In digital systems such as fiber optical communications, the ratio between probability of errors of type $1\to 0$ and $0 \to 1$ can be large. Practically, one can assume that only one type of error can occur. These errors arecalled asymmetric. Unidirectional errors differ from asymmetric type of errors; here both $1 \to 0$ and $0 \to 1$ type of errors are possible, but in any submittedcodeword all the errors are of the same type. This can be generalized for the $q$-ary case. We consider $q$-ary unidirectional channels with feedback and give bounds for the capacity error function. It turns out that the bounds depend on the parity of the alphabet $q$. Furthermore, we show that for feedback, the capacity error function for the binary asymmetric channel is different from the symmetric channel. This is in contrast to the behavior of the function without feedback.
This paper concerns the capacity of the discrete noiseless channel introduced by Shannon. A sufficient condition is given for the capacity to be well-defined. For a general discrete noiseless channel allowing non-integer valued symbol weights, it is shown that the capacity--if well-defined--can be determined from the radius of convergence of its generating function, from the smallest positive pole of its generating function, or from the rightmost real singularity of its complex generating function. A generalisation is given for Pringsheim's Theorem and for the Exponential Growth Formula to gen…
We study the discrete memoryless Z-interference channel (ZIC) where the transmitter of the pair that suffers from interference is cognitive. We first provide upper and lower bounds on the capacity of this channel. We then show that, when the channel of the transmitter-receiver pair that does not face interference is noiseless, the two bounds coincide and therefore yield the capacity region. The obtained results imply that, unlike in the Gaussian cognitive ZIC, in the considered channel superposition encoding at the non-cognitive transmitter as well as Gel'fand-Pinsker encoding at the cognitive…
Previous works established the capacity region for some special cases of discrete memoryless degraded cognitive interference channel (CIC) with unidirectional destination cooperation (UDC). In this letter, we characterize the capacity region of the general discrete memoryless degraded CIC-UDC. The obtained results imply that the capacity region is achieved by the Gel'fand-Pinsker coding at the cognitive transmitter, superposition coding at the primary transmitter and decode-and-forward at the relay. Furthermore, using this general result and a novel converse analysis, we establish the capacity…
In this paper, we consider the problem of evaluating capacity expression of a multiple access channel (MAC) with noiseless feedback. So far, the capacity expression for this channel is known through a multi letter directed information by Kramer [1]. Recently, it was shown in [2] that one can pose it as a dynamic optimization problem, however, no dynamic program was provided as the authors claimed there is no notion of state that is observed by both the senders. In this paper, we build upon [2] to show that there indeed exists a state and therefore a dynamic program (DP) that decomposes this dy…
The performance of the generalized belief propagation algorithm for computing the noiseless capacity and mutual information rates of finite-size two-dimensional and three-dimensional run-length limited constraints is investigated. For each constraint, a method is proposed to choose the basic regions and to construct the region graph. Simulation results for the capacity of different constraints as a function of the size of the channel and mutual information rates of different constraints as a function of signal-to-noise ratio are reported. Convergence to the Shannon capacity is also discussed.
We define capacity for group testing problems and deduce bounds for the capacity of a variety of noisy models, based on the capacity of equivalent noisy communication channels. For noiseless adaptive group testing we prove an information-theoretic lower bound which tightens a bound of Chan et al. This can be combined with a performance analysis of a version of Hwang's adaptive group testing algorithm, in order to deduce the capacity of noiseless and erasure group testing models.
