My research falls into the general areas of communications, networks, and signal processing. More specifically, my study and research have focused on applications related to coding theory, information theory, algorithms, and game theory. These topics provide extensive opportunities for interdisciplinary and collaborative research, leading to fundamental advances in secure and reliable communications, data storage, and decision-making processes in complex environments.
Coding for Multi-User and Physical Layer Communication
One of the classical goals in the fields of coding and information theory has been to construct schemes that guarantee reliable communications in the presence of noise by means of designing error-correcting codes. Today, error-correcting codes are among the fundamental parts of any wireless communication system. The invention of polar codes by Arikan is undoubtedly one of the most original and profound developments in coding theory in the past decade. Polar codes achieve the capacity of general symmetric channels with low encoding and decoding complexity. One of the primary lines of my research has been to investigate different aspects of polar coding including finite-length performance improvement, compatibility with coded modulation schemes, extensions to multi-user scenarios, complexity reduction of encoding and decoding, and rate compatibility for hybrid automatic repeat request (HARQ) process in order to establish their suitability for future wireless communication systems.
Reliability of Packet Transmission over Networks via Subspace Codes
Consider a communication network where the nodes are able to process the data they transmit and receive. Instead of simply relaying the information packets, the network nodes combine them together for transmission. This technique, called network coding, is used to improve the network’s throughput, efficiency, and scalability. The randomized network coding is a completely distributed and decentralized protocol for implementing network coding which makes it the most promising practical approach to network coding to-date. Yet, it is highly susceptible to transmission errors, caused by noise or intentional jamming. Even a single packet error injected into the network could potentially render the entire transmission useless. Subspace codes have recently been introduced in order to enable reliable communication of messages in randomized network coding. We proposed a novel construction of subspace codes, which enables list-decoding, hence achieving a significantly improved tradeoff between the rate and the error correction capability of the code.
Coding for Secure Communication
The tremendous growth of wireless communication networks presents countless improvement opportunities for everyday life through an almost ubiquitous expansion of access to information resources. At the same time, it poses a higher risk of malicious attacks against message confidentiality in communication systems. Anyone within the geographical range of a wireless network can potentially gain unauthorized access to the data transmitted over the wireless links. Such security threats are among the primary concerns in the design of any communication system. A well-known model for private communication is the wiretap channel. We used polar codes in combination with a carefully designed secrecy scheme to construct a new coding scheme that enables both reliable and secure communication, while achieving the fundamental limit of secrecy capacity for a wide range of wiretap channels.
Coding for Non-Volatile Memories
Flash memories are, by far, the most important type of non-volatile memory in use today. They are employed widely in mobile, embedded, and mass-storage applications, and the growth in this sector continues at a staggering pace. Moreover, since flash memories do not suffer from the mechanical limitations of magnetic disk drives, flash drives (also known as solid-state drives) have the potential to upstage the magnetic recording industry in the foreseeable future. We have designed nearly optimal codes for flash memories, which can utilize all the available cell levels of a flash memory before a block erasure must be performed, which then improves the performance and increases the life-time of flash memories. In an alternative technology for non-volatile memories, the memory cells are composed of special materials that can store data through their thermal behavior. This new technology, called phase change memory, suffers from the problem of stuck-at cells, which are not able to change their state; hence being stuck at their current state. We have constructed combinatorial finite-length designs and have proposed asymptotically optimal coding schemes with explicit construction and polynomial-time encoding/decoding for memories with stuck-at errors.
Decision-Making in Games of Incomplete Information
Coordination and decision-making problems arise in a variety of social and economic contexts. A scenario of interest is the behavior of political opposition against a regime, where a group of citizens decides whether to take a risky action by participating in a revolution to overthrow the regime or not. The revolution is successful and the participants receive a positive pay-off if they appear to be stronger than the regime, i.e., their number is greater than a fundamental parameter which represents the power of the regime. Otherwise, the participants receive a negative pay-off, while the pay-off of taking the safe action of not participating in the revolution is zero. It is also naturally assumed that each citizen has a private noisy observation of the fundamental parameter, which is interpreted as his or her belief about the power of the regime. This is an example of a game of incomplete information, which is called a global game. Global games have been used to model and to study various socio-economical behaviors in social networks. In order to incorporate the global game model into a complex social network of information exchange, we assumed a model in which the agents share their beliefs about the fundamental of the regime in a noisy environment. We showed that, under certain conditions, a Bayesian Nash equilibrium exists, where each agent takes the risky action, if a certain function, called the threshold function, of his or her observations is less than a threshold, and takes the safe action otherwise.
Communication via Diffusion of Particles
Molecular signaling is used naturally by many kinds of biological cells for action coordination in biological networks. Therefore, an in-depth understanding of molecular communication networks not only paves the way for the better understanding of this natural communication mechanism among biological cells, it would provide a potential means of communication that suits biological media such as the human body. In molecular communication, the transmitter (which can be thought of as a biological cell) secretes signaling molecules that are subject to Brownian motion in the medium. The receiver senses the concentration of the signaling molecules using ligand receptors. The input to the communication channel model is a stochastic process that represents the rate of releasing particles in the medium by the transmitter, and the output is a doubly stochastic Poisson process that represents the number of received particles at the receiver. We characterized the end-to-end mutual information of the continuous time diffusion channel discussed above and provided lower bounds on the capacity by constructing pulse amplitude modulation (PAM) signaling strategies assuming a power constraint on the power of input signal.