Abbas El Gamal

Capacity theorems for the relay channel

A relay channel consists of an input x_{l} , a relay output y_{1} , a channel output y , and a relay sender x_{2} (whose transmission is allowed to depend on the past symbols y_{1} . The dependence of the received symbols upon the inputs is given by p(y,y_{1}|x_{1},x_{2}) . The channel is assumed to be memoryless. In this paper the following capacity theorems are proved. 1)If y is a degraded form of y_{1} , then C \: = \: \max \!_{p(x_{1},x_{2})} \min \,{I(X_{1},X_{2};Y), I(X_{1}; Y_{1}|X_{2})} . 2)If y_{1} is a degraded form of y , then C \: = \: \max \!_{p(x_{1})} \max_{x_{2}} I(X_{1};Y|x_{2}) . 3)If p(y,y_{1}|x_{1},x_{2}) is an arbitrary relay channel with feedback from (y,y_{1}) to both x_{1} \and x_{2} , then C\: = \: \max_{p(x_{1},x_{2})} \min \,{I(X_{1},X_{2};Y),I \,(X_{1};Y,Y_{1}|X_{2})} . 4)For a general relay channel, C \: \leq \: \max_{p(x_{1},x_{2})} \min \,{I \,(X_{1}, X_{2};Y),I(X_{1};Y,Y_{1}|X_{2}) . Superposition block Markov encoding is used to show achievability of C , and converses are established. The capacities of the Gaussian relay channel and certain discrete relay channels are evaluated. Finally, an achievable lower bound to the capacity of the general relay channel is established.

Network Information Theory: Subject Index

This comprehensive treatment of network information theory and its applications provides the first unified coverage of both classical and recent results. With an approach that balances the introduction of new models and new coding techniques, readers are guided through Shannons point-to-point information theory, single-hop networks, multihop networks, and extensions to distributed computing, secrecy, wireless communication, and networking. Elementary mathematical tools and techniques are used throughout, requiring only basic knowledge of probability, whilst unified proofs of coding theorems are based on a few simple lemmas, making the text accessible to newcomers. Key topics covered include successive cancellation and superposition coding, MIMO wireless communication, network coding, and cooperative relaying. Also covered are feedback and interactive communication, capacity approximations and scaling laws, and asynchronous and random access channels. This book is ideal for use in the classroom, for self-study, and as a reference for researchers and engineers in industry and academia.

Network Information Theory: Multihop Networks

This comprehensive treatment of network information theory and its applications provides the first unified coverage of both classical and recent results. With an approach that balances the introduction of new models and new coding techniques, readers are guided through Shannons point-to-point information theory, single-hop networks, multihop networks, and extensions to distributed computing, secrecy, wireless communication, and networking. Elementary mathematical tools and techniques are used throughout, requiring only basic knowledge of probability, whilst unified proofs of coding theorems are based on a few simple lemmas, making the text accessible to newcomers. Key topics covered include successive cancellation and superposition coding, MIMO wireless communication, network coding, and cooperative relaying. Also covered are feedback and interactive communication, capacity approximations and scaling laws, and asynchronous and random access channels. This book is ideal for use in the classroom, for self-study, and as a reference for researchers and engineers in industry and academia.

Achievable rates for multiple descriptions

Consider a sequence of independent identically distributed (i.i.d.) random variables X_{l},X_{2}, \cdots, X_{n} and a distortion measure d(X_{i},X_{i}) on the estimates X_{i} of X_{i} . Two descriptions i(X)\in \{1,2, \cdots ,2^{nR_{1}\} and j(X)\in \{1,2, \cdots,2^{nR_{2}\} are given of the sequence X=(X_{1}, X_{2}, \cdots ,X_{n}) . From these two descriptions, three estimates (i(X)), X2(j(X)) , and \hat{X}_{O}(i(X),j(X)) are formed, with resulting expected distortions E \frac{1/n} \sum^{n}_{k=1} d(X_{k}, \hat{X}_{mk})=D_{m}, m=0,1,2. We find that the distortion constraints D_{0}, D_{1}, D_{2} are achievable if there exists a probability mass distribution p(x)p(\hat{x}_{1},\hat{x}_{2},\hat{x}_{0}|x) with Ed(X,\hat{x}_{m})\leq D_{m} such that R_{1}>I(X;\hat{X}_{1}), R_{2}>I(X;\hat{X}_{2}), where I(\cdot) denotes Shannon mutual information. These rates are shown to be optimal for deterministic distortion measures.

