The capacity of multiple-input multiple-output additive white Gaussian noise channels is investigated under peak amplitude constraints on the norm of the input vector. New insights on the capacity-achieving input distribution are presented. Furthermore, it is provided an iterative algorithm to numerically evaluate both the information capacity and the optimal input distribution of such channel.
A Markov chain approach is applied to determine the capacity of a general class of q-ary ICI-free constrained systems that satisfy an arbitrary count constraint.
This paper slightly improves the upper bound in Thangaraj et al. for the capacity of the amplitude-constrained scalar AWGN channel. This improvement makes the upper bound within 0.002 bits of the capacity for $\frac{E_b}{N_0}\leq 2.5$ dB.
Binary-input memoryless channels with a runlength constrained input are considered. Upper bounds to the capacity of such noisy runlength constrained channels are derived using the dual capacity method with Markov test distributions satisfying the Karush-Kuhn-Tucker (KKT) conditions for the capacity-achieving output distribution. Simplified algebraic characterizations of the bounds are presented for the binary erasure channel (BEC) and the binary symmetric channel (BSC). These upper bounds are very close to achievable rates, and improve upon previously known feedback-based bounds for a large ra…
In many information-theoretic channel coding problems, adding an input cost constraint to the operational setup amounts to restricting the optimization domain in the capacity formula. This paper shows that, in contrast to common belief, such a simple modification does not hold for the cost-constrained (CC) wiretap channel (WTC). The secrecy-capacity of the discrete memoryless (DM) WTC without cost constraints is described by a single auxiliary random variable. For the CC DM-WTC, however, we show that two auxiliaries are necessary to achieve capacity. Specifically, we first derive the secrecy-c…
In this paper, we examine an input-constrained erasure channel and we characterize the asymptotics of its capacity when the erasure rate is low. More specifically, for a general memoryless erasure channel with its input supported on an irreducible finite-type constraint, we derive partial asymptotics of its capacity, using some series expansion type formulas of its mutual information rate; and for a binary erasure channel with its first-order Markovian input supported on the $(1, \infty)$-RLL constraint, based on the concavity of its mutual information rate with respect to some parameterizatio…
The input-constrained erasure channel with feedback is considered, where the binary input sequence contains no consecutive ones, i.e., it satisfies the $(1,\infty)$-RLL constraint. We derive the capacity for this setting, which can be expressed as $C_ε=\max_{0 \leq p \leq \frac{1}{2}}\frac{H_{b}(p)}{p+\frac{1}{1-ε}}$, where $ε$ is the erasure probability and $ H_{b}(\cdot)$ is the binary entropy function. Moreover, we prove that a-priori knowledge of the erasure at the encoder does not increase the feedback capacity. The feedback capacity was calculated using an equivalent dynamic programming …
The capacity-achieving input distribution of the discrete-time, additive white Gaussian noise (AWGN) channel with an amplitude constraint is discrete and seems difficult to characterize explicitly. A dual capacity expression is used to derive analytic capacity upper bounds for scalar and vector AWGN channels. The scalar bound improves on McKellips' bound and is within 0.1 bits of capacity for all signal-to-noise ratios (SNRs). The two-dimensional bound is within 0.15 bits of capacity provably up to 4.5 dB, and numerical evidence suggests a similar gap for all SNRs.
