a slope that depends on the diversity gain of the cooperative protocol, whereas the AOD asymptotically decays with a slope of -1/2 independent of the diversity gain. View full abstract»

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  • The Diversity-Multiplexing Tradeoff of the Dynamic Decode-and-Forward Protocol on a MIMO Half-Duplex Relay Channel

    Publication Year: 2011 , Page(s): 6569 - 6590
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (5571 KB) |  | HTML iconHTML  

    The diversity-multiplexing tradeoff of the dynamic decode-and-forward protocol is characterized for the half-duplex three-terminal (m, k, n)-relay channel where the source, relay and the destination terminals have m, k and n antennas, respectively. The tradeoff curve is obtained as a solution to a simple, two-variable, convex optimization problem which is explicitly solved in closed-form for certain special classes of relay channels, namely, the (1, k, 1) relay channel, the (n, 1, n) relay channel and the (2, k, 2) relay channel. Moreover, the tradeoff curves for a certain class of relay channels, such as the (m, k, n >; k) channels, are found to be identical to those for the decode-and-forward protocol for the full duplex channel while for other classes of channels they are marginally lower at high multiplexing gains. Our results also show that for some classes of relay channels and at low multiplexing gains the diversity orders of the dynamic decode-and-forward protocol are greater than those of the static compress-and-forward protocol which in turn is known to be tradeoff optimal over all static half duplex protocols. In general, the dynamic decode-and-forward protocol has a performance that is comparable to that of the static compress-and-forward protocol which, unlike the dynamic decode-and-forward protocol, requires global channel state information at the relay node. Its performance is also close to that of the decode-and-forward protocol over the full-duplex relay channel thereby indicating that the half-duplex constraint can be compensated for by the dynamic operation of the relay wherein the relay switches from the receive to the transmit mode based on the source-relay channel quality. View full abstract»

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  • Beamforming Codebooks for Two Transmit Antenna Systems Based on Optimum Grassmannian Packings

    Publication Year: 2011 , Page(s): 6591 - 6602
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2260 KB) |  | HTML iconHTML  

    Precoding codebook design for limited feedback MIMO systems is known to reduce to a discretization problem on a Grassmann manifold. The case of two-antenna beamforming is special in that it is equivalent to quantizing the real sphere. The isometry between the Grassmannian G2,1 and the real sphere S2 shows that discretization problems in the Grassmannian G2,1 are directly solved by corresponding spherical codes. Notably, the Grassmannian line packing problem in ℂ2, namely maximizing the minimum distance, is equivalent to the Tammes problem on the real sphere, so that optimum spherical packings give optimum Grassmannian packings. Moreover, a simple isomorphism between G2,1 and S2 enables to analytically derive simple codebooks in closed-form having low implementation complexity. Using the simple geometry of some of these codebooks, we derive closed-form expressions of the probability density function of the relative SNR loss due to limited feedback. We also investigate codebooks based on other spherical arrangements, such as solutions maximizing the harmonic mean of the mutual distances among the codewords, which is known as the Thomson problem. We find that in some special cases, Grassmannian codebooks based on these other spherical arrangements outperform codebooks from Grassmannian packing. View full abstract»

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  • Beam Selection Gain Versus Antenna Selection Gain

    Publication Year: 2011 , Page(s): 6603 - 6618
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (4650 KB) |  | HTML iconHTML  

    We consider beam selection using a fixed beamforming network (FBN) at a base station with M array antennas. In our setting, a Butler matrix is deployed at the RF stage to form M beams, and then the best beam is selected for transmission. We introduce some properties of the noncentral chi-square distribution and prove the resulting properties of the beam selection gain verifying that beam selection is superior to antenna selection in Rician channels with any K-factors. Furthermore, we find asymptotically tight stochastic bounds of the beam selection gain, which yield approximate closed form expressions of the expected selection gain and the ergodic capacity. Beam selection has the order of growth of the ergodic capacity Θ(logM) regardless of user location in contrast to Θ(log(logM)) for antenna selection. View full abstract»

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  • On Communication Over Unknown Sparse Frequency-Selective Block-Fading Channels

    Publication Year: 2011 , Page(s): 6619 - 6632
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (418 KB) |  | HTML iconHTML  