Berlekamp and Zigangirov completely determined the capacity error function for binary error correcting codes with noiseless feedback. It is still an unsolved problem if the upper bound for the capacity error function in the non-binary case of Ahlswede, Lebedev, and Deppe is sharp. We consider wraparound channels with limited magnitude and noiseless feedback. We completely determine the capacity error function for all $q$-ary wraparound channels with a magnitude of level $r$. All of our algorithms use partial noiseless feedback. Furthermore, a special case of the problem is equivalent to Shanno…
The cognitive interference channel with unidirectional destination cooperation (CIFC-UDC) is a variant of the cognitive interference channel (CIFC) where the cognitive (secondary) destination not only decodes the information sent from its sending dual but also helps enhance the communication of the primary user. This channel is an extension of the original CIFC to achieve a win-win solution under the coexistence condition. The CIFC-UDC comprises a broadcast channel (BC), a relay channel (RC), as well as a partially cooperative relay broadcast channel (PCRBC), and can be degraded to any one of …
A coding scheme for the discrete memoryless broadcast channel with {noiseless, noisy, generalized} feedback is proposed, and the associated achievable region derived. The scheme is based on a block-Markov strategy combining the Marton scheme and a lossy version of the Gray-Wyner scheme with side-information. In each block the transmitter sends fresh data and update information that allows the receivers to improve the channel outputs observed in the previous block. For a generalization of Dueck's broadcast channel our scheme achieves the noiseless-feedback capacity, which is strictly larger tha…
In this paper, first, we investigate the model of degraded broadcast channel with side information and confidential messages. This work is from Steinberg's work on the degraded broadcast channel with causal and noncausal side information, and Csisz$\acute{a}$r-Körner's work on broadcast channel with confidential messages. Inner and outer bounds on the capacity-equivocation regions are provided for the noncausal and causal cases. Superposition coding and double-binning technique are used in the corresponding achievability proofs. Then, we investigate the degraded broadcast channel with side inf…
We consider the transmission of a memoryless bivariate Gaussian source over a two-user additive Gaussian multiple-access channel with unidirectional conferencing encoders. Here, prior to each transmission block, Encoder 1, which observes the first source component, is allowed to communicate with Encoder 2, which observes the second source component, via a unidirectional noise-free bit-pipe of given capacity. The main results of this work are sufficient conditions and a necessary condition for the achievability of a distortion pair expressed as a function of the channel SNR and of the source co…
A two-user symmetric Gaussian Interference Channel (IC) is considered in which a noiseless unidirectional link connects one encoder to the other. Having a constant capacity, the additional link provides partial cooperation between the encoders. It is shown that the available cooperation can dramatically increase the sum-capacity of the channel. This fact is proved based on comparison of proposed lower and upper bounds on the sum-capacity. Partitioning the data into three independent messages, namely private, common, and cooperative ones, the transmission strategy used to obtain the lower bound…
This paper derives outer bounds on the secrecy capacity region of the 2-user Z interference channel (Z-IC) with rate-limited unidirectional cooperation between the transmitters. First, the model is studied under the linear deterministic setting. The derivation of the outer bounds on the secrecy capacity region involves careful selection of the side information to be provided to the receivers and using the secrecy constraints at the receivers in a judicious manner. To this end, a novel partitioning of the encoded messages and outputs is proposed for the deterministic model based on the strength…
The physical layer security in the up-link of the wireless communication systems is often modeled as the multiple access wiretap channel (MAC-WT), and recently it has received a lot attention. In this paper, the MAC-WT has been re-visited by considering the situation that the legitimate receiver feeds his received channel output back to the transmitters via two noiseless channels, respectively. This model is called the MAC-WT with noiseless feedback. Inner and outer bounds on the secrecy capacity region of this feedback model are provided. To be specific, we first present a decode-and-forward …
In this work, the role of unidirectional limited rate transmitter cooperation is studied in the case of the 2-user Z interference channel (Z-IC) with secrecy constraints at the receivers, on achieving two conflicting goals simultaneously: mitigating interference and ensuring secrecy. First, the problem is studied under the linear deterministic model. The achievable schemes for the deterministic model use a fusion of cooperative precoding and transmission of a jamming signal. The optimality of the proposed scheme is established for the deterministic model for all possible parameter settings usi…