In this work, novel upper and lower bounds for the capacity of channels with arbitrary constraints on the support of the channel input symbols are derived. As an immediate practical application, the case of multiple-input multiple-output channels with amplitude constraints is considered. The bounds are shown to be within a constant gap if the channel matrix is invertible and are tight in the high amplitude regime for arbitrary channel matrices. Moreover, in the high amplitude regime, it is shown that the capacity scales linearly with the minimum between the number of transmit and receive anten…
Molecular communication is set to play an important role in the design of complex biological and chemical systems. An important class of molecular communication systems is based on the timing channel, where information is encoded in the delay of the transmitted molecule---a synchronous approach. At present, a widely used modeling assumption is the perfect synchronization between the transmitter and the receiver. Unfortunately, this assumption is unlikely to hold in most practical molecular systems. To remedy this, we introduce a clock into the model---leading to the molecular timing channel wi…
This paper studies secrecy-capacity of an $n$-dimensional Gaussian wiretap channel under the peak-power constraint. This work determines the largest peak-power constraint $\bar{\mathsf{R}}_n$ such that an input distribution uniformly distributed on a single sphere is optimal; this regime is termed the small-amplitude regime. The asymptotic of $\bar{\mathsf{R}}_n$ as $n$ goes to infinity is completely characterized as a function of noise variance at both receivers. Moreover, the secrecy-capacity is also characterized in a form amenable for computation. Furthermore, several numerical examples ar…
An interference-limited noise-free CDMA downlink channel operating under a complexity constraint on the receiver is introduced. According to this paradigm, detected bits, obtained by performing hard decisions directly on the channel's matched filter output, must be the same as the transmitted binary inputs. This channel setting, allowing the use of the simplest receiver scheme, seems to be worthless, making reliable communication at any rate impossible. We prove, by adopting statistical mechanics notion, that in the large-system limit such a complexity-constrained CDMA channel gives rise to a …
This paper considers the memoryless input-constrained binary erasure channel (BEC). The channel input constraint is the $(d,\infty)$-runlength limited (RLL) constraint, which mandates that any pair of successive $1$s in the input sequence be separated by at least $d$ $0$s. We consider a scenario where there is causal, noiseless feedback from the decoder. We demonstrate a simple, labelling-based, zero-error feedback coding scheme, which we prove to be feedback capacity-achieving, and, as a by-product, obtain an explicit characterization of the feedback capacity. Our proof is based on showing th…
In the first chapter of Shannon's "A Mathematical Theory of Communication," it is shown that the maximum entropy rate of an input process of a constrained system is limited by the combinatorial capacity of the system. Shannon considers systems where the constraints define regular languages and uses results from matrix theory in his derivations. In this work, the regularity constraint is dropped. Using generating functions, it is shown that the maximum entropy rate of an input process is upper-bounded by the combinatorial capacity in general. The presented results also allow for a new approach …
We derive bounds on the noncoherent capacity of a very general class of multiple-input multiple-output channels that allow for selectivity in time and frequency as well as for spatial correlation. The bounds apply to peak-constrained inputs; they are explicit in the channel's scattering function, are useful for a large range of bandwidth, and allow to coarsely identify the capacity-optimal combination of bandwidth and number of transmit antennas. Furthermore, we obtain a closed-form expression for the first-order Taylor series expansion of capacity in the limit of infinite bandwidth. From this…
This work considers a Poisson noise channel with an amplitude constraint. It is well-known that the capacity-achieving input distribution for this channel is discrete with finitely many points. We sharpen this result by introducing upper and lower bounds on the number of mass points. Concretely, an upper bound of order $\mathsf{A} \log^2(\mathsf{A})$ and a lower bound of order $\sqrt{\mathsf{A}}$ are established where $\mathsf{A}$ is the constraint on the input amplitude. In addition, along the way, we show several other properties of the capacity and capacity-achieving distribution. For examp…
The input-constrained binary erasure channel (BEC) with strictly causal feedback is studied. The channel input sequence must satisfy the $(0,k)$-runlength limited (RLL) constraint, i.e., no more than $k$ consecutive `$0$'s are allowed. The feedback capacity of this channel is derived for all $k\geq 1$, and is given by $$C^\mathrm{fb}_{(0,k)}(\varepsilon) = \max\frac{\overline{\varepsilon}H_2(δ_0)+\sum_{i=1}^{k-1}\left(\overline{\varepsilon}^{i+1}H_2(δ_i)\prod_{m=0}^{i-1}δ_m\right)}{1+\sum_{i=0}^{k-1}\left(\overline{\varepsilon}^{i+1} \prod_{m=0}^{i}δ_m\right)},$$ where $\varepsilon$ is the era…
This paper studies a scalar Gaussian wiretap channel where instead of an average input power constraint, we consider a peak amplitude constraint on the input. The goal is to obtain insights into the secrecy-capacity and the structure of the secrecy-capacity-achieving distribution. Capitalizing on the recent theoretical progress on the structure of the secrecy-capacity-achieving distribution, this paper develops a numerical procedure, based on the gradient ascent algorithm and a version of the Blahut-Arimoto algorithm, for computing the secrecy-capacity and the secrecy-capacity-achieving input …
We propose a decoder for Trellis-Constrained Codes, a super-class of Turbo- and LDPC codes. Inspired by amplitude amplification from quantum computing, we attempt to amplify the relative likelihood of the most likely codeword until it stands out from all other codewords.
