In this article, we are proposing a closed-form solution for the capacity of the single quantum channel. The Gaussian distributed input has been considered for the analytical calculation of the capacity. In our previous couple of papers, we invoked models for joint quantum noise and the corresponding received signals; in this current research, we proved that these models are Gaussian mixtures distributions. In this paper, we showed how to deal with both of cases, namely (I)the Gaussian mixtures distribution for scalar variables and (II) the Gaussian mixtures distribution for random vectors. Our target is to calculate the entropy of the joint noise and the entropy of the received signal in order to calculate the capacity expression of the quantum channel. The main challenge is to work with the function type of the Gaussian mixture distribution. The entropy of the Gaussian mixture distributions cannot be calculated in the closed-form solution due to the logarithm of a sum of exponential functions. As a solution, we proposed a lower bound and a upper bound for each of the entropies of joint noise and the received signal, and finally upper inequality and lower inequality lead to the upper bound for the mutual information and hence the maximum achievable data rate as the capacity. In this paper reader will able to visualize an closed-form capacity experssion which make this paper distinct from our previous works. These capacity experssion and coresses ponding bounds are calculated for both the cases: the Gaussian mixtures distribution for scalar variables and the Gaussian mixtures distribution for random vectors as well.
A method for achieving the continuous-space electromagnetic channel capacity bound using loaded N-port structures is described. It is relevant for the design of compact multiple-input multiple-output (MIMO) antennas that can achieve channel capacity bounds when constrained by size. The method is not restricted to a specific antenna configuration and a closed-form expression for the channel capacity limits are provided with various constraints. Furthermore, using loaded N-port structures to represent arbitrary antenna geometries, an efficient optimization approach is proposed for finding the op…
The capacity region of a multiple access channel is discussed. It was found that orthogonal multiple access and non orthogonal multiple access have the same capacity region under the constraint of same sum power.
We consider the class of channels formed from the concatenation of a deletion channel and a finite-state channel. For this class of channels, we show that the operational capacity is equal to the stationary capacity, which can be approached by a sequence of Markov processes with increasing Markovian orders. As a by-product, we show that the polar coding scheme constructed by Tal, Pfister, Fazeli and Vardy achieves the capacity of the deletion channel.
The sum capacity of a class of discrete memoryless interference channels is determined. This class of channels is defined analogous to the Gaussian Z-interference channel with weak interference; as a result, the sum capacity is achieved by letting the transceiver pair subject to the interference communicates at a rate such that its message can be decoded at the unintended receiver using single user detection. Moreover, this class of discrete memoryless interference channels is equivalent in capacity region to certain discrete degraded interference channels. This allows the construction of a ca…
This paper establishes the capacity region of a class of broadcast channels with random state in which each channel component is selected from two possible functions and each receiver knows its state sequence. This channel model does not fit into any class of broadcast channels for which the capacity region was previously known and is useful in studying wireless communication channels when the fading state is known only at the receivers. The capacity region is shown to coincide with the UV outer bound and is achieved via Marton coding.
Channel coding over arbitrarily-permuted parallel channels was first studied by Willems et al. (2008). This paper introduces capacity-achieving polar coding schemes for arbitrarily-permuted parallel channels where the component channels are memoryless, binary-input and output-symmetric.
The adaptive zero-error capacity of discrete memoryless channels (DMC) with noiseless feedback has been shown to be positive whenever there exists at least one channel output "disprover", i.e. a channel output that cannot be reached from at least one of the inputs. Furthermore, whenever there exists a disprover, the adaptive zero-error capacity attains the Shannon (small-error) capacity. Here, we study the zero-error capacity of a DMC when the channel feedback is noisy rather than perfect. We show that the adaptive zero-error capacity with noisy feedback is lower bounded by the forward channel…
Low-capacity scenarios have become increasingly important in the technology of the Internet of Things (IoT) and the next generation of wireless networks. Such scenarios require efficient and reliable transmission over channels with an extremely small capacity. Within these constraints, the state-of-the-art coding techniques may not be directly applicable. Moreover, the prior work on the finite-length analysis of optimal channel coding provides inaccurate predictions of the limits in the low-capacity regime. In this paper, we study channel coding at low capacity from two perspectives: fundament…
We establish the capacity region for a class of discrete memoryless cognitive interference channel (DM-CIC) called cognitive-more-capable channel, and we show that superposition coding is the optimal encoding technique. This is the largest capacity region for the DM-CIC to date, as the existing capacity results are explicitly shown to be its subsets.