Energy-efficient packet transmission over a wireless link

The paper considers the problem of minimizing the energy used to transmit packets over a wireless link via lazy schedules that judiciously vary packet transmission times. The problem is motivated by the following observation. With many channel coding schemes, the energy required to transmit a packet can be significantly reduced by lowering transmission power and code rate, and therefore transmitting the packet over a longer period of time. However, information is often time-critical or delay-sensitive and transmission times cannot be made arbitrarily long. We therefore consider packet transmission schedules that minimize energy subject to a deadline or a delay constraint. Specifically, we obtain an optimal offline schedule for a node operating under a deadline constraint. An inspection of the form of this schedule naturally leads us to an online schedule which is shown, through simulations, to perform closely to the optimal offline schedule. Taking the deadline to infinity, we provide an exact probabilistic analysis of our offline scheduling algorithm. The results of this analysis enable us to devise a lazy online algorithm that varies transmission times according to backlog. We show that this lazy schedule is significantly more energy-efficient compared to a deterministic (fixed transmission time) schedule that guarantees queue stability for the same range of arrival rates.

Multiple access channels with arbitrarily correlated sources

Let \{(U_{i},V_{i})\}_{i=1}^{n} be a source of independent identically distributed (i.i.d.) discrete random variables with joint probability mass function p(u,v) and common part w=f(u)=g(v) in the sense of Witsenhausen, Gacs, and Korner. It is shown that such a source can be sent with arbitrarily small probability of error over a multiple access channel (MAC) \{\cal X_{1} \times \cal X_{2},\cal Y,p(y|x_{1},x_{2})\}, with allowed codes \{x_{l}(u), x_{2}(v)\} if there exist probability mass functions p(s), p(x_{1}|s,u),p(x_{2}|s,v) , such that H(U|V) H(V|U ) H(U,V|W) H(U,V) \mbox{where} p(s,u,v,x_{1},x_{2},y), Xl, X2, y)=p(s)p(u,v)p(x_{1}|u,s)p(x_{2}|v,s)p(y|x_{1},x_{2}). lifts region includes the multiple access channel region and the Slepian-Wolf data compression region as special cases.

A 640/spl times/512 CMOS image sensor with ultra wide dynamic range floating-point pixel-level ADC

The dynamic range of an image sensor is often not wide enough to capture scenes with both high lights and dark shadows. A 640/spl times/512 image sensor with Nyquist rate pixel level ADC implemented in a 0.35 /spl mu/m CMOS technology shows how a pixel level ADC enables flexible efficient implementation of multiple sampling. Since pixel values are available to the ADCs at all times, the number and timing of the samples as well as the number of bits obtained from each sample can be freely selected without the long readout time of APS. Typically, hundreds of nanoseconds of settling time per row are required for APS readout. In contrast, using pixel level ADC, digital data is read out at fast SRAM speeds. This demonstrates another fundamental advantage of pixel level ADC-the ability to programmably widen dynamic range with no loss in SNR.

On the capacity of computer memory with defects

A computer memory with defects is modeled as a discrete memoryless channel with states that are statistically determined. The storage capacity is found when complete defect information is given to the encoder or to the decoder, and when the defect information is given completely to the decoder but only partially to the encoder. Achievable storage rates are established when partial defect information is provided at varying rates to both the encoder and the decoder. Arimoto-Blahut type algorithms are used to compute the storage capacity.

Miniaturized integration of a fluorescence microscope

The light microscope is traditionally an instrument of substantial size and expense. Its miniaturized integration would enable many new applications based on mass-producible, tiny microscopes. Key prospective usages include brain imaging in behaving animals for relating cellular dynamics to animal behavior. Here we introduce a miniature (1.9 g) integrated fluorescence microscope made from mass-producible parts, including a semiconductor light source and sensor. This device enables high-speed cellular imaging across ∼0.5 mm2 areas in active mice. This capability allowed concurrent tracking of Ca2+ spiking in >200 Purkinje neurons across nine cerebellar microzones. During mouse locomotion, individual microzones exhibited large-scale, synchronized Ca2+ spiking. This is a mesoscopic neural dynamic missed by prior techniques for studying the brain at other length scales. Overall, the integrated microscope is a potentially transformative technology that permits distribution to many animals and enables diverse usages, such as portable diagnostics or microscope arrays for large-scale screens.

Analysis of temporal noise in CMOS photodiode active pixel sensor

Temporal noise sets the fundamental limit on image sensor performance, especially under low illumination and in video applications. In a CCD image sensor, temporal noise is primarily due to the photodetector shot noise and the output amplifier thermal and 1/f noise. CMOS image sensors suffer from higher noise than CCDs due to the additional pixel and column amplifier transistor thermal and 1/f noise. Noise analysis is further complicated by the time-varying circuit models, the fact that the reset transistor operates in subthreshold during reset, and the nonlinearity of the charge to voltage conversion, which is becoming more pronounced as CMOS technology scales. The paper presents a detailed and rigorous analysis of temporal noise due to thermal and shot noise sources in CMOS active pixel sensor (APS) that takes into consideration these complicating factors. Performing time-domain analysis, instead of the more traditional frequency-domain analysis, we find that the reset noise power due to thermal noise is at most half of its commonly quoted kT/C value. This result is corroborated by several published experimental data including data presented in this paper. The lower reset noise, however, comes at the expense of image lag. We find that alternative reset methods such as overdriving the reset transistor gate or using a pMOS transistor can