    This paper considers the problem of reliable communication over discrete-time channels whose impulse responses have length L and exactly SL non-zero coefficients, and whose support and coefficients remain fixed over blocks of N >; L channel uses but change independently from block to block. Here, it is assumed that the channel's support and coefficient realizations are both unknown, although their statistics are known. Assuming Gaussian non-zero-coefficients and noise, and focusing on the high-SNR regime, it is first shown that the ergodic noncoherent channel capacity has pre-log factor 1-(S)/(N) for any L. It is then shown that, to communicate with arbitrarily small error probability at rates in accordance with the capacity pre-log factor, it suffices to use pilot-aided orthogonal frequency-division multiplexing (OFDM) with S pilots per fading block, in conjunction with an appropriate noncoherent decoder. Since the achievability result is proven using a noncoherent decoder whose complexity grows exponentially in the number of fading blocks K, a simpler decoder, based on S+1 pilots, is also proposed. Its ε-achievable rate is shown to have pre-log factor equal to 1-(S+1)/(N) with the previously considered channel, while its achievable rate is shown to have pre-log factor 1-(S+1)/(N) when the support of the block-fading channel remains fixed over time. View full abstract»

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  • Concatenated Coding for the AWGN Channel With Noisy Feedback

    Publication Year: 2011 , Page(s): 6633 - 6649
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1643 KB) |  | HTML iconHTML  

    The use of open-loop coding can be easily extended to a closed-loop concatenated code if the transmitter has access to feedback. This can be done by introducing a feedback transmission scheme as an inner code. In this paper, this process is investigated for the case when a linear feedback scheme is implemented as an inner code and, in particular, over an additive white Gaussian noise (AWGN) channel with noisy feedback. To begin, we look to derive an optimal linear feedback scheme by optimizing over the received signal-to-noise ratio (SNR). From this optimization, a linear feedback scheme is produced that is asymptotically optimal in the sense of blocklength-normalized SNR; it is then compared to other well-known schemes. Then, the linear feedback scheme is implemented as an inner code to a concatenated code over the AWGN channel with noisy feedback. This code shows improvements not only in error exponent bounds, but also in bit error rate (BER) and frame error rate (FER). It is also shown that if the concatenated code has total blocklength L and the inner code has blocklength, N, the inner code blocklength should scale as N = O(C/R), where C is the capacity of the channel and R is the rate of the concatenated code. Simulations with low-density parity-check (LDPC) and turbo codes are provided to display practical applications and their error rate benefits. View full abstract»

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  • Optimal Alphabets and Binary Labelings for BICM at Low SNR

    Publication Year: 2011 , Page(s): 6650 - 6672
    Cited by:  Papers (16)
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    Optimal binary labelings, input distributions, and input alphabets are analyzed for the so-called bit-interleaved coded modulation (BICM) capacity, paying special attention to the low signal-to-noise ratio (SNR) regime. For 8-ary pulse amplitude modulation (PAM) and for 0.75 bit/symbol, the folded binary code results in a higher capacity than the binary reflected Gray code (BRGC) and the natural binary code (NBC). The 1 dB gap between the additive white Gaussian noise (AWGN) capacity and the BICM capacity with the BRGC can be almost completely removed if the input symbol distribution is properly selected. First-order asymptotics of the BICM capacity for arbitrary input alphabets and distributions, dimensions, mean, variance, and binary labeling are developed. These asymptotics are used to define first-order optimal (FOO) constellations for BICM, i.e., constellations that make BICM achieve the Shannon limit -1.59 dB. It is shown that the Eb/N0 required for reliable transmission at asymptotically low rates in BICM can be as high as infinity, that for uniform input distributions and 8-PAM there are only 72 classes of binary labelings with a different first-order asymptotic behavior, and that this number is reduced to only 26 for 8-ary phase shift keying (PSK). A general answer to the question of FOO constellations for BICM is also given: using the Hadamard transform, it is found that for uniform input distributions, a constellation for BICM is FOO if and only if it is a linear projection of a hypercube. A constellation based on PAM or quadrature amplitude modulation input alphabets is FOO if and only if they are labeled by the NBC; if the constellation is based on PSK input alphabets instead, it can never be FOO if the input alphabet has more than four points, regardless of the labeling. View full abstract»

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