Some simple bounds on the symmetric capacity and outage probabilityfor QAM wireless channels with Rice and Nakagami fadings

In this article, quickly computable upper and lower bounds are presented on the symmetric capacity of flat-faded Rice and Nakagami channels with side information (SI) for data-transmissions via finite-size quadrature amplitude modulation (QAM) constellations. The proposed bounds exhibit the appealing feature to be tight and asymptotically exact both for high and low signal-to-noise ratios (SNRs). Furthermore, exponentially tight Chernoff-like formulas are also presented for an analytical evaluation of the resulting system outage probabilities when interleaved packet transmissions are carried out     

Bounds on the symmetric cutoff rate for QAM transmissions overtime-correlated flat-faded channels

This article presents new upper and lower bounds on the symmetric cutoff rate for block-coded quadrature-amplitude-modulated (QAM) signaling over links affected by time-correlated Rayleigh-distributed flat-faded phenomena. The proposed bounds assume maximum-likelihood soft-decoding with perfect channel-state-information at the receiving side and hold for any form of QAM constellations. These bounds are quickly computable and constitute an efficient means to estimate the cutoff rate of systems employing very long codewords, so that an exact evaluation of the cutoff rate results. Analytical and numerical evidence of the tightness of the presented bounds is also provided     

Bounds on the maximum-likelihood decoding error probability oflow-density parity-check codes

We derive both upper and lower bounds on the decoding error probability of maximum-likelihood (ML) decoded low-density parity-check (LDPC) codes. The results hold for any binary-input symmetric-output channel. Our results indicate that for various appropriately chosen ensembles of LDPC codes, reliable communication is possible up to channel capacity. However, the ensemble averaged decoding error probability decreases polynomially, and not exponentially. The lower and upper bounds coincide asymptotically, thus showing the tightness of the bounds. However, for ensembles with suitably chosen parameters, the error probability of almost all codes is exponentially decreasing, with an error exponent that can be set arbitrarily close to the standard random coding exponent     

Capacity bounds for power- and band-limited optical intensity channels corrupted by Gaussian noise

We determine upper and lower bounds on the channel capacity of power- and bandwidth-constrained optical intensity channels corrupted by white Gaussian noise. These bounds are shown to converge asymptotically at high optical signal-to-noise ratios (SNRs). Unlike previous investigations on low-intensity Poisson photon counting channels, such as some fiber optic links, this channel model is realistic for indoor free space optical channels corrupted by intense ambient light. An upper bound on the capacity is found through a sphere-packing argument while a lower bound is computed through the maxentropic source distribution. The role of bandwidth is expressed by way of the effective dimension of the set of signals and, together with an average optical power constraint, is used to determine bounds on the spectral efficiency of time-disjoint optical intensity signaling schemes. The bounds show that, at high optical SNRs, pulse sets based on raised-quadrature amplitude modulation (QAM) and prolate spheroidal wave functions have larger achievable maximum spectral efficiencies than traditional rectangular pulse basis sets. This result can be considered as an extension of previous work on photon counting channels which closely model low optical intensity channels with rectangular pulse shapes.     

Asymptotically tight bounds on the capacity and outage probabilityfor QAM transmissions over Rayleigh-faded data channels with CSI

In this article, novel quickly computable analytical upper and lower bounds are presented on the symmetric capacity for flat-faded Rayleigh channels with finite-size quadrature amplitude modulation constellations when perfect channel-state information at the receiving site is available; the proposed bounds are asymptotically tight both for high and low signal-to-noise ratios. Furthermore, an easily computable expression is also provided for a reasonably tight evaluation of the resulting outage probability     

Network s-t reliability bounds using a 2-dimensional reliabilitypolynomial

Computing the reliability of a generic network is computationally difficult, and an exact solution is unattainable for many problems. Faced with this computational difficulty, two compromises are usually made: (1) be content with reliability bounds instead of exact reliability; and (2) simplify analysis by assuming that all but 1 component-type are perfectly reliable. This paper relaxes the assumption of perfect components and computes the s-t reliability of a network whose operation is a function of the reliability of 2 component types (nodes and links.) The extension of the reliability polynomial to 2 dimensions removes the need to assume that links or nodes are perfectly reliable     