The ergodic and outage channel capacity of different optimal and suboptimal combinations of transmit power and modulation rate adaptation strategies over a joint fading and two-path shadowing (JFTS) fading/shadowing channel is studied in this paper. Analytically tractable expressions for channel capacity are obtained, assuming perfect channel side information (CSI) at the receiver and/or the transmitter with negligible feedback delay. Furthermore, the impacts of the JFTS parameters on the channel capacity achieved by these adaptive transmission techniques are determined.
In this paper, we initiate a first information-theoretic study on multilevel NAND flash memory channels with intercell interference. More specifically, for a multilevel NAND flash memory channel under mild assumptions, we first prove that such a channel is indecomposable and it features asymptotic equipartition property; we then further prove that stationary processes achieve its information capacity, and consequently, as its order tends to infinity, its Markov capacity converges to its information capacity; eventually, we establish that its operational capacity is equal to its information cap…
This article studies the zero-error feedback capacity of {\em causal} discrete channels with memory. First, by extending the classical zero-error feedback capacity concept, a new notion of {\em uniform zero-error feedback capacity} $ C_{0f} $ for such channels is introduced. Using this notion a tight condition for {bounded} stabilization of unstable {noisy} linear systems via causal channels is obtained, assuming no {channel} state information at either end of the channel.
The capacity regions of multiple-input multiple-output Gaussian Z-interference channels are established for the very strong interference and aligned strong interference cases. The sum-rate capacity of such channels is established under noisy interference. These results generalize known results for scalar Gaussian Z-interference channels.
In this paper, the capacity of the additive white Gaussian noise (AWGN) channel, affected by time-varying Wiener phase noise is investigated. Tight upper and lower bounds on the capacity of this channel are developed. The upper bound is obtained by using the duality approach, and considering a specific distribution over the output of the channel. In order to lower-bound the capacity, first a family of capacity-achieving input distributions is found by solving a functional optimization of the channel mutual information. Then, lower bounds on the capacity are obtained by drawing samples from the…
We establish the capacity region of several classes of broadcast channels with random state in which the channel to each user is selected from two possible channel state components and the state is known only at the receivers. When the channel components are deterministic, we show that the capacity region is achieved via Marton coding. This channel model does not belong to any class of broadcast channels for which the capacity region was previously known and is useful in studying wireless communication channels when the fading state is known only at the receivers. We then establish the capacit…
This paper studies the capacity of a class of discrete memoryless interference channels where interference is defined analogous to that of Gaussian interference channel with one-sided weak interference. The sum-rate capacity of this class of channels is determined. As with the Gaussian case, the sum-rate capacity is achieved by letting the transceiver pair subject to interference communicate at a rate such that its message can be decoded at the unintended receiver using single user detection. It is also established that this class of discrete memoryless interference channels is equivalent in c…
The capacity of classical channels is convex. This is not the case for the quantum capacity of a channel: the capacity of a mixture of different quantum channels exceeds the mixture of the individual capacities and thus is non-convex. Here we show that this effect goes beyond the quantum capacity and holds for the private and classical environment-assisted capacities of quantum channels.
There are currently a plurality of capacity theories of fading channels, including the ergodic capacity for fast fading channels and outage capacity for slow fading channels. However, analyses show that the outage capacity is a misconception. In this paper we use the 1st order Gaussian-Markov process with coherence coefficient $α$ as the unified model for slow and fast fading channels, the capacity of which without channel side information is studied. We demonstrate that the information rate of a fading channel has a structure that the rate of user message is always accompanied by a rate of ch…
A single-letter characterization is provided for the capacity region of finite-state multiple access channels. The channel state is a Markov process, the transmitters have access to delayed state information, and channel state information is available at the receiver. The delays of the channel state information are assumed to be asymmetric at the transmitters. We apply the result to obtain the capacity region for a finite-state Gaussian MAC, and for a finite-state multiple-access fading channel. We derive power control strategies that maximize the capacity region for these channels.
This paper derives an outer bound on the capacity region of a general memoryless interference channel with an arbitrary number of users. The derivation follows from a generalization of the techniques developed by Kramer and by Etkin et al for the Gaussian two-user channel. The derived bound is the first known outer bound valid for any memoryless channel. In Gaussian noise, classes of channels for which the proposed bound gives the sum-rate capacity are identified, including degraded channels and a class of Z-channels.