In this paper, we derive UWB version of (i) general best achievable rate for the relay channel with decode-andforward strategy and (ii) max-flow min-cut upper bound, such that the UWB relay channel can be studied considering the obtained lower and upper bounds. Then, we show that by appropriately choosing the noise correlation coefficients, our new upper bound coincides with the lower bound in special cases of degraded and reversely degraded UWB relay channels. Finally, some numerical results are illustrated.
In this paper, we investigate the sum-capacity of the two-user Gaussian interference channel with Gaussian superposition coding and successive decoding. We first examine an approximate deterministic formulation of the problem, and introduce the complementarity conditions that capture the use of Gaussian coding and successive decoding. In the deterministic channel problem, we find the constrained sum-capacity and its achievable schemes with the minimum number of messages, first in symmetric channels, and then in general asymmetric channels. We show that the constrained sum-capacity oscillates a…
For a stationary additive Gaussian-noise channel with a rational noise power spectrum of a finite-order $L$, we derive two new results for the feedback capacity under an average channel input power constraint. First, we show that a very simple feedback-dependent Gauss-Markov source achieves the feedback capacity, and that Kalman-Bucy filtering is optimal for processing the feedback. Based on these results, we develop a new method for optimizing the channel inputs for achieving the Cover-Pombra block-length-$n$ feedback capacity by using a dynamic programming approach that decomposes the comput…
We revisit Shannon's problem of bounding the capacity of bandlimited Gaussian channel (BLGC) with peak power constraint, and extend the problem to the peak-to-average-power-ratio (PAPR) constrained case. By lower bounding the achievable information rate of pulse amplitude modulation with independent and identically distributed input under a PAPR constraint, we obtain a general capacity lower bound with respect to the shaping pulse. We then evaluate and optimize the lower bound by employing some parametric pulses, thereby improving the best existing result. Following Shannon's approach, capacit…
We study the classical problem of noisy constrained capacity in the case of the binary symmetric channel (BSC), namely, the capacity of a BSC whose inputs are sequences chosen from a constrained set. Motivated by a result of Ordentlich and Weissman [In Proceedings of IEEE Information Theory Workshop (2004) 117--122], we derive an asymptotic formula (when the noise parameter is small) for the entropy rate of a hidden Markov chain, observed when a Markov chain passes through a BSC. Using this result, we establish an asymptotic formula for the capacity of a BSC with input process supported on an …
Upper bounds on the capacity of vector Gaussian channels affected by fading are derived under peak amplitude constraints at the input. The focus is on constraint regions that can be decomposed in a Cartesian product of sub-regions. This constraint models a transmitter configuration employing a number of power amplifiers less than or equal to the total number of transmitting antennas. In general, the power amplifiers feed distinct subsets of the transmitting antennas and partition the input in independent subspaces. Two upper bounds are derived: The first one is suitable for high signal-to-nois…
The per-sample zero-dispersion channel model of the optical fiber is considered. It is shown that capacity is uniquely achieved by an input probability distribution that has continuous uniform phase and discrete amplitude that takes on finitely many values. This result holds when the channel is subject to general input cost constraints, that include a peak amplitude constraint and a joint average and peak amplitude constraint.
