On the reliability function of the ideal Poisson channel withnoiseless feedback

A coding scheme for the channel under peak power and average power constraints on the input is presented, and its asymptotic error exponent is shown to coincide, at all rates below capacity, with the sphere packing error exponent, which, for the case at hand, is known to be unachievable without feedback for rates below the critical rate. An upper bound on the error exponent achievable with feedback is also derived and shown, under a capacity reducing average power constraint, to coincide with the error exponent achieved by the proposed coding scheme; in such a case the coding scheme is asymptotically optimal. Thus, the ideal Poisson channel, limited by a capacity-reducing average power constraint, provides a nontrivial example of a channel for which the reliability function is known exactly both with and without feedback. It is shown that a slight modification of the coding scheme to one of random transmission time can achieve zero-error probability for any rate lower than the ordinary average-error channel capacity     

Error exponents for the two-user Poisson multiple-access channel

The error exponent of the two-user Poisson multiple-access channel under peak and average power constraints, but unlimited in bandwidth, is considered. First, a random coding lower bound on the error exponent is obtained, and an extension of Wyner's (1988) single-user codes is shown to be exponentially optimum for this case as well. Second, the sphere-packing bounding technique suggested by Burnashev and Kutoyants (see Probl. Inform. Transm., vol.35, no.2, p.3-22, 1999) is generalized to the case at hand and an upper bound on the error exponent, which coincides with the lower bound, is derived. Thus, this channel joins its single-user partner as one of very few for which the reliability function is known     

Transmission capacity of wireless ad hoc networks with outage constraints

In this paper, upper and lower bounds on the transmission capacity of spread-spectrum (SS) wireless ad hoc networks are derived. We define transmission capacity as the product of the maximum density of successful transmissions multiplied by their data rate, given an outage constraint. Assuming that the nodes are randomly distributed in space according to a Poisson point process, we derive upper and lower bounds for frequency hopping (FH-CDMA) and direct sequence (DS-CDMA) SS networks, which incorporate traditional modulation types (no spreading) as a special case. These bounds cleanly summarize how ad hoc network capacity is affected by the outage probability, spreading factor, transmission power, target signal-to-noise ratio (SNR), and other system parameters. Using these bounds, it can be shown that FH-CDMA obtains a higher transmission capacity than DS-CDMA on the order of M/sup 1-2//spl alpha//, where M is the spreading factor and /spl alpha/>2 is the path loss exponent. A tangential contribution is an (apparently) novel technique for obtaining tight bounds on tail probabilities of additive functionals of homogeneous Poisson point processes.     

On the capacity-achieving distribution of the discrete-time noncoherent and partially coherent AWGN channels

We investigate the communication limits over rapid phase-varying channels and consider the capacity of a discrete- time noncoherent additive white Gaussian noise (NCAWGN) channel under the average power constraint. We obtain necessary and sufficient conditions for the capacity-achieving input distribution and show that this distribution is discrete and possesses an infinite number of mass points. Using this characterization of the capacity-achieving distribution we compute a tight lower bound on the capacity of the channel based on examining suboptimal input distributions. In addition, we provide some easily computable lower and upper bounds on the channel capacity. Finally, we extend some of these results to the partially coherent channel, where it is assumed that a phase-locked loop (PLL) is used to track the carrier phase at the receiver, and that an ideal interleaver and de-interleaver are employed-rendering the Tikhonov distributed residual phase errors statistically independent from one symbol interval to another.     

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.     