The capacity of a network in which a multiple access channel (MAC) generates interference to a single-user channel is studied. An achievable rate region based on superposition coding and joint decoding is established for the discrete case. If the interference is very strong, the capacity region is obtained for both the discrete memoryless channel and the Gaussian channel. For the strong interference case, the capacity region is established for the discrete memoryless channel; for the Gaussian case, we attain a line segment on the boundary of the capacity region. Moreover, the capacity region f…
The wiretap channel model of Wyner is one of the first communication models with both reliability and security constraints. Capacity-achieving schemes for various models of the wiretap channel have received considerable attention in recent literature. In this paper, we show that capacity of the general (not necessarily degraded or symmetric) wiretap channel under a "strong secrecy constraint" can be achieved using a transmission scheme based on polar codes. We also extend our construction to the case of broadcast channels with confidential messages defined by Csisz{á}r and K{örner}, achieving …
We correct an alleged contradiction to Gallager's capacity theorem for waveform channels as presented in a poster at the 2012 IEEE International Symposium on Information Theory.
We study finite alphabet channels with Unit Memory on the previous Channel Outputs called UMCO channels. We identify necessary and sufficient conditions, to test whether the capacity achieving channel input distributions with feedback are time-invariant, and whether feedback capacity is characterized by single letter, expressions, similar to that of memoryless channels. The method is based on showing that a certain dynamic programming equation, which in general, is a nested optimization problem over the sequence of channel input distributions, reduces to a non-nested optimization problem. More…
We consider a unit memory channel, called Binary State Symmetric Channel (BSSC), in which the channel state is the modulo2 addition of the current channel input and the previous channel output. We derive closed form expressions for the capacity and corresponding channel input distribution, of this BSSC with and without feedback and transmission cost. We also show that the capacity of the BSSC is not increased by feedback, and it is achieved by a first order symmetric Markov process.
In this paper, capacity inner and outer bounds are established for the multiuser channels with Channel State Information (CSI) known non-causally at the transmitters: The Multiple Access Channel (MAC), the Broadcast Channel (BC) with common information, and the Relay Channel (RC). For each channel, the actual capacity region is also derived in some special cases. Specifically, it is shown that for some deterministic models with non-causal CSI at the transmitters, similar to Costa's Gaussian channel, the availability of CSI at the deterministic receivers does not affect the capacity region.
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.
We obtain new sum capacity results for the Gaussian many-to-one and one-to-many interference channels in channel parameter regimes where the sum capacity was known only up to a constant gap. Simple Han-Kobayashi (HK) schemes, i.e., HK schemes with Gaussian signaling, no time-sharing, and no common-private power splitting, achieve sum capacity under the channel conditions for which the new results are obtained. To obtain sum capacity results, we show that genie-aided upper bounds match the achievable sum rate of simple HK schemes under certain channel conditions.
The capacity of a class of multi-way relay channels, where L users communicate via a relay (at possibly different rates), is derived for the case where the channel outputs are modular sums of the channel inputs and the receiver noise. The cut-set upper bound to the capacity is shown to be achievable. More specifically, the capacity is achieved using (i) rate splitting, (ii) functional-decode-forward, and (iii) joint source-channel coding. We note that while separate source-channel coding can achieve the common-rate capacity, joint source-channel coding is used to achieve the capacity for the g…
This paper studies a layered erasure interference channel model, which is a simplification of the Gaussian interference channel with fading using the deterministic model approach. In particular, the capacity region of the layered erasure one-sided interference channel is completely determined, assuming that the channel state information (CSI) is known to the receivers, but there is no CSI at transmitters (CSIT). The result holds for arbitrary fading statistics. Previous results of Aggarwal, Sankar, Calderbank and Poor on the capacity region or sum capacity under several interference configurat…
The capacity of the multiple-access channel with any distribution of messages among the transmitting nodes was determined by Han in 1979 and the expression of the capacity region contains a number of rate bounds and that grows exponentially with the number of messages. We derive a more compact expression for the capacity region of this channel in which the number of rate bounds depends on the distribution of the messages at the encoders. Using this expression we prove capacity for a class of general cognitive network that we denote as "very strong interference" regime. In this regime there is …
The superactivation of zero-capacity quantum channels makes it possible to use two zero-capacity quantum channels with a positive joint capacity at the output. Currently, we have no theoretical background for describing all possible combinations of superactive zero-capacity channels; hence, there may be many other possible combinations. In this PhD Thesis I provide an algorithmic solution to the problem of superactivation and prove that superactivation effect is rooted in information geometric issues.