Bounds on the zero-error capacity of the input-constrainedbit-shift channel

New lower and upper bounds on a maximal achievable rate fur runlength-limited codes, capable of correcting any combination of bit-shift errors (i.e. a zero-error capacity of the bit-shift channel), are presented. The lower bound is a generalization of the bound obtained by Shamai and Zehavi (1991). It is shown that in certain cases, the upper and the lower bounds asymptotically coincide     

Parity-check density versus performance of binary linear block codes over memoryless symmetric channels

We derive lower bounds on the density of parity-check matrices of binary linear codes which are used over memoryless binary-input output-symmetric (MBIOS) channels. The bounds are expressed in terms of the gap between the rate of these codes for which reliable communications is achievable and the channel capacity; they are valid for every sequence of binary linear block codes if there exists a decoding algorithm under which the average bit-error probability vanishes. For every MBIOS channel, we construct a sequence of ensembles of regular low-density parity-check (LDPC) codes, so that an upper bound on the asymptotic density of their parity-check matrices scales similarly to the lower bound. The tightness of the lower bound is demonstrated for the binary erasure channel by analyzing a sequence of ensembles of right-regular LDPC codes which was introduced by Shokrollahi, and which is known to achieve the capacity of this channel. Under iterative message-passing decoding, we show that this sequence of ensembles is asymptotically optimal (in a sense to be defined in this paper), strengthening a result of Shokrollahi. Finally, we derive lower bounds on the bit-error probability and on the gap to capacity for binary linear block codes which are represented by bipartite graphs, and study their performance limitations over MBIOS channels. The latter bounds provide a quantitative measure for the number of cycles of bipartite graphs which represent good error-correction codes.     

Error bounds for trellis-coded MPSK on a fading mobile satellitechannel

Analytical performance bounds are presented for trellis-coded MPSK, transmitted over a satellite-based land mobile channel. Upper bounds are evaluated using the well-known transfer function bounding technique, and lower bounds are achieved through knowledge of exact pairwise error probabilities. In order to analyze practical trellis-codes (four or more states), the uniform properties displayed by a certain class of trellis-codes are exploited, enabling the encoder transfer function to be obtained from a modified state transition diagram, having no more states than the encoder itself. Monte Carlo simulation results are presented in confirmation of all performance bounds and indicate a general weakness in the transfer function upper bounds. A new asymptotically tight upper bound is derived based on a simple modification to the standard transfer function bound, and results are presented for the four- and eight-state trellis-codes in Rician and Rayleigh fading     

Analysis of Optimum Frame Synchronization Based on Periodically Embedded Sync Words

We present new tight bounds for evaluating the performance of sync word-based frame synchronization algorithms in the periodically embedded case. We consider antipodal signaling with coherent detection over additive white Gaussian noise and both optimal and suboptimal search techniques. Our bounds are very close to results obtained through simulation and tend asymptotically (for increasing signal-to-noise ratios) to the exact performance.     

Bounds on the capacity of a spectrally constrained Poisson channel

An upper bound is derived on the capacity of a Poisson channel that has a stationary input process of a given spectrum and is subjected to peak and average power constraints. The bound is shown to be asymptotically tight with the relaxation of the spectral constraints. Its maximization over a given set of admissible spectra is closely related to an analogous problem in the AWGN regime. The results are used for bounding the capacity of a Poisson channel under a second-moment-bandwidth constraint, as well as the capacity under a strict bandwidth constraint. Asymptotically tight lower bounds on the channel capacity for the above two cases are also presented. The approach for lower bounding the capacity for the latter case yields, as a by-product, improved bounds on the bit-error probability in uncoded amplitude shift keying (and on-off modulation as a special case) operating over a Poisson channel impaired by intersymbol interference     

