Distributed Successive Approximation Coding using Broadcast Advantage: The Two-Encoder Case

Traditional distributed source coding rarely considers the possible link between separate encoders. However, the broadcast nature of wireless communication in sensor networks provides a free gossip mechanism which can be used to simplify encoding/decoding and reduce transmission power. Using this broadcast advantage, we present a new two-encoder scheme which imitates the ping-pong game and has a successive approximation structure. For the quadratic Gaussian case, we prove that this scheme is successively refinable on the {sum-rate, distortion pair} surface, which is characterized by the rate-distortion region of the distributed two-encoder source coding. A potential energy saving over conventional distributed coding is also illustrated. This ping-pong distributed coding idea can be extended to the multiple encoder case and provides the theoretical foundation for a new class of distributed image coding method in wireless scenarios.Comment: In Proceedings of the 48th Annual Allerton Conference on Communication, Control and Computing, University of Illinois, Monticello, IL, September 29 - October 1, 201

Secure Lossy Function Computation with Multiple Private Remote Source Observations

We consider that multiple noisy observations of a remote source are used by different nodes in the same network to compute a function of the noisy observations under joint secrecy, joint privacy, and individual storage constraints, as well as a distortion constraint on the function computed. Suppose that an eavesdropper has access to one of the noisy observations in addition to the public messages exchanged between legitimate nodes. This model extends previous models by 1) considering a remote source as the source of dependency between the correlated random variables observed at different nodes; 2) allowing the function computed to be a distorted version of the target function, which allows to reduce the storage rate as compared to a reliable function computation scenario in addition to reducing secrecy and privacy leakages; 3) introducing a privacy metric that measures the information leakage about the remote source to the fusion center in addition to the classic privacy metric that measures the leakage to an eavesdropper; 4) considering two transmitting nodes to compute a function rather than one node. Single-letter inner and outer bounds are provided for the considered lossy function computation problem, and simplified bounds are established for two special cases, in which either the computed function is partially invertible or the function is invertible and the measurement channel of the eavesdropper is physically degraded with respect to the measurement channel of the fusion center

Multiple Noisy Private Remote Source Observations for Secure Function Computation

The problem of reliable function computation is extended by imposing privacy, secrecy, and storage constraints on a remote source whose noisy measurements are observed by multiple parties. The main additions to the classic function computation problem include 1) privacy leakage to an eavesdropper is measured with respect to the remote source rather than the transmitting terminals\u27 observed sequences; 2) the information leakage to a fusion center with respect to the remote source is considered as another privacy leakage metric; 3) two transmitting node observations are used to compute a function. Inner and outer bounds on the rate regions are derived for lossless single-function computation with two transmitting nodes, which recover previous results in the literature, and for special cases that consider invertible functions simplified bounds are established

Capacity Bounds For Multi-User Channels With Feedback, Relaying and Cooperation

Recent developments in communications are driven by the goal of achieving high data rates for wireless communication devices. To achieve this goal, several new phenomena need to be investigated from an information theoretic perspective. In this dissertation, we focus on three of these phenomena: feedback, relaying and cooperation. We study these phenomena for various multi-user channels from an information theoretic point of view. One of the aims of this dissertation is to study the performance limits of simple wireless networks, for various forms of feedback and cooperation. Consider an uplink communication system, where several users wish to transmit independent data to a base-station. If the base-station can send feedback to the users, one can expect to achieve higher data-rates since feedback can enable cooperation among the users. Another way to improve data-rates is to make use of the broadcast nature of the wireless medium, where the users can overhear each other's transmitted signals. This particular phenomenon has garnered much attention lately, where users can help in increasing each other's data-rates by utilizing the overheard information. This overheard information can be interpreted as a generalized form of feedback. To take these several models of feedback and cooperation into account, we study the two-user multiple access channel and the two-user interference channel with generalized feedback. For all these models, we derive new outer bounds on their capacity regions. We specialize these results for noiseless feedback, additive noisy feedback and user-cooperation models and show strict improvements over the previously known bounds. Next, we study state-dependent channels with rate-limited state information to the receiver or to the transmitter. This state-dependent channel models a practical situation of fading, where the fade information is partially available to the receiver or to the transmitter. We derive new bounds on the capacity of such channels and obtain capacity results for a special sub-class of such channels. We study the effect of relaying by considering the parallel relay network, also known as the diamond channel. The parallel relay network considered in this dissertation comprises of a cascade of a general broadcast channel to the relays and an orthogonal multiple access channel from the relays to the receiver. We characterize the capacity of the diamond channel, when the broadcast channel is deterministic. We also study the diamond channel with partially separated relays, and obtain capacity results when the broadcast channel is either semi-deterministic or physically degraded. Our results also demonstrate that feedback to the relays can strictly increase the capacity of the diamond channel. In several sensor network applications, distributed lossless compression of sources is of considerable interest. The presence of adversarial nodes makes it important to design compression schemes which serve the dual purpose of reliable source transmission to legitimate nodes while minimizing the information leakage to the adversarial nodes. Taking this constraint into account, we consider information theoretic secrecy, where our aim is to limit the information leakage to the eavesdropper. For this purpose, we study a secure source coding problem with coded side information from a helper to the legitimate user. We derive the rate-equivocation region for this problem. We show that the helper node serves the dual purpose of reducing the source transmission rate and increasing the uncertainty at the adversarial node. Next, we considered two different secure source coding models and provide the corresponding rate-equivocation regions

Successive Encoding of Correlated Sources

The encoding of a discrete memoryless multiple source  for reconstruction of a sequence  with  is considered. We require that the encoding should be such that  is encoded first without any consideration of  , while in a seeond part of the encoding this latter sequence is encoded based on knowledge of the outcome of the first encoding. The resulting scheme is called successive encoding. We find general outer and inner bounds for the corresponding set of achievable rates along with a complete single letter characterization for the special case  . Comparisons with the Slepian-Wolf problem [3] and the Ahlswede-Körner-Wyner side information problem [2 ], [9) are carried out

Successive Encoding of Correlated Sources

The encoding of a discrete memoryless multiple source  for reconstruction of a sequence  with  is considered. We require that the encoding should be such that  is encoded first without any consideration of  , while in a seeond part of the encoding this latter sequence is encoded based on knowledge of the outcome of the first encoding. The resulting scheme is called successive encoding. We find general outer and inner bounds for the corresponding set of achievable rates along with a complete single letter characterization for the special case  . Comparisons with the Slepian-Wolf problem [3] and the Ahlswede-Körner-Wyner side information problem [2 ], [9) are carried out