Capacity bounds for waveform channels under square-law detection of time-limited complex-valued signals are derived. The upper bound is the capacity of the channel under (complex-valued) coherent detection. The lower bound is one bit less, per dimension, than the upper bound.
The cognitive interference channel models cognitive overlay radio systems, where cognitive radios overhear the transmission of neighboring nodes. Capacity for this channel is not known in general. For the Gaussian case capacity is known in three regimes, usually denoted as the "weak interference", "very strong interference" and "primary decodes cognitive". This paper provides a new capacity result, based on rate-splitting of the primary user's message into a public and private part and that generalizes the capacity results in the "very strong interference" and "primary decodes cognitive" regim…
In this paper we consider point-to-point multiantenna channels with certain block distributional symmetries which do not require the entries of the channel matrix to be either Gaussian, or independent, or identically distributed. A main contribution is a capacity theorem for these channels, which might be regarded as a generalization of Telatar's theorem (1999), which reduces the numerical optimization domain in the capacity computation. With this information theoretic result and some free probability arguments, we prove an asymptotic capacity theorem that, in addition to reducing the optimiza…
The beta-binomial (BBM) channel model was recently proposed to model the overdispersed statistics of empirically observed bit errors in multi-level cell (MLC) flash memories. In this paper, we study the capacity of the BBM channel model for MLC flash memories. Using the compound channel approach, we first show that the BBM channel model capacity is zero. However, through empirical observation, this appears to be a very pessimistic estimate of the flash memory channel capacity. We propose a refined channel model called the truncated-support beta-binomial (TS-BBM) channel model and derive its ca…
In this paper, we study, information theoretically, the impact of transmitter and or receiver cognition on the channel capacity. The cognition can be described by state information, dependent on the channel noise and or input. Specifically, as a new idea, we consider the receiver cognition as a state information dependent on the noise and we derive a capacity theorem based on the Gaussian version of the Cover-Chiang capacity theorem for two-sided state information channel. As intuitively expected, the receiver cognition increases the channel capacity and our theorem shows this increase quantit…
One of the most surprising recent results in quantum Shannon theory is the superactivation of the quantum capacity of a quantum channel. This phenomenon has its roots in the extreme violation of additivity of the channel capacity and enables to reliably transmit quantum information over zero-capacity quantum channels. In this work we demonstrate a similar effect for the classical capacity of a quantum channel which previously was thought to be impossible. We show that a nonzero classical capacity can be achieved for all zero-capacity quantum channels and it only requires the assistance of an e…
Optical wireless communication (OWC) using intensity-modulation and direct-detection (IM/DD) has a channel model which possesses unique features, due to the constraints imposed on the channel input. The aim of this tutorial is to overview results on the capacity of IM/DD channels with input-independent Gaussian noise as a model of OWC channels. It provides the reader with an entry point to the topic, and highlights some major contributions in this area. It begins with a discussion on channel models and how this IM/DD Gaussian channel model comes about, in addition to an explanation of input co…
Memoryless channels with synchronization errors as defined by a stochastic channel matrix allowing for symbol insertions and deletions in addition to random errors are considered. Such channels are information stable, hence their Shannon capacity exists. However, computation of the channel capacity is formidable, and only some upper and lower bounds on the capacity (for some special cases) exist. In this short paper, using a simple methodology, we prove that the channel capacity is a convex function of the stochastic channel matrix. Since the more widely studied model of an independent identic…
For the class of the memoryless binary-input channels which are not necessarily symmetric, we derive tight bounds on the capacity in terms of the Bhattacharyya parameter. As it turns out, the bounds derived under the symmetric channel assumption in [1] are valid for the general case as well.
We study a nonlinear fiber optical channel impaired by cross-phase modulation and dispersion from the viewpoint of an interference channel. We characterize an outer bound on the capacity region of simultaneously achievable rate pairs, assuming a two-user perturbative channel model.
Channel symmetry properties that imply the tightness of Shannon's random coding inner bound have recently been used to determine the capacity region of discrete-memoryless two-way channels (DM-TWCs). For channels without such symmetry properties, outer bounds are often needed to estimate the capacity region. However, validating symmetry conditions and/or evaluating non-trivial outer bounds are computationally demanding, especially for channels with large input and output alphabets. In this paper, three easy-to-check conditions that identify DM-TWCs with no such symmetry properties as well as a…