Tight bounds on the error probability of coded modulation schemesin Rayleigh fading channels

This paper presents a tight upper bound on the bit error performance of coded modulation schemes in Rayleigh fading channels. Upper and lower bounds on the pairwise error probability are first derived. The upper bound is then expressed in a product form to be used with the transfer function bounding technique. This upper bound has the same simplicity as the union-Chernoff bound while providing closer results to the exact expression. Examples for the case of four-state and eight-state TCM 8PSK schemes are also given to illustrate the tightness and the application of this upper bound     

On the performance of peaky capacity-achieving signaling on multipath fading channels

We analyze the error probability of peaky signaling on bandlimited multipath fading channels, the signaling strategy that achieves the capacity of such channels in the limit of infinite bandwidth under an average power constraint. We first derive an upper bound for general fading, then specialize to the case of Rayleigh fading, where we obtain upper and lower bounds that are exponentially tight and, therefore, yield the reliability function. These bounds constitute a strong coding theorem for the channel, as they not only delimit the range of achievable rates, but also give us a relationship among the error probability, data rate, bandwidth, peakiness, and fading parameters, such as the coherence time. They can be used to compare peaky signaling systems to other large bandwidth systems over fading channels, such as ultra-wideband radio and wideband code-division multiple access. We find that the error probability decreases slowly with the bandwidth W; under Rayleigh fading, the error probability varies roughly as W/sup -/spl alpha//, where /spl alpha/>0. With parameters typical of indoor wireless situations, we study the behavior of the upper and lower bounds on the error probability and the reliability function numerically.     

Improved bit-stuffing bounds on two-dimensional constraints

We derive lower bounds on the capacity of certain two-dimensional (2-D) constraints by considering bounds on the entropy of measures induced by bit-stuffing encoders. A more detailed analysis of a previously proposed bit-stuffing encoder for (d,/spl infin/)-runlength-limited (RLL) constraints on the square lattice yields improved lower bounds on the capacity for all d /spl ges/ 2. This encoding approach is extended to (d,/spl infin/)-RLL constraints on the hexagonal lattice, and a similar analysis yields lower bounds on the capacity for d /spl ges/ 2. For the hexagonal (1,/spl infin/)-RLL constraint, the exact coding ratio of the bit-stuffing encoder is calculated and is shown to be within 0.5% of the (known) capacity. Finally, a lower bound is presented on the coding ratio of a bit-stuffing encoder for the constraint on the square lattice where each bit is equal to at least one of its four closest neighbors, thereby providing a lower bound on the capacity of this constraint.     

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.     

Mismatched decoding and the multiple-access channel

An achievable region is derived for the multiple-access channel under decoding mismatch conditions. It is shown that achievable rates higher than the random coding capacity of the single-user mismatched channel can sometimes be demonstrated by treating the single-user channel as a multiple-access channel. Refining these ideas we derive a lower bound on the capacity of the mismatched single-user channel, which is tighter than previously published bounds. Using this bound, we are able to answer in the negative the question raised by Csiszar and Narayan (see ibid., vol.41, no.1, p.35, 1995) as to whether equality between the mismatch capacity and the matched capacity implies that the random coding lower bound to the mismatch capacity is tight     

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     

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     

Performance analysis of coherent TCM systems with diversityreception in slow Rayleigh fading

Coherent trellis-coded modulation (TCM) systems employing diversity combining are analyzed. Three different kinds of combining are considered: maximal ratio, equal gain, and selection combining (SC). First, the cutoff rate parameter is derived for equal gain combining (EGG) and SC assuming transmission over a fully interleaved channel with flat slow Rayleigh fading, which permits comparison with previously derived results for maximal ratio combining (MRC). Then, tight upper bounds on the pairwise error probabilities are derived for all three combining techniques. These upper bounds are expressed in product form to permit bounding of the bit error rate (BER) via the transfer function approach. In each case, it is assumed that the diversity branches are independent and that the channel state information (CSI) can be recovered perfectly. Also included is an analysis of MRC when the diversity branches are correlated-the cutoff rate and a tight upper bound on the pairwise error probability are derived. It is shown that with double diversity a branch correlation coefficient as high as 0.5 results in only slight performance degradation     

Source and channel rate allocation for channel codes satisfying theGilbert-Varshamov or Tsfasman-Vladut-Zink bounds