This paper considers the problem of secret-key agreement with public discussion subject to a peak power constraint $A$ on the channel input. The optimal input distribution is proved to be discrete with finite support. The result is obtained by first transforming the secret-key channel model into an equivalent Gaussian wiretap channel with better noise statistics at the legitimate receiver and then using the fact that the optimal distribution of the Gaussian wiretap channel is discrete. To overcome the computationally heavy search for the optimal discrete distribution, several suboptimal scheme…
Parallel, additive white Gaussian noise (AWGN) channels with an average sum power constraint are considered. It is shown how the waterfilling Shannon capacity can be approached by higher order modulation and probabilistic amplitude shaping (PAS). This is achieved by a new distribution matching approach called product distribution matching (PDM). The asymptotic performance of PDM is analyzed by achievable rates. A heuristic for optimizing the input distribution is proposed, which enables signaling at a target spectral efficiency with a fixed-rate forward error correction (FEC) code, while the o…
In this paper, we study the capacity and degree-of-freedom (DoF) scaling for the continuous-time amplitude limited AWGN channels in radio frequency (RF) and intensity modulated optical communication (OC) channels. More precisely, we study how the capacity varies in terms of the OFDM block transmission time $T$, bandwidth $W$, amplitude $A$, and the noise spectral density $N_0$. We first find suitable discrete encoding spaces for both cases, and prove that they are convex sets that have a semi-definite programming (SDP) representation. Using tools from convex geometry, we find lower and upper b…
When transmitting information over a noisy channel, two approaches, dating back to Shannon's work, are common: assuming the channel errors are independent of the transmitted content and devising an error-correcting code, or assuming the errors are data dependent and devising a constrained-coding scheme that eliminates all offending data patterns. In this paper we analyze a middle road, which we call a semiconstrained system. In such a system, which is an extension of the channel with cost constraints model, we do not eliminate the error-causing sequences entirely, but rather restrict the frequ…
The paper considers the input-constrained binary erasure channel (BEC) with causal, noiseless feedback. The channel input sequence respects the $(d,\infty)$-runlength limited (RLL) constraint, i.e., any pair of successive $1$s must be separated by at least $d$ $0$s. We derive upper and lower bounds on the feedback capacity of this channel, for all $d\geq 1$, given by: $\max\limits_{δ\in [0,\frac{1}{d+1}]}R(δ) \leq C^{\text{fb}}_{(d\infty)}(ε) \leq \max\limits_{δ\in [0,\frac{1}{1+dε}]}R(δ)$, where the function $R(δ) = \frac{h_b(δ)}{dδ+ \frac{1}{1-ε}}$, with $ε\in [0,1]$ denoting the channel era…
The dirty paper channel (DPC) under a peak amplitude constraint arises in an optical wireless broadcast channel (BC), where the state at one receiver is the transmitted signal intended for the other receiver(s). This paper studies a class of peak-constrained DPC that is applicable to the optical wireless BC, where the channel state (i.e, `dirt') takes values from some evenly-spaced grid. For the discrete-state DPC studied this paper, a capacity upper bound is obtained from its state-free counterpart. To lower bound its capacity, classical dirty paper coding schemes are revisited, including Cos…
This paper studies the capacity of an $n$-dimensional vector Gaussian noise channel subject to the constraint that an input must lie in the ball of radius $R$ centered at the origin. It is known that in this setting the optimizing input distribution is supported on a finite number of concentric spheres. However, the number, the positions and the probabilities of the spheres are generally unknown. This paper characterizes necessary and sufficient conditions on the constraint $R$ such that the input distribution supported on a single sphere is optimal. The maximum $\bar{R}_n$, such that using on…
This paper provides new inner and outer bounds on the capacity region of optical intensity multiple access channel (OIMAC) with per-user average or peak power constraint. For the average power constrained OIMAC, our bounds at high power are asymptotically tight, thereby characterizing the asymptotic capacity region. The bounds are extended to K-user OIMAC with average power constraint without loss of asymptotic optimality. For the peak power constrained OIMAC, at high power, we bound the asymptotic capacity region to within 0.09 bits, and determine the asymptotic capacity region in the symmetr…
