Non-causal State Research Articles

Non-Causal State Estimation for Improved State Tracking in Iterative Learning Control

State-tracking Iterative Learning Control (ILC) yields perfect state-tracking performance at each n sample instances for systems that perform repetitive tasks, where n stands for the order of the system. By achieving perfect state-tracking, oscillatory intersample behavior often encountered in output-tracking ILC has been mitigated. However, state-tracking ILC only assures the estimated state error to converge to a significantly small value, meaning the accuracy of the state estimation takes a critical role. State estimation using a causal state observer has had an inevitable trade-off between the estimation delay and the noise sensitivity. By utilizing the non-causal operation of ILC, a non-causal state estimation can be designed. This non-causal state estimation performs beyond the trade-off of causal estimation, improving the estimation delay without compromising the noise sensitivity. The aim of this paper is to implement the non-causal state observer to state-tracking ILC, and present the improved state tracking by applying it to a second order system.

Wiretap Channels With Causal and Non-Causal State Information: Revisited

The coding problem for wiretap channels (WTCs) with causal and/or non-causal channel state information (CSI) available at the encoder (Alice) and/or the decoder (Bob) is studied, particularly focusing on achievable secret-message secret-key (SM-SK) rate pairs under the semantic security criterion. One of our main results is summarized as Theorem 3 on causal inner bounds for SM-SK rate pairs, which follows immediately by leveraging the unified seminal theorem for WTCs with non-causal CSI at Alice that has been recently established by Bunin et al.. The only thing to do here is just to re-interpret the latter non-causal scheme in a causal manner by restricting the range of auxiliary random variables appearing in non-causal encoding to a subclass of auxiliary random variables for the causal encoder. This technique is referred to as “plugging.” Then, we are able to dispense with the block-Markov encoding scheme used in the previous works by Chia and El Gamal, Fujita, and Han and Sasaki and then extend all the known results on achievable rates. The other main results include the exact SM-SK capacity region for WTCs with non-causal CSI at “both” Alice and Bob (Theorem 2), a “tighter” causal SM-SK outer bound for state-reproducing coding schemes with CSI at Alice (Proposition 4), and the exact SM-SK capacity region for degraded WTCs with causal/non-causal CSI at both Alice and Bob (Theorem 4).

New Result on the Feedback Capacity of the Action-Dependent Dirty Paper Wiretap Channel.

The Gaussian wiretap channel with noncausal state interference available at the transmitter, which is also called the dirty paper wiretap channel (DP-WTC), has been extensively studied in the literature. Recently, it has been shown that taking actions on the corrupted state interference of the DP-WTC (also called the action-dependent DP-WTC) helps to increase the secrecy capacity of the DP-WTC. Subsequently, it has been shown that channel feedback further increases the secrecy capacity of the action-dependent DP-WTC (AD-DP-WTC), and a sub-optimal feedback scheme is proposed for this feedback model. In this paper, a two-step hybrid scheme and a corresponding new lower bound on the secrecy capacity of the AD-DP-WTC with noiseless feedback are proposed. The proposed new lower bound is shown to be optimal (achieving the secrecy capacity) and tighter than the existing one in the literature for some cases, and the results of this paper are further explained via numerical examples.

Cooperative Binning for Semi-Deterministic Channels With Non-Causal State Information

The capacity of the semi-deterministic relay channel (SD-RC) with non-causal channel state information (CSI) only at the encoder and decoder is characterized. The capacity is achieved by a scheme based on cooperative-bin-forward . This scheme allows cooperation between the transmitter and the relay without the need of the later to decode a part of the message. The transmission is divided into blocks, and each deterministic output of the channel (observed by the relay) is mapped to a bin. The bin index is used by the encoder and the relay to choose the cooperation codeword in the next transmission block. In causal settings, the cooperation is independent of the state. In non-causal settings, dependence between the relay’s transmission and the state can increase the transmission rates. The encoder implicitly conveys partial state information to the relay. In particular, it uses the states of the next block and selects a cooperation codeword accordingly, and the relay transmission depends on the cooperation codeword and, therefore, also on the states. We also consider the multiple access channel with partial cribbing as a semi-deterministic channel. The capacity region of this channel with non-causal CSI is achieved by the new scheme. Examining the result in several cases, we introduce a new problem of a point-to-point (PTP) channel where the state is provided to the transmitter by a state encoder. Interestingly, even though the CSI is also available at the receiver, we provide an example showing that the capacity with non-causal CSI at the state encoder is strictly larger than the capacity with causal CSI.