Composition bounds for channel block codes

The performance of Channel block codes for a general channel is studied by examining the relationship between the rate of a code, the joint composition of pairs of codewords, and the probability of decoding error. At fixed rate, lower bounds and upper bounds, both on minimum Bhattacharyya distance between codewords and on minimum equivocation distance between codewords, are derived. These bounds resemble, respectively, the Gilbert and the Elias bounds on the minimum Hamming distance between codewords. For a certain large class of channels, a lower bound on probability of decoding error for low-rate channel codes is derived as a consequence of the upper bound on Bhattacharyya distance. This bound is always asymptotically tight at zero rate. Further, for some channels, it is asymptotically tighter than the straight line bound at low rates. Also studied is the relationship between the bounds on codeword composition for arbitrary alphabets and the expurgated bound for arbitrary channels having zero error capacity equal to zero. In particular, it is shown that the expurgated reliability-rate function for blocks of letters is achieved by a product distribution whenever it is achieved by a block probability distribution with strictly positive components.     

Performance analysis of asymptotically optimal noncoherentdetection of trellis-coded multi-amplitude/-phase modulation signals inGaussian noise and ISI channels

Performance upper bounds for noncoherent receivers employed in conjunction with single and multi-amplitude/-phase signals, transmitted over time dispersive and Gaussian noise channels are derived. Based upon a metric which has been previously derived by the authors, we present analytical expressions and computer generated results for the performance of asymptotically optimal noncoherent detection over such channels. As a typical application of the developed theoretical analysis, we consider wideband telecommunication systems. Where time dispersion resulting in intersymbol interference (ISI) is one of the significant sources of system performance degradation. Numerical evaluation of the optimal noncoherent decoding algorithms, shows the proposed bounds to be an effective and efficient means of evaluating the performance of the noncoherent receivers under investigation. Using the derived bounds, performance evaluation results for modulation schemes such as π/4-shift DQPSK (differential quadrature phase shift keying), 8- and 16-DQAM (differential quadrature amplitude modulation), at very low bit-error rates (BER), which would otherwise pose impractically high computational loads when using Monte-Carlo error counting techniques, are readily obtained. At BER>10^-4 evaluation results generated via computer simulation have verified the tightness of the bounds     

Bounds on the delay-constrained capacity of UWB communication with a relay node

We derive bounds on the expected capacity and outage capacity of a three-node relay network for UWB communications. We also provide a simple tight approximation for the derived upper bound on the capacity and then using this bound we obtain the outage probability of the network. Numerical results show that a significant improvement in the system capacity and outage probability is obtained by adding a relay node. Moreover, our theoretical results reveal that the diversity gain of a relay channel substantially increases by using UWB links instead of NB links. We also derive these bounds when we have a constraint on the total transmitted power of the source and the relay nodes.     

An Exact Close-form PEP and a new PEP for Space-Time Codes in Rayleigh Fading Channels

A close-form expression for the exact Pair-wise Error Probability (PEP) of Space-Time (S-T) codes in Rayleigh fading channel is derived using the general and close-form solution for the probability-density function (PDF) of a sum of independent exponential distributed random variables. The expression requires evaluating the coefficients for partial fraction expansion, so an easy analytical way is proposed for doing this. The exact PEP is subsequently used to develop a simple PEP using the upper bound. Both PEPs are used in the Union bound for error rate evaluation. Numerical calculations and Monte Carlo computer simulation are used to study the accuracies of these Union bounds for error rate evaluation of a rotation-based diagonal S-T code (D code) in Rayleigh fading channels. Four other PEPs based on different bounds, i.e., the Chernoff bound, the asymptotic bound, the tight asymptotic bound, and the Eigen-Geometric-Mean (EGM) bound, are also studied for comparison. Results show that our derived close-form PEP is an exact PEP and our proposed PEP is a very tight bound to the exact PEP.     