We propose coding techniques that limit the length of homopolymers runs, ensure the GC-content constraint, and are capable of correcting a single edit error in strands of nucleotides in DNA-based data storage systems. In particular, for given $\ell, ε > 0$, we propose simple and efficient encoders/decoders that transform binary sequences into DNA base sequences (codewords), namely sequences of the symbols A, T, C and G, that satisfy the following properties: (i) Runlength constraint: the maximum homopolymer run in each codeword is at most $\ell$, (ii) GC-content constraint: the GC-content of e…
In this paper, we analyze the performance of a secondary link in a cognitive radio (CR) system operating under statistical quality of service (QoS) delay constraints. In particular, we quantify analytically the performance improvement for the secondary user (SU) when applying a feedback based sensing scheme under the "SINR Interference" model. We leverage the concept of effective capacity (EC) introduced earlier in the literature to quantify the wireless link performance under delay constraints, in an attempt to opportunistically support real-time applications. Towards this objective, we study…
This paper investigates reducing sub-packetization of capacity-achieving schemes for uncoded Storage Constrained Private Information Retrieval (SC-PIR) systems. In the SC-PIR system, a user aims to retrieve one out of $K$ files from $N$ servers while revealing nothing about its identity to any individual server, in which the $K$ files are stored at the $N$ servers in an uncoded form and each server can store up to $μK$ equivalent files, where $μ$ is the normalized storage capacity of each server. We first prove that there exists a capacity-achieving SC-PIR scheme for a given storage design if …
In this paper, we derive upper and lower bounds as well as a simple closed-form approximation for the capacity of the continuous-time, bandlimited, additive white Gaussian noise channel in a three-dimensional free-space electromagnetic propagation environment subject to constraints on the total effective antenna aperture area of the link and a total transmitter power constraint. We assume that the communication range is much larger than the radius of the sphere containing the antennas at both ends of the link, and we show that, in general, the capacity can only be achieved by transmitting mult…
Transmission of information over a discrete-time memoryless Rician fading channel is considered where neither the receiver nor the transmitter knows the fading coefficients. First the structure of the capacity-achieving input signals is investigated when the input is constrained to have limited peakedness by imposing either a fourth moment or a peak constraint. When the input is subject to second and fourth moment limitations, it is shown that the capacity-achieving input amplitude distribution is discrete with a finite number of mass points in the low-power regime. A similar discrete structur…
This paper presents a 3-D statistical channel model of the impulse response with small-scale spatially correlated random coefficients for multi-element transmitter and receiver antenna arrays, derived using the physically-based time cluster - spatial lobe (TCSL) clustering scheme. The small-scale properties of multipath amplitudes are modeled based on 28 GHz outdoor millimeter-wave small-scale local area channel measurements. The wideband channel capacity is evaluated by considering measurement-based Rician-distributed voltage amplitudes, and the spatial autocorrelation of multipath amplitudes…
This paper studies an $n$-dimensional additive Gaussian noise channel with a peak-power-constrained input. It is well known that, in this case, when $n=1$ the capacity-achieving input distribution is discrete with finitely many mass points, and when $n>1$ the capacity-achieving input distribution is supported on finitely many concentric shells. However, due to the previous proof technique, neither the exact number of mass points/shells of the optimal input distribution nor a bound on it was available. This paper provides an alternative proof of the finiteness of the number mass points/shells o…
