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Information Theory, IEEE Transactions on

Issue 6 • Date June 2009

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Displaying Results 1 - 25 of 40
  • Table of contents

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

    Page(s): C2
    Save to Project icon | Request Permissions | PDF file iconPDF (41 KB)  
    Freely Available from IEEE
  • Compound Multiple-Access Channels With Partial Cooperation

    Page(s): 2425 - 2441
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (377 KB) |  | HTML iconHTML  

    A two-user discrete memoryless compound multiple-access channel (MAC) with a common message and conferencing decoders is considered. The capacity region is characterized in the special cases of physically degraded channels and unidirectional cooperation, and achievable rate regions are provided for the general case. The results are then extended to the corresponding Gaussian model. In the Gaussian setup, the provided achievable rates are shown to lie within some constant number of bits from the boundary of the capacity region in several special cases. An alternative model, in which the encoders are connected by conferencing links rather than having a common message, is studied as well, and the capacity region for this model is also determined for the cases of physically degraded channels and unidirectional cooperation. Numerical results are also provided to obtain insights about the potential gains of conferencing at the decoders and encoders. View full abstract»

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  • On the Loss of Single-Letter Characterization: The Dirty Multiple Access Channel

    Page(s): 2442 - 2454
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (358 KB) |  | HTML iconHTML  

    For general memoryless systems, the existing information-theoretic solutions have a ldquosingle-letterrdquo form. This reflects the fact that optimum performance can be approached by a random code (or a random binning scheme), generated using independent and identically distributed copies of some scalar distribution. Is that the form of the solution of any (information-theoretic) problem? In fact, some counter examples are known. The most famous one is the ldquotwo help onerdquo problem: Korner and Marton showed that if we want to decode the modulo-two sum of two correlated binary sources from their independent encodings, then linear coding is better than random coding. In this paper we provide another counter example, the ldquodoubly-dirtyrdquo multiple-access channel (MAC). Like the Korner-Marton problem, this is a multiterminal scenario where side information is distributed among several terminals; each transmitter knows part of the channel interference while the receiver only observes the channel output. We give an explicit solution for the capacity region of the binary doubly-dirty MAC, demonstrate how this region can be approached using a linear coding scheme, and prove that the ldquobest known single-letter regionrdquo is strictly contained in it. We also state a conjecture regarding the capacity loss of single-letter characterization in the Gaussian case. View full abstract»

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  • Capacity Region of the Finite-State Multiple-Access Channel With and Without Feedback

    Page(s): 2455 - 2477
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (513 KB) |  | HTML iconHTML  

    The capacity region of the finite-state multiple-access channel (FS-MAC) with feedback that may be an arbitrary time-invariant function of the channel output samples is considered. We characterize both an inner and an outer bound for this region, using Massey's directed information. These bounds are shown to coincide, and hence yield the capacity region, of indecomposable FS-MACs without feedback and of stationary and indecomposable FS-MACs with feedback, where the state process is not affected by the inputs. Though multiletter in general, our results yield explicit conclusions when applied to specific scenarios of interest. For example, our results allow us to do the following. 1. Identify a large class of FS-MACs, that includes the additive mod2 noise MAC where the noise may have memory, for which feedback does not enlarge the capacity region. 2. Deduce that, for a general FS-MAC with states that are not affected by the input, if the capacity (region) without feedback is zero, then so is the capacity (region) with feedback. 3. Deduce that the capacity region of a MAC that can be decomposed into a multiplexer concatenated by a point-to-point channel (with, without, or with partial feedback), the capacity region is given by Sigmam Rm les C, where C is the capacity of the point to point channel and m indexes the encoders. Moreover, we show that for this family of channels source-channel coding separation holds. View full abstract»

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  • The Capacity of Wireless Networks in Nonergodic Random Fading

    Page(s): 2478 - 2493
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (566 KB) |  | HTML iconHTML  