Cooperative Binning for Semi-DeterministicChannels With Non-Causal State Information

Cooperative Binning for Semi-DeterministicChannels With Non-Causal State Information

Feedback Schemes for the Action-Dependent Wiretap Channel with Noncausal State at the Transmitter.

In this paper, we propose two feedback coding schemes for the action-dependent wiretap channel with noncausal state at the transmitter. The first scheme follows from the already existing secret key based feedback coding scheme for the wiretap channel. The second one follows from our recently proposed hybrid feedback scheme for the wiretap channel. We show that, for the action-dependent wiretap channel with noncausal state at the transmitter, the second feedback scheme performs better than the first one, and the capacity results of this paper are further explained via a Gaussian example, which we call the action-dependent dirty paper wiretap channel with noiseless feedback.

The Arbitrarily Varying Channel Under Constraints With Side Information at the Encoder

We study the arbitrarily varying channel (AVC) with input and state constraints, when the encoder has state information in a causal or noncausal manner. For the causal state information setting, we develop lower and upper bounds on the random code capacity. A lower bound on the deterministic code capacity is established in the case of a message-averaged input constraint. In the setting where a state constraint is imposed on the jammer, while the user is under no constraints, the random code bounds coincide, and the random code capacity is determined. Furthermore, for this scenario, a generalized non-symmetrizability condition is stated, under which the deterministic code capacity coincides with the random code capacity. For the noncausal state information setting, we determine the random code capacity of the AVC under input and state constraints. In addition, a condition on the channel is stated, under which the deterministic code capacity coincides with the random code capacity.

A New Feedback Scheme for the State-Dependent Wiretap Channel With Noncausal State at the Transmitter

Recently, it has been shown that channel feedback helps to enhance the physical layer security (PLS) of communication systems. The current use of feedback focuses on generating secret keys protecting the transmitted messages, and this feedback scheme is proved to be optimal for some physically degraded channel models. In this paper, we revisit the model of the state-dependent wiretap channel with the noncausal state at the transmitter, which plays an important role in the PLS of the wireless communication systems. We propose a new feedback scheme for this model and show that the proposed new scheme performs better than the already existing secret key-based feedback scheme. The results of this paper are further explained via a Gaussian example.

Capacity region of the 3 receiver state dependent multilevel BC with noncausal state information

We consider a three receiver state dependent multilevel broadcast channel (BC), where the state information is known non-causally at the encoder as well as all the decoders. This is an extension of Nair and El Gamal’s three receiver multilevel BC (Nair and El Gamal, 2009), wherein two of the receivers decode only a common message while a third receiver decodes a private message as well. The objective is to characterize the rate tuples that are simultaneously achievable while ensuring negligible probability of error at each of the receivers. We characterize the capacity region of this setup in the paper.

Multicoding Schemes for Interference Channels

The best known inner bound for the two-user discrete memoryless interference channel is the Han–Kobayashi rate region. The coding schemes that achieve this region are based on rate-splitting and superposition coding. In this paper, we develop a multicoding scheme to achieve the same rate region. A key advantage of the multicoding nature of the proposed coding scheme is that it can be naturally extended to more general settings, such as when encoders have state information or can overhear each other. In particular, we extend our coding scheme to characterize the capacity region of the state-dependent deterministic Z-interference channel when noncausal state information is available at the interfering transmitter. We specialize our results to the case of the linear deterministic model with ON/OFF interference, which models a wireless system where a cognitive transmitter is noncausally aware of the times it interferes with a primary transmission. For this special case, we provide an explicit expression for the capacity region and discuss some interesting properties of the optimal strategy. We also extend our multicoding scheme to find the capacity region of the deterministic Z-interference channel when the signal of the interfering transmitter can be overheard at the other transmitter (also known as unidirectional partial cribbing).

On State-Dependent Degraded Broadcast Channels With Cooperation

In this paper, we investigate problems of communication over physically degraded, state-dependent broadcast channels (BCs) with cooperating decoders. Two different setups are considered, and their capacity regions are characterized. First, we study a setting in which one decoder can use a finite capacity link to send the other decoder information regarding the messages or the channel states. In this scenario, we analyze two cases: one, where noncausal state information, is available to the encoder and the strong decoder, and the other, where state information, is available only to the encoder in a causal manner. Second, we examine a setting in which the cooperation between the decoders is limited to taking place before the outputs of the channel are given. In this case, one decoder, which is informed of the state sequence noncausally, can cooperate only to send the other decoder rate-limited information about the state sequence. The proofs of the capacity regions introduce a new idea of coding for channels with cooperation between different users, where we exploit the link between the decoders for multiple binnings. Finally, we discuss the optimality of using rate-splitting techniques when coding for cooperative BCs. In particular, we show that rate splitting is not necessarily optimal when coding for cooperative BCs by solving an example in which our method of coding outperforms rate splitting.