In this paper, the Dynamic-Assignment Blahut-Arimoto (DAB) algorithm identifies finite-support probability mass functions (PMFs) with small cardinality that achieve capacity for amplitude-constrained (AC) Additive White Gaussian Noise (AWGN) Channels, or approach capacity to within less than 1% for power-constrained (PC) AWGN Channels. While a continuous Gaussian PDF is well-known to be a theoretical capacity-achieving distribution for the PC-AWGN channel, DAB identifies PMFs with small-cardinality that are, for practical purposes, indistinguishable in performance. We extend the results of Oza…
This paper considers the input-constrained binary memoryless symmetric (BMS) channel, without feedback. The channel input sequence respects the $(d,\infty)$-runlength limited (RLL) constraint, which mandates that any pair of successive $1$s be separated by at least $d$ $0$s. We consider the problem of designing explicit codes for such channels. In particular, we work with the Reed-Muller (RM) family of codes, which were shown by Reeves and Pfister (2021) to achieve the capacity of any unconstrained BMS channel, under bit-MAP decoding. We show that it is possible to pick $(d,\infty)$-RLL subcod…
This work studies the secrecy-capacity of a scalar-Gaussian wiretap channel with an amplitude constraint on the input. It is known that for this channel, the secrecy-capacity-achieving distribution is discrete with finitely many points. This work improves such result by showing an upper bound of the order $\frac{\mathsf{A}}{σ_1^2}$ where $\mathsf{A}$ is the amplitude constraint and $σ_1^2$ is the variance of the Gaussian noise over the legitimate channel.
We establish in closed-form the capacity and the optimal signaling scheme for a MISO channel with per-antenna power constraint. Two cases of channel state information are considered: constant channel known at both the transmitter and receiver, and Rayleigh fading channel known only at the receiver. For the first case, the optimal signaling scheme is beamforming with the phases of the beam weights matched to the phases of the channel coefficients, but the amplitudes independent of the channel coefficients and dependent only on the constrained powers. For the second case, the optimal scheme is t…
Hypergraphical sources are a natural class of sources for secret key generation, within which different subsets of terminals sharing secrets are allowed to discuss publicly in order to agree upon a global secret key. While their secrecy capacity, i.e., the maximum rate of a secret key that can be agreed upon by the entire set of terminals, is well-understood, what remains open is the maximum rate of a secret key that can be generated when there is a restriction on the overall rate of public discussion allowed. In this work, we obtain a family of explicitly computable upper bounds on the number…
A joint communication and channel state estimation problem is investigated, in which reliable information transmission over a noisy channel, and high-fidelity estimation of the channel state, are simultaneously sought. The tradeoff between the achievable information rate and the estimation distortion is quantified by formulating the problem as a constrained channel coding problem, and the resulting capacity-distortion function characterizes the fundamental limit of the joint communication and channel estimation problem. The analytical results are illustrated through case studies, and further i…
In "Reliable Communication in the Absence of a Common Clock" (Yeung et al., 2009), the authors introduce general run-length sets, which form a class of constrained systems that permit run-lengths from a countably infinite set. For a particular definition of probabilistic capacity, they show that probabilistic capacity is equal to combinatorial capacity. In the present work, it is shown that the same result also holds for Shannon's original definition of probabilistic capacity. The derivation presented here is based on generating functions of constrained systems as developed in "On the Capacity…
With the complication of future communication scenarios, most conventional signal processing technologies of multi-user multiple-input multiple-output (MU-MIMO) become unreliable, which are designed based on ideal assumptions, such as Gaussian signaling and independent identically distributed (IID) channel matrices. As a result, this paper considers a generalized MU-MIMO (GMU-MIMO) system with more general assumptions, i.e., arbitrarily fixed input distributions, and general unitarily-invariant channel matrices. However, there is still no accurate capacity analysis and capacity optimal transce…