    We find the exact per-node capacity scaling in an extended, distributed wireless network where the node locations are random, the channel attenuation between pairs of nodes exhibits independent random fading, and data forwarding is restricted to multihop delivery. We establish a per-node throughput upper bound equal to (Cmax)/(radicn) (bps)/(Hz), and a constructive lower bound equal to (Cmin)/(radicn) (bps)/(Hz), where Cmax and Cmin are constants and n is the expected number of nodes in the network. The results apply with probability approaching unity as n becomes large, under independent, frequency flat, fading channel conditions where the tail probability exhibits an exponential decay (e.g., any mixture of line-of-sight and Rayleigh, Rice and Nakagami distributions). Our lower bound is mainly motivated by a clever bond-percolation-based protocol construction, introduced by Franceschetti et al., where it was shown that a per-node throughput equal to a constant times 1/(radicn) (bps)/(Hz) is achievable in networks with random node locations under a deterministic channel gain modeling path-loss and absorption. We extend the result to more realistic channel gain models in which the channel gains are modeled as random due to multipath effects. The protocol systematically leverages multiuser diversity to overcome the added uncertainty. The key to the upper bound is to establish an upper bound for the total network transport capacity. This upper bound proves that, relative to the lower bound construction, any attempt to leverage multiuser diversity further will result in no more than a constant factor of throughput gain. View full abstract»

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  • On the Capacity of Ad Hoc Networks Under Random Packet Losses

    Page(s): 2494 - 2498
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (131 KB) |  | HTML iconHTML  

    We consider the problem of determining asymptotic bounds on the capacity of a random ad hoc network. Previous approaches assumed a link layer model in which if a transmitter-receiver pair can communicate with each other, i.e., the signal to interference and noise ratio (SINR) is above a certain threshold, then the transmitted packet is received error-free by the receiver thereby. Using this model, the per node capacity of the network was shown to be Theta(radic(n log n)/1). In reality, for any finite link SINR, there is a nonzero probability of erroneous reception of the packet. We show that in a large network, as the packet travels an asymptotically large number of hops from source to destination, the cumulative impact of packet losses over intermediate links results in a per-node throughput of only O(radic(n)/1) under the previously proposed routing and scheduling strategy. We then propose a new scheduling scheme to counter this effect. The proposed scheme provides tight guarantees on end-to-end packet loss probability, and improves the per-node throughput to Omega(radic(n)(log n)/12(alpha-2)/alpha+2) where alpha > 2 is the path loss exponent. View full abstract»

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  • Network Beamforming Using Relays With Perfect Channel Information

    Page(s): 2499 - 2517
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (606 KB) |  | HTML iconHTML  

    This paper deals with beamforming in wireless relay networks with perfect channel information at the relays, receiver, and transmitter if there is a direct link between the transmitter and receiver. It is assumed that every node in the network has its own power constraint. A two-step amplify-and-forward protocol is used, in which the transmitter and relays not only use match filters to form a beam at the receiver but also adaptively adjust their transmit powers according to the channel strength information. For networks with no direct link, an algorithm is proposed to analytically find the exact solution with linear (in network size) complexity. It is shown that the transmitter should always use its maximal power while the optimal power of a relay ca.n take any value between zero and its maxima. Also, this value depends on the quality of all other channels in addition to the relay's own. Despite this coupling fact, distributive strategies are proposed in which, with the aid of a low-rate receiver broadcast, a relay needs only its own channel information to implement the optimal power control. Then, beamforming in networks with a direct link is considered. When the direct link exists during the first step only, the optimal power control is the same as that of networks with no direct link. For networks with a direct link during the second step only and both steps, recursive numerical algorithms are proposed. Simulation shows that network beamforming achieves the maximal diversity order and outperforms other existing schemes. View full abstract»

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  • On Maximizing Coverage in Gaussian Relay Channels

    Page(s): 2518 - 2536
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (740 KB) |  | HTML iconHTML  

    Results for Gaussian relay channels typically focus on maximizing transmission rates for given locations of the source, relay, and destination. We introduce an alternative perspective, where the objective is maximizing coverage for a given rate. The new objective captures the problem of how to deploy relays to provide a given level of service to a particular geographic area, where the relay locations become a design parameter that can be optimized. We evaluate the decode-and-forward (DF) and compress-and-forward (CF) strategies for the relay channel with respect to the new objective of maximizing coverage. When the objective is maximizing rate, different locations of the destination favor different strategies. When the objective is coverage for a given rate, and the relay is able to decode, DF is uniformly superior in that it provides coverage at any point served by CF. When the channel model is modified to include random fading, we show that the monotone ordering of coverage regions is not always maintained. While the coverage provided by DF is sensitive to changes in the location of the relay and the path loss exponent, CF exhibits a more graceful degradation with respect to such changes. The techniques used to approximate coverage regions are new and may be of independent interest. View full abstract»

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  • On Complementary Graph Entropy

    Page(s): 2537 - 2546
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (229 KB) |  | HTML iconHTML  