We study the activated quantum no-signalling-assisted zero-error classical capacity by first allowing the assistance from some noiseless forward communication channel and later paying back the cost of the helper. This activated communication model considers the additional forward noiseless channel as a catalyst for communication. First, we show that the one-shot activated capacity can be formulated as a semidefinite program and we derive a number of striking properties of this capacity. We further present a sufficient condition under which a noisy channel can be activated. Second, we show that…
The capacity of non-coherent stationary Gaussian fading channels with memory under a peak-power constraint is studied in the asymptotic weak-signal regime. It is assumed that the fading law is known to both transmitter and receiver but that neither is cognizant of the fading realization. A connection is demonstrated between the asymptotic behavior of channel capacity in this regime and the asymptotic behavior of the prediction error incurred in predicting the fading process from very noisy observations of its past. This connection can be viewed as the low signal-to-noise ratio (SNR) analog of …
For a multi-source multi-terminal noiseless network, the key-dissemination problem involves the task of multicasting a secret key K from the network sources to its terminals. As in secure multicast network-coding, in the key-dissemination problem the source nodes have access to independent randomness and, as the network is noiseless, the resulting key K is a function of the sources' information. However, different from traditional forms of multicast, in key-dissemination the key K need not consist of source messages, but rather may be any function of the information generated at the sources, a…
We consider the problem of communication over a two-user Additive White Gaussian Noise Broadcast Channel (AWGN-BC) with an AWGN Multiple Access (MAC) active feedback. We describe a constructive reduction from this setup to the well-studied setup of linear-feedback coding over the AWGN-BC with noiseless feedback (and different parameters). This reduction facilitates the design of linear-feedback coding schemes in the (passive) noiseless feedback regime, which can then be easily and constructively transformed into coding schemes in the MAC feedback regime that attain the exact same rates. Our co…
This paper considers the capacity gains due to unidirectional destination cooperation in cognitive radio channels. We propose a novel channel, interference channel with degraded message sets with unidirectional destination cooperation (IC-DMS-UDC), to allow the receiver of cognitive radio (secondary user) to participate in relaying the information for primary system (legitimate user). Our main result is the development of an achievable rate region which combines Gel'fand-Pinkser coding with partial-decode-and-forward strategy employed in the relay channel. A numerical evaluation of the region …
We consider the problem of decentralized sequential active hypothesis testing (DSAHT), where two transmitting agents, each possessing a private message, are actively helping a third agent--and each other--to learn the message pair over a discrete memoryless multiple access channel (DM-MAC). The third agent (receiver) observes the noisy channel output, which is also available to the transmitting agents via noiseless feedback. We formulate this problem as a decentralized dynamic team, show that optimal transmission policies have a time-invariant domain, and characterize the solution through a dy…
We initiate the study of zero-error communication via quantum channels when the receiver and sender have at their disposal a noiseless feedback channel of unlimited quantum capacity, generalizing Shannon's zero-error communication theory with instantaneous feedback. We first show that this capacity is a function only of the linear span of Choi-Kraus operators of the channel, which generalizes the bipartite equivocation graph of a classical channel, and which we dub "non-commutative bipartite graph". Then we go on to show that the feedback-assisted capacity is non-zero (with constant activating…
In this paper, we propose capacity-achieving communication schemes for Gaussian finite-state Markov channels (FSMCs) subject to an average channel input power constraint, under the assumption that the transmitters can have access to delayed noiseless output feedback as well as instantaneous or delayed channel state information (CSI). We show that the proposed schemes reveals connections between feedback communication and feedback control.
We generalize the uniform common randomness capacity formula, initially established by Ahslwede and Csiszár for a two-source model for common randomness generation from independent and identically distributed (i.i.d.) discrete sources with unidirectional communication over rate-limited discrete noiseless channels to the case when the one-way communication is over arbitrary single-user channels. In our proof, we will make use of the transmission capacity formula established by Verdú and Han for arbitrary point-to-point channels.
