Stochastic Encoding Research Articles

Coding for Secrecy: An Overview of Error-Control Coding Techniques for Physical-Layer Security

While secrecy in communication systems has historically been obtained through cryptographic means in the upper layers, recent research efforts have focused on the physical layer and have unveiled ample opportunities for security design. In particular, the combination of signal processing techniques with channel coding for secrecy has been central to the development of physical-layer security efforts. Although implicit coding techniques for secrecy have been known since the 1970s, explicit code constructions have only been discovered within the last decade. The purpose of this article is to provide a synopsis of the state of the art in coding for secrecy. We discuss the general principles of coding, and we illustrate them with several examples. In particular, we discuss the importance of a nested code structure and stochastic encoding, which allow for both data reliability and security.

Codes Against Online Adversaries: Large Alphabets

In this paper, we consider the communication of information in the presence of an online adversarial jammer. In the setting under study, a sender wishes to communicate a message to a receiver by transmitting a codeword x=(x1,...,xn) symbol-by-symbol over a communication channel. The adversarial jammer can view the transmitted symbols xi one at a time and can change up to a p-fraction of them. However, for each symbol xi, the jammer's decision on whether to corrupt it or not (and on how to change it) must depend only on xj for j ≤ i. This is in contrast to the “classical” adversarial jammer which may base its decisions on its complete knowledge of x. More generally, for a delay parameter δ ∈ (0,1), we study the scenario in which the jammer's decision on the corruption of xi must depend solely on xj for j ≤ i-δn. In this study, the transmitted symbols are assumed to be over a sufficiently large field F. The sender and receiver do not share resources such as common randomness (though the sender is allowed to use stochastic encoding). We present a tight characterization of the amount of information one can transmit in both the 0-delay and, more generally, the δ-delay online setting. We show that for 0-delay adversaries, the achievable rate asymptotically equals that of the classical adversarial model. For positive values of δ, we consider two types of jamming: additive and overwrite. We also extend our results to a jam-or-listen online model, where the online adversary can either jam a symbol or eavesdrop on it. We present computationally efficient achievability schemes even against computationally unrestricted jammers.

Channel Coding and Lossy Source Coding Using a Generator of Constrained Random Numbers

Stochastic encoders for channel coding and lossy source coding are introduced with a rate close to the fundamental limits, where the only restriction is that the channel input alphabet and the reproduction alphabet of the lossy source code are finite. Random numbers, which satisfy a condition specified by a function and its value, are used to construct stochastic encoders. The proof of the theorems is based on the hash property of an ensemble of functions, where the results are extended to general channels/sources and alternative formulas are introduced for channel capacity and the rate-distortion region. Since an ensemble of sparse matrices has a hash property, we can construct a code by using sparse matrices, where the sum-product algorithm can be used for encoding and decoding by assuming that channels/sources are memoryless.

Analysis of data reconstruction efficiency using stochastic encoding and an integrating receiver

We derive a relationship between quality of data reconstruction, data transmission rate, and integration decay rate for a stochastic transmitter and integrating receiver. This relationship can be used to quantify frame and directly compare the efficiencies of scanned and address-event data representations. We find that high quality reconstruction of stochastic data requires time and dynamic range at the receiver, but a stochastic representation can provide advantages over scanning for some applications. As an example, we provide the design of a simple receiver based on these results.

Stochastic encoding in sensory neurons: impulse patterns of mammalian cold receptors

Intrinsic oscillations at the level of the membrane potential are a widespread feature of nerve cells. Several evidences exist that, in particular, sensory neurons combine their oscillatory membrane potentials with intrinsic, membrane and/or synaptic noise to obtain sensitive encoding properties. An interesting example are mammalian cold receptors where stimulus transduction results from modulation of intrinsic receptor oscillations with essential contribution of noise thereby generating a rich spectrum of impulse patterns. To further explore the dynamics of these receptors we here investigate an HH-type model for oscillations and spike initiation in cold receptors. By use of a biophysically plausible temperature scaling and with addition of noise, the model successfully mimicks the principle temperature-dependence of stationary impulse patterns of real cold receptors. Our results suggest that interactions between stochastic and deterministic dynamics are of functional importance for the encoding charcteristics of cold receptors.

A method for proving multiterminal source coding theorems

The two-step method used by Wyner and Ziv to prove the Wyner-Ziv theorem is extended to prove sliding-block source coding theorems for coding a general finite-alphabet ergodic multiterminal source with respect to a single-letter fidelity criterion. The first step replaces every stochastic encoding in the network by a deterministic sliding-block encoding. The second step involves using the Slepian-Wolf theorem to adjust the sliding-block encodings so that they will have the desired rate. while introducing little additional distortion. The method is applied to give quick proofs of sliding-block versions of theorems of Berger, Kaspi, and Tung. Since the method obtains sliding-block coders directly without first obtaining block coders, the block coding results can be obtained as an easy corollary. The direct methods for proving results on block coding are more difficult and do not imply the corresponding results on sliding-block coding. Indeed, in the multiterminal case it is, in general, not known how to construct good sliding-block coders from good block coders.