    It has been recently discovered that complementary graph entropy characterizes (and offers new insights into) the minimum asymptotic rate for zero-error source coding with decoder side information. This paper presents new results that build on and complement this discovery. Specifically, i) previously unknown subadditivity properties of complementary graph entropy are derived, and ii) zero-error coding rates are characterized in terms of complementary graph entropy for two multiterminal coding scenarios. For both scenarios, the rate characterization implies no rate loss relative to point-to-point source coding. View full abstract»

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  • A Note on the Secrecy Capacity of the Multiple-Antenna Wiretap Channel

    Page(s): 2547 - 2553
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (156 KB) |  | HTML iconHTML  

    The secrecy capacity of the multiple-antenna wiretap channel under the average total power constraint was recently characterized, independently, by Khisti and Wornell and Oggier and Hassibi using a Sato-like argument and matrix analysis tools. This paper presents an alternative characterization of the secrecy capacity of the multiple-antenna wiretap channel under a more general matrix constraint on the channel input using a channel-enhancement argument. This characterization is by nature information-theoretic and is directly built on the intuition regarding to the optimal transmission strategy in this communication scenario. View full abstract»

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  • Logarithmic Sobolev Inequalities for Information Measures

    Page(s): 2554 - 2561
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (207 KB) |  | HTML iconHTML  

    For alpha ges 1, the new Vajda-type information measure J alpha (X) is a quantity generalizing Fisher's information (FI), to which it is reduced for alpha = 2 . In this paper, a corresponding generalized entropy power N alpha (X) is introduced, and the inequality N alpha (X) J alpha(X) ges n is proved, which is reduced to the well-known inequality of Stam for alpha = 2. The cases of equality are also determined. Furthermore, the Blachman-Stam inequality for the FI of convolutions is generalized for the Vajda information J alpha (X) and both families of results in the context of measure of information are discussed. That is, logarithmic Sobolev inequalities (LSIs) are written in terms of new more general entropy-type information measure, and therefore, new information inequalities are arisen. This generalization for special cases yields to the well known information measures and relative bounds. View full abstract»

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  • Superposition Coded Modulation With Peak-Power Limitation

    Page(s): 2562 - 2576
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (437 KB) |  | HTML iconHTML  

    We apply clipping to superposition coded modulation (SCM) systems to reduce the peak-to-average power ratio (PAPR) of the transmitted signal. The impact on performance is investigated by evaluating the mutual information driven by the induced peak-power-limited input signals. It is shown that the rate loss is marginal for moderate clipping thresholds if optimal encoding/decoding is used. This fact is confirmed in examples where capacity-approaching component codes are used together with the maximum a posteriori probability (MAP) detection. In order to reduce the detection complexity of SCM with a large number of layers, we develop a suboptimal soft compensation (SC) method that is combined with soft-input soft-output (SISO) decoding algorithms in an iterative manner. A variety of simulation results for additive white Gaussian noise (AWGN) and fading channels are presented. It is shown that with the proposed method, the effect of clipping can be efficiently compensated and a good tradeoff between PAPR and bit-error rate (BER) can be achieved. Comparisons with other coded modulation schemes demonstrate that SCM offers significant advantages for high-rate transmissions over fading channels. View full abstract»

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  • Pseudocodeword Performance Analysis for LDPC Convolutional Codes

    Page(s): 2577 - 2598
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (951 KB) |  | HTML iconHTML  

    Message-passing iterative decoders for low-density parity-check (LDPC) block codes are known to be subject to decoding failures due to so-called pseudocodewords. These failures can cause the large signal-to-noise ratio (SNR) performance of message-passing iterative decoding to be worse than that predicted by the maximum-likelihood (ML) decoding union bound. In this paper, we address the pseudocodeword problem from the convolutional code perspective. In particular, we compare the performance of LDPC convolutional codes with that of their "wrapped" quasi-cyclic block versions and we show that the minimum pseudoweight of an LDPC convolutional code is at least as large as the minimum pseudoweight of an underlying quasi-cyclic code. This result, which parallels a well-known relationship between the minimum Hamming weight of convolutional codes and the minimum Hamming weight of their quasi-cyclic counterparts, is due to the fact that every pseudocodeword in the convolutional code induces a pseudocodeword in the block code with pseudoweight no larger than that of the convolutional code's pseudocodeword. This difference in the weight spectra leads to improved performance at low-to-moderate SNRs for the convolutional code, a conclusion supported by simulation results. View full abstract»

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  • On the Values of Kloosterman Sums

    Page(s): 2599 - 2601
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (110 KB) |  | HTML iconHTML  