In this paper, we consider the problem of sequential transmission over the binary symmetric channel (BSC) with full, noiseless feedback. Naghshvar et al. proposed a one-phase encoding scheme, for which we refer to as the small-enough difference (SED) encoder, which can achieve capacity and Burnashev's optimal error exponent for symmetric binary-input channels. They also provided a non-asymptotic upper bound on the average blocklength, which implies an achievability bound on rates. However, their achievability bound is loose compared to the simulated performance of SED encoder, and even lies be…
Shannon's theory of zero-error communication is re-examined in the broader setting of using one classical channel to simulate another exactly, and in the presence of various resources that are all classes of non-signalling correlations: Shared randomness, shared entanglement and arbitrary non-signalling correlations. Specifically, when the channel being simulated is noiseless, this reduces to the zero-error capacity of the channel, assisted by the various classes of non-signalling correlations. When the resource channel is noiseless, it results in the "reverse" problem of simulating a noisy ch…
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…
A two-user discrete memoryless compound multiple access channel with a common message and conferencing decoders is considered. The capacity region is characterized in the special cases of physically degraded channels and unidirectional cooperation, and achievable rate regions are provided for the general case. The results are then extended to the corresponding Gaussian model. In the Gaussian setup, the provided achievable rates are shown to lie within some constant number of bits from the boundary of the capacity region in several special cases. An alternative model, in which the encoders are …
In this paper, we obtain a family of lower bounds for the sum capacity of Code Division Multiple Access (CDMA) channels assuming binary inputs and binary signature codes in the presence of additive noise with an arbitrary distribution. The envelope of this family gives a relatively tight lower bound in terms of the number of users, spreading gain and the noise distribution. The derivation methods for the noiseless and the noisy channels are different but when the noise variance goes to zero, the noisy channel bound approaches the noiseless case. The behavior of the lower bound shows that for s…
Building on the work of Horstein, Shayevitz and Feder, and Naghshvar \emph{et al.}, this paper presents algorithms for low-complexity sequential transmission of a $k$-bit message over the binary symmetric channel (BSC) with full, noiseless feedback. To lower complexity, this paper shows that the initial $k$ binary transmissions can be sent before any feedback is required and groups messages with equal posteriors to reduce the number of posterior updates from exponential in $k$ to linear in $k$. Simulation results demonstrate that achievable rates for this full, noiseless feedback system approa…
We derive a new Sequential-Monte-Carlo-based algorithm to estimate the capacity of two-dimensional channel models. The focus is on computing the noiseless capacity of the 2-D one-infinity run-length limited constrained channel, but the underlying idea is generally applicable. The proposed algorithm is profiled against a state-of-the-art method, yielding more than an order of magnitude improvement in estimation accuracy for a given computation time.
We study the problem of the transmission of currently observed time variable signals via a channel that is capable of sending a single binary signal only for each measurement of the underlying process. For encoding and decoding, we suggest a modification othe adaptive delta modulation algorithm. This modification ensures tracking of time variable signals. We obtained upper estimates for the error for the case of noiseless transmission.