Bounds on the information rate of intertransition-time-restrictedbinary signaling over an AWGN channel

Upper and lower bounds on the capacity of a continuous-time additive white Gaussian noise (AWGN) channel with bilevel (±√P) input signals subjected to a minimum inter-transition time (T_min) constraint are derived. The channel model and input constraints reflect basic features of certain magnetic recording systems. The upper bounds are based on Duncan's relation between the average mutual information in an AWGN regime and the mean-square error (MSE) of an optimal causal estimator. Evaluation or upper-bounding the MSE of suboptimal causal estimators yields the desired upper bounds. The lower bound is found by invoking the extended “Mrs. Gerber's” lemma and asymptotic properties of the entropy of max-entropic bipolar (d, k) codes. Asymptotic results indicate that at low SNR=PT_min/N₀, with N₀ designating the noise one-sided power spectral density, the capacity tends to P/N ₀ nats per second (nats/s), i.e., it equals the capacity in the simplest average power limited case. At high SNR, the capacity in the simplest average power limited case. At high SNR, the capacity behaves asymptotically as T_min^-1ln(SNR/ln(SNR)) (nats/s), demonstrating the degradation relatively to T_avg ^-1 lnSNR, which is the asymptotic known behavior of the capacity with a bilevel average intertransition-time (T_avg) restricted channel input. Additional lower bounds are obtained by considering specific signaling formats such as pulsewidth modulation. The effect of mild channel filtering on the lower bounds on capacity is also addressed, and novel techniques to lower-bound the capacity in this case are introduced     

Estimation for maximum instantaneous current through supply linesfor CMOS circuits

We present new techniques for estimating the maximum instantaneous current through the power supply lines for CMOS circuits. We investigate four different approaches: (1) timed-ATPG-based approach; (2) probability-based approach; (3) genetic algorithm-based approach; and (4) integer linear programming (ILP) approach. The first three approaches produce a tight lower bound on the maximum current. The ILP-based approach produces the exact solutions for small circuits, and tight upper bounds of the solutions for large circuits. Our experimental results show that the upper bounds produced by the ILP approach combined with the lower bounds produced by the other three approaches confine the exact solution for the maximum instantaneous current to a small range     

On the capacity of MIMO relay channels

We study the capacity of multiple-input multiple- output (MIMO) relay channels. We first consider the Gaussian MIMO relay channel with fixed channel conditions, and derive upper bounds and lower bounds that can be obtained numerically by convex programming. We present algorithms to compute the bounds. Next, we generalize the study to the Rayleigh fading case. We find an upper bound and a lower bound on the ergodic capacity. It is somewhat surprising that the upper bound can meet the lower bound under certain regularity conditions (not necessarily degradedness), and therefore the capacity can be characterized exactly; previously this has been proven only for the degraded Gaussian relay channel. We investigate sufficient conditions for achieving the ergodic capacity; and in particular, for the case where all nodes have the same number of antennas, the capacity can be achieved under certain signal-to-noise ratio (SNR) conditions. Numerical results are also provided to illustrate the bounds on the ergodic capacity of the MIMO relay channel over Rayleigh fading. Finally, we present a potential application of the MIMO relay channel for cooperative communications in ad hoc networks.     

Bounds for Queue Lengths in a Contention Packet Broadcast System

A finite number of users communicating through a broadcast channel is considered. Each user has a buffer of infinite capacity, and a user randomly accesses the channel (ALOHA-type protocol). Moreover, only one packet per user might be sent in an access time. Both symmetric and asymmetric models are considered; that is, we assume either indistinguishable or distinguishable users. An exact analysis of the queue lengths in that type of system is not now available, and therefore, based on some algebraic studies, we shall present some lower and some upper bounds for the average queue lengths. These bounds are quite tight for a small number of users and acceptable for a wide range of input parameters in the symmetric case. In the asymmetric case the bounds are acceptable only for light input traffic and a small number of users.     

Error rate performance of coded free-space optical links over strong turbulence channels

Error control coding can be used over free-space optical (FSO) links to mitigate turbulence-induced fading. We present error rate performance bounds for coded FSO communication systems operating over atmospheric turbulence channels, which are modeled as a correlated K distribution under strong turbulence conditions. We derive an upper bound on the pairwise error probability (PEP) and then apply the union-bound technique in conjunction with the derived PEP to obtain upper bounds on the bit error rate. Simulation results are further demonstrated to verify the analytical results.