    Given a prime p and a positive integer n, we show that the shifted Kloosterman sums SigmaxisinF p nPsi(x + alphaxpn-2)=SigmaxisinF* p nPsi(x+alphax-1)+1, alphaisinF*pn where Psi is a nontrivial additive character of a finite field Fpn of pn elements, do not vanish if alpha belongs to a small subfield Fpm sube Fpn. This complements recent results of P. Charpin and G. Gong which in turn were motivated by some applications to bent functions. View full abstract»

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  • Bounds on the Number of Iterations for Turbo-Like Ensembles Over the Binary Erasure Channel

    Page(s): 2602 - 2617
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (380 KB) |  | HTML iconHTML  

    This paper provides simple lower bounds on the number of iterations which is required for successful message-passing decoding of some important families of graph-based code ensembles (including low-density parity-check (LDPC) codes and variations of repeat-accumulate codes). The transmission of the code ensembles is assumed to take place over a binary erasure channel, and the bounds refer to the asymptotic case where we let the block length tend to infinity. The simplicity of the bounds derived in this paper stems from the fact that they are easily evaluated and are expressed in terms of some basic parameters of the ensemble which include the fraction of degree-2 variable nodes, the target bit erasure probability, and the gap between the channel capacity and the design rate of the ensemble. This paper demonstrates that the number of iterations which is required for successful message-passing decoding scales at least like the inverse of the gap (in rate) to capacity, provided that the fraction of degree-2 variable nodes of these turbo-like ensembles does not vanish (hence, the number of iterations becomes unbounded as the gap to capacity vanishes). View full abstract»

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  • On Cyclic q -ary Images in Concatenated Form

    Page(s): 2618 - 2621
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (153 KB) |  | HTML iconHTML  

    This paper shows that q-ary images of some cyclic codes can be put into concatenated form in the sense of Jensen (1985). This description utilizes an isomorphism between the GF(q)-algebras GF(q) [z] / (znm - 1) and GF (q )[x, y] / (xn - 1, ym - x). We also describe an element of the constacyclic outer code, which is of great help in determining one of its generator polynomials. View full abstract»

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  • Reconstructing Extended Perfect Binary One-Error-Correcting Codes From Their Minimum Distance Graphs

    Page(s): 2622 - 2625
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (109 KB) |  | HTML iconHTML  

    The minimum distance graph of a code has the codewords as vertices and edges exactly when the Hamming distance between two codewords equals the minimum distance of the code. A constructive proof for reconstructibility of an extended perfect binary one-error-correcting code from its minimum distance graph is presented. Consequently, inequivalent such codes have nonisomorphic minimum distance graphs. Moreover, it is shown that the automorphism group of a minimum distance graph is isomorphic to that of the corresponding code. View full abstract»

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  • Simplification of Packet-Symbol Decoding With Errors, Deletions, Misordering of Packets, and No Sequence Numbers

    Page(s): 2626 - 2639
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (515 KB) |  | HTML iconHTML  

    In this paper, a new method is described which builds on Mitzenmacher's idea of adding a different pseudorandom number to each packet to help decode packet-symbol low-density codes, with deletions, errors, and out-of-order reception, without sequence numbers. The new method has lower decoding complexity than the original method. The most basic form of the new method applies to any parity-check code structure, but is limited to a rather small number of packets in the code. Decoding success is slightly inferior to an ideal erasure channel, which would require sequence numbering and error detection in each packet. Error detection is needed only for the whole code, amounting to usually less than one bit per packet symbol. Moreover, if error detection can resolve one of a small number of alternatives, the ordered case performs almost as well as the ideal erasure channel. Ways are shown to modify the basic algorithm for use with long codes, possibly approaching the erasure channel capacity limit. View full abstract»

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  • Braided Block Codes

    Page(s): 2640 - 2658
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1089 KB) |  | HTML iconHTML  

    A new class of binary iteratively decodable codes with good decoding performance is presented. These codes, called braided block codes (BBCs), operate on continuous data streams and are constructed by interconnection of two component block codes. BBCs can be considered as convolutional (or sliding) version of either Elias' product codes or expander codes. In this paper, we define BBCs, describe methods of their construction, analyze code properties, and study asymptotic iterative decoding performance. View full abstract»

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  • Rank Modulation for Flash Memories

    Page(s): 2659 - 2673
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (401 KB) |  | HTML iconHTML  