We consider networks of noisy degraded wiretap channels in the presence of an eavesdropper. For the case where the eavesdropper can wiretap at most one channel at a time, we show that the secrecy capacity region, for a broad class of channels and any given network topology and communication demands, is equivalent to that of a corresponding network where each noisy wiretap channel is replaced by a noiseless wiretap channel. Thus in this case there is a separation between wiretap channel coding on each channel and secure network coding on the resulting noiseless network. We show with an example …
We study a special class of diamond channels which was introduced by Schein in 2001. In this special class, each diamond channel consists of a transmitter, a noisy relay, a noiseless relay and a receiver. We prove the capacity of this class of diamond channels by providing an achievable scheme and a converse. The capacity we show is strictly smaller than the cut-set bound. Our result also shows the optimality of a combination of decode-and-forward (DAF) and compress-and-forward (CAF) at the noisy relay node. This is the first example where a combination of DAF and CAF is shown to be capacity a…
In this paper, the k-th order autoregressive moving average (ARMA(k)) Gaussian wiretap channel with noiseless causal feedback is considered, in which an eavesdropper receives noisy observations of the signals in both forward and feedback channels. It is shown that a variant of the generalized Schalkwijk-Kailath scheme, a capacity-achieving coding scheme for the feedback Gaussian channel, achieves the same maximum rate for the same channel with the presence of an eavesdropper. Therefore, the secrecy capacity is equal to the feedback capacity without the presence of an eavesdropper for the feedb…
The rate regions of many variations of the standard and wire-tap channels have been thoroughly explored. Secrecy capacity characterizes the loss of rate required to ensure that the adversary gains no information about the transmissions. Authentication does not have a standard metric, despite being an important counterpart to secrecy. While some results have taken an information-theoretic approach to the problem of authentication coding, the full rate region and accompanying trade-offs have yet to be characterized. In this paper, we provide an inner bound of achievable rates with an average aut…
A diamond network is considered in which the central processor is connected, via backhaul noiseless links, to multiple conferencing base stations, which communicate with a single user over a multiple access channel. We propose coding techniques along with lower and upper bounds on the capacity. Our achievability scheme uses a common cloud coding strategy based on the technique proposed by Wand, Wigger, and Zaidi (2018) and extends it beyond two relays. Our upper bounds generalize the method proposed by Bidokhti and Kramer for the two relay diamond network without cooperation (2016) and lead to…
The cognitive interference channel with unidirectional destination cooperation (CIFC-UDC) is a cognitive interference channel (CIFC) where the cognitive (secondary) destination not only decodes the information sent from its sending dual but also helps enhance the communication of the primary user. This channel model is an extension of the original CIFC to achieve a win-win solution under the coexistence condition. From an information-theoretic perspective, the CIFC-UDC comprises a broadcast channel (BC), a relay channel (RC) and a partially cooperative relay broadcast channel (PCRBC), and can …
For a classical channel, neither the Shannon capacity, nor the sum of conditional probabilities corresponding to the cases of successful transmission can be increased by the use of shared entanglement, or, more generally, a non-signaling resource. Yet, perhaps somewhat counterintuitively, entanglement assistance can help and actually elevate the chances of success even in a one-way communicational task that is to be completed by a single-shot use of a noiseless classical channel. To quantify the help that a non-signaling resource provides to a noiseless classical channel, one might ask how man…
The problem of characterising the zero-error capacity region for multiple access channels even in the noiseless case has remained an open problem for over three decades. Motivated by this challenging question, a recently developed theory of nonstochastic information is applied to characterise the zero-error capacity region for the case of two correlated transmitters. Unlike previous contributions, this analysis does not assume that the blocklength is asymptotically large. Finally, a new notion of nonstochastic information is proposed for a noncooperative problem involving three agents. These r…
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…
The role of cooperation in managing interference - a fundamental feature of the wireless channel - is investigated by studying the two-user Gaussian interference channel where the source nodes can both transmit and receive in full-duplex. The sum-capacity of this channel is obtained within a gap of a constant number of bits. The coding scheme used builds up on the superposition scheme of Han and Kobayashi (1981) for the two-user interference channel without cooperation. New upperbounds on the sum-capacity are also derived. The same coding scheme is shown to obtain the sum-capacity of the symme…