We derive bounds for optimal rate allocation between source and channel coding for linear channel codes that meet the Gilbert-Varshamov or Tsfasman-Vladut-Zink (1984) bounds. Formulas giving the high resolution vector quantizer distortion of these systems are also derived. In addition, we give bounds on how far below the channel capacity the transmission rate should be for a given delay constraint. The bounds obtained depend on the relationship between channel code rate and relative minimum distance guaranteed by the Gilbert-Varshamov bound, and do not require sophisticated decoding beyond the error correction limit. We demonstrate that the end-to-end mean-squared error decays exponentially fast as a function of the overall transmission rate, which need not be the case for certain well-known structured codes such as Hamming codes     

基于MIMO几何信道模型的容量界研究

MIMO技术是LTE的最重要技术之一。为了研究MIMO系统中信道容量界限,提出了基于双反射的几何信道模型。基于此模型,推导了信道相关系数及信道容量的表达式,证明了收发相关的MIMO信道容量上、下界。MonteCarlo信道容量仿真结果表明,MIMO信道容量上界在低信噪比的条件下具有紧性;而在高信噪比的条件下,MIMO信道容量的下界具有紧性。     

Probability of Error and Capacity of PPM Photon Counting Channel

Calculation of the capacity for a Poisson channel with a source noise as modeled by Pierce is done by bounding the error Probability. Based on Chernoff's bound properties, a more general method yielding a formula for the channel capacity is outlined.     

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.     

Bounds on capacity and minimum energy-per-bit for AWGN relay channels

Upper and lower bounds on the capacity and minimum energy-per-bit for general additive white Gaussian noise (AWGN) and frequency-division AWGN (FD-AWGN) relay channel models are established. First, the max-flow min-cut bound and the generalized block-Markov coding scheme are used to derive upper and lower bounds on capacity. These bounds are never tight for the general AWGN model and are tight only under certain conditions for the FD-AWGN model. Two coding schemes that do not require the relay to decode any part of the message are then investigated. First, it is shown that the "side-information coding scheme" can outperform the block-Markov coding scheme. It is also shown that the achievable rate of the side-information coding scheme can be improved via time sharing. In the second scheme, the relaying functions are restricted to be linear. The problem is reduced to a "single-letter" nonconvex optimization problem for the FD-AWGN model. The paper also establishes a relationship between the minimum energy-per-bit and capacity of the AWGN relay channel. This relationship together with the lower and upper bounds on capacity are used to establish corresponding lower and upper bounds on the minimum energy-per-bit that do not differ by more than a factor of 1.45 for the FD-AWGN relay channel model and 1.7 for the general AWGN model.     

Interference and Outage in Clustered Wireless Ad Hoc Networks

In the analysis of large random wireless networks, the underlying node distribution is almost ubiquitously assumed to be the homogeneous Poisson point process. In this paper, the node locations are assumed to form a Poisson cluster process on the plane. We derive the distributional properties of the interference and provide upper and lower bounds for its distribution. We consider the probability of successful transmission in an interference-limited channel when fading is modeled as Rayleigh. We provide a numerically integrable expression for the outage probability and closed-form upper and lower bounds. We show that when the transmitter–receiver distance is large, the success probability is greater than that of a Poisson arrangement. These results characterize the performance of the system under geographical or MAC-induced clustering. We obtain the maximum intensity of transmitting nodes for a given outage constraint, i.e., the transmission capacity (of this spatial arrangement) and show that it is equal to that of a Poisson arrangement of nodes. For the analysis, techniques from stochastic geometry are used, in particular the probability generating functional of Poisson cluster processes, the Palm characterization of Poisson cluster processes, and the Campbell–Mecke theorem.      

Performance bounds for space-time trellis codes

We derive the union bound for space-time trellis codes over quasi-static fading channels. We first observe that the standard approach for evaluating the union bound yields very loose, in fact divergent, bounds over the quasi-static fading channel. We then develop a method for obtaining a tight bound on the error probability. We derive the union bound by performing expurgation of the standard union bound. In addition, we limit the conditional union bound before averaging over the fading process. We demonstrate that this approach provides a tight bound on the error probability of space-time codes. The bounds can be used for the case when the fading coefficients among different transmit/receive antenna pairs are correlated as well. We present several examples of the bounds to illustrate their usefulness.