    We explore a novel data representation scheme for multilevel flash memory cells, in which a set of n cells stores information in the permutation induced by the different charge levels of the individual cells. The only allowed charge-placement mechanism is a ldquopush-to-the-toprdquo operation, which takes a single cell of the set and makes it the top-charged cell. The resulting scheme eliminates the need for discrete cell levels, as well as overshoot errors, when programming cells. We present unrestricted Gray codes spanning all possible n-cell states and using only "push-to-the-top" operations, and also construct balanced Gray codes. One important application of the Gray codes is the realization of logic multilevel cells, which is useful in conventional storage solutions. We also investigate rewriting schemes for random data modification. We present both an optimal scheme for the worst case rewrite performance and an approximation scheme for the average-case rewrite performance. View full abstract»

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  • Upper Bound on Error Exponent of Regular LDPC Codes Transmitted Over the BEC

    Page(s): 2674 - 2681
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (270 KB) |  | HTML iconHTML  

    The error performance of the ensemble of typical low-definition parity-check (LDPC ) codes transmitted over the binary erasure channel (BEC) is analyzed. In the past, lower bounds on the error exponents were derived. In this paper, a probabilistic upper bound on this error exponent is derived. This bound holds with some confidence level. View full abstract»

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  • High-Rate, Multisymbol-Decodable STBCs From Clifford Algebras

    Page(s): 2682 - 2695
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (523 KB) |  | HTML iconHTML  

    It is well known that space-time block codes (STBCs) obtained from orthogonal designs (ODs) are single-symbol decodable (SSD) and from quasi-orthogonal designs (QODs) are double-symbol decodable (DSD). However, there are SSD codes that are not obtainable from ODs and DSD codes that are not obtainable from QODs. In this paper, a method of constructing g-symbol decodable ( g-SD) STBCs using representations of Clifford algebras are presented which when specialized to g=1,2 gives SSD and DSD codes, respectively. For the number of transmit antennas 2a the rate (in complex symbols per channel use) of the g -SD codes presented in this paper is [(a+1-g)/(2a-g)]. The maximum rate of the DSD STBCs from QODs reported in the literature is [(a)/(2a-1)] which is smaller than the rate [(a-1)/(2a-2)] of the DSD codes of this paper, for 2a transmit antennas. In particular, the reported DSD codes for 8 and 16 transmit antennas offer rates 1 and 3/4 , respectively, whereas the known STBCs from QODs offer only 3/4 and 1/2, respectively. The construction of this paper is applicable for any number of transmit antennas. The diversity sum and diversity product of the new DSD codes are studied. It is shown that the diversity sum is larger than that of all known QODs and hence the new codes perform better than the comparable QODs at low signal-to-noise ratios (SNRs) for identical spectral efficiency. Simulation results for DSD codes at various spectral efficiencies are provided. View full abstract»

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  • Algebraic Number Precoding for Space–Time Block Codes

    Page(s): 2696 - 2704
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (647 KB) |  | HTML iconHTML  

    We propose a space-time block coding framework based on linear precoding. The codes for P transmit antennas are formed by transmitting the information vector (with P independent information symbols) L times where each time it is rotated by a distinct precoding matrix. The framework generalizes conventional spatial multiplexing techniques and facilitates tradeoff between rate and diversity. We propose a simple construction for precoding matrices whose parameters are chosen to guarantee maximal diversity using algebraic number theory. Our codes exhibit circular structure, which greatly simplifies the performance analysis and facilitates linear decoding. Theoretical analysis and numerical simulations demonstrated excellent performance of the proposed algebraic precoding framework. View full abstract»

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  • A Class of Errorless Codes for Overloaded Synchronous Wireless and Optical CDMA Systems

    Page(s): 2705 - 2715
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (528 KB) |  | HTML iconHTML  

    In this paper, we introduce a new class of codes for overloaded synchronous wireless and optical code-division multiple-access (CDMA) systems which increases the number of users for fixed number of chips without introducing any errors. Equivalently, the chip rate can be reduced for a given number of users, which implies bandwidth reduction for downlink wireless systems. An upper bound for the maximum number of users for a given number of chips is derived. Also, lower and upper bounds for the sum channel capacity of a binary overloaded CDMA are derived that can predict the existence of such overloaded codes. We also propose a simplified maximum likelihood method for decoding these types of overloaded codes. Although a high percentage of the overloading factor degrades the system performance in noisy channels, simulation results show that this degradation is not significant. More importantly, for moderate values of E b/N0 (in the range of 6-10 dB) or higher, the proposed codes perform much better than the binary Welch bound equality sequences. View full abstract»

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Aims & Scope

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

Full Aims & Scope

Meet Our Editors

Editor-in-Chief
Frank R. Kschischang

Department of Electrical and Computer Engineering