We consider communication over a multiple-input single-output (MISO) block fading channel in the presence of an independent noiseless feedback link. We assume that the transmitter and receiver have no prior knowledge of the channel state realizations, but the transmitter and receiver can acquire the channel state information (CSIT/CSIR) via downlink training and feedback. For this channel, we show that increasing the number of transmit antennas to infinity will not achieve an infinite capacity, for a finite channel coherence length and a finite input constraint on the second or fourth moment. …
A two-user Gaussian Z-Interference Channel (GZIC) is considered, in which encoders are connected through noiseless links with finite capacities. In this setting, prior to each transmission block the encoders communicate with each other over the cooperative links. The capacity region and the sum-capacity of the channel are characterized within 1.71 bits per user and 2 bits in total, respectively. It is also established that properly sharing the total limited cooperation capacity between the cooperative links may enhance the achievable region, even when compared to the case of unidirectional tra…
This paper studies the capacity of single-source single-sink noiseless networks under adversarial or arbitrary errors on no more than z edges. Unlike prior papers, which assume equal capacities on all links, arbitrary link capacities are considered. Results include new upper bounds, network error correction coding strategies, and examples of network families where our bounds are tight. An example is provided of a network where the capacity is 50% greater than the best rate that can be achieved with linear coding. While coding at the source and sink suffices in networks with equal link capaciti…
We demonstrate that the Maximum Lyapunov Exponent for computable dynamical systems is isomorphic to the maximum capacity of a noiseless, memoryless channel in a Shannon communication model. The isomorphism allows the understanding of Lyapunov exponents in the simplified terms of Information Theory, rather than the traditional definitions in Chaos Theory. This work provides a bridge between fundamental physics and Information Theory to the mutual benefit of both fields. The result suggests, among other implications, that machine learning and other information theory methods can be successfully …
The K-user cyclic Z-interference channel models a situation in which the kth transmitter causes interference only to the (k-1)th receiver in a cyclic manner, e.g., the first transmitter causes interference only to the Kth receiver. The impact of noiseless feedback on the capacity of this channel is studied by focusing on the Gaussian cyclic Z-interference channel. To this end, the symmetric feedback capacity of the linear shift deterministic cyclic Z-interference channel (LD-CZIC) is completely characterized for all interference regimes. Using insights from the linear deterministic channel mod…
Message Authentication Code (MAC) is a keyed function $f_K$ such that when Alice, who shares the secret $K$ with Bob, sends $f_K(M)$ to the latter, Bob will be assured of the integrity and authenticity of $M$. Traditionally, it is assumed that the channel is noiseless. However, Maurer showed that in this case an attacker can succeed with probability $2^{-\frac{H(K)}{\ell+1}}$ after authenticating $\ell$ messages. In this paper, we consider the setting where the channel is noisy. Specifically, Alice and Bob are connected by a discrete memoryless channel (DMC) $W_1$ and a noiseless but insecure …
We consider the capacity of an energy harvesting communication channel with a finite-sized battery. As an abstraction of this problem, we consider a system where energy arrives at the encoder in multiples of a fixed quantity, and the physical layer is modeled accordingly as a finite discrete alphabet channel based on this fixed quantity. Further, for tractability, we consider the case of binary energy arrivals into a unit-capacity battery over a noiseless binary channel. Viewing the available energy as state, this is a state-dependent channel with causal state information available only at the…
In this paper, capacity bounds for the two-user Interference Channel (IC) with cooperative receivers via conferencing links of finite capacities is investigated. The capacity results known for this communication scenario are limited to a very few special cases of the one-sided IC. One of the major challenges in analyzing such cooperative networks is how to establish efficient capacity outer bounds for them. In this paper, by applying new techniques, novel capacity outer bounds are presented for the ICs with conferencing users. Using the outer bounds, several new capacity results are proved for…
We address the problem of finding the capacity of noisy networks with either independent point-to-point compound channels (CC) or arbitrarily varying channels (AVC). These channels model the presence of a Byzantine adversary which controls a subset of links or nodes in the network. We derive equivalence results showing that these point-to-point channels with state can be replaced by noiseless bit-pipes without changing the network capacity region. Exact equivalence results are found for the CC model, and for some instances of the AVC, including all nonsymmetrizable AVCs. These results show tha…
The symmetric K user interference channel with fully connected topology is considered, in which (a) each receiver suffers interference from all other (K-1) transmitters, and (b) each transmitter has causal and noiseless feedback from its respective receiver. The number of generalized degrees of freedom (GDoF) is characterized in terms of α, where the interference-to-noise ratio (INR) is given by INR=SNR^α. It is shown that the per-user GDoF of this network is the same as that of the 2-user interference channel with feedback, except for α=1, for which existence of feedback does not help in term…