Nonasymptotic and Second-Order Achievability Bounds for Coding With Side-Information

We present a novel nonasymptotic or finite blocklength achievability bounds for three side-information problems in network information theory. These include: 1) the Wyner-Ahlswede-Korner (WAK) problem of almost-lossless source coding with rate-limited side-information; 2) the Wyner–Ziv (WZ) problem of lossy source coding with side-information at the decoder; and 3) the Gel’fand–Pinsker (GP) problem of channel coding with noncausal state information available at the encoder. The bounds are proved using ideas from channel simulation and channel resolvability. Our bounds for all three problems improve on all previous nonasymptotic bounds on the error probability of the WAK, WZ, and GP problems—in particular those derived by Verdu. Using our novel nonasymptotic bounds, we recover the general formulas for the optimal rates of these side-information problems. Finally, we also present achievable second-order coding rates by applying the multidimensional Berry–Esseen theorem to our new nonasymptotic bounds. Numerical results show that the second-order coding rates obtained using our nonasymptotic achievability bounds are superior to those obtained using existing finite blocklength bounds.

Degraded Broadcast Diamond Channels With Noncausal State Information at the Source

A state-dependent degraded broadcast diamond channel is studied where the source-to-relays cut is modeled with two noiseless, finite-capacity digital links with a degraded broadcasting structure, while the relays-to-destination cut is a general multiple access channel controlled by a random state. It is assumed that the source has noncausal channel state information and the relays have no state information. Under this model, first, the capacity is characterized for the case where the destination has state information, i.e., has access to the state sequence. It is demonstrated that in this case, a joint message and state transmission scheme via binning is optimal. Next, the case where the destination does not have state information, i.e., the case with state information at the source only, is considered. For this scenario, lower and upper bounds on the capacity are derived for the general discrete memoryless model. Achievable rates are then computed for the case in which the relays-to-destination cut is affected by an additive Gaussian state. Numerical results are provided that illuminate the performance advantages that can be accrued by leveraging noncausal state information at the source.

The State-Dependent Semideterministic Broadcast Channel

We derive the capacity region of the state-dependent semideterministic broadcast channel with noncausal state information at the transmitter. One of the two outputs of this channel is a deterministic function of the channel input and the channel state, and the state is assumed to be known noncausally to the transmitter but not to the receivers. We show that appending the state to the deterministic output does not increase capacity. We also derive an outer bound on the capacity of general (not necessarily semideterministic) state-dependent broadcast channels.

State-Dependent Relay Channel: Achievable Rate and Capacity of a Semideterministic Class

This paper considers the problem of communicating over a relay channel with state when noncausal state information is partially available at the nodes. We first establish a lower bound on the achievable rates based on noisy network coding and Gelfand-Pinsker coding, and show that it provides an alternative characterization of a previously known bound. We then introduce the class of state-decoupled relay channels and show that our lower bound is tight for a subclass of semideterministic channels. We also compute the capacity for two specific examples of this subclass - a channel with multiplicative binary fading and a channel with additive Gaussian interference. These examples are not special cases of previous classes of semideterministic relay channels with known capacity.

Bounds on the Capacity of the Relay Channel With Noncausal State at the Source

We consider a three-terminal state-dependent relay channel with the channel state available non-causally at only the source. Such a model may be of interest for node cooperation in the framework of cognition, i.e., collaborative signal transmission involving cognitive and non-cognitive radios. We study the capacity of this communication model. One principal problem is caused by the relay's not knowing the channel state. For the discrete memoryless (DM) model, we establish two lower bounds and an upper bound on channel capacity. The first lower bound is obtained by a coding scheme in which the source describes the state of the channel to the relay and destination, which then exploit the gained description for a better communication of the source's information message. The coding scheme for the second lower bound remedies the relay's not knowing the states of the channel by first computing, at the source, the appropriate input that the relay would send had the relay known the states of the channel, and then transmitting this appropriate input to the relay. The relay simply guesses the sent input and sends it in the next block. The upper bound is non trivial and it accounts for not knowing the state at the relay and destination. For the general Gaussian model, we derive lower bounds on the channel capacity by exploiting ideas in the spirit of those we use for the DM model; and we show that these bounds are optimal for small and large noise at the relay irrespective to the strength of the interference. Furthermore, we also consider a special case model in which the source input has two components one of which is independent of the state. We establish a better upper bound for both DM and Gaussian cases and we also characterize the capacity in a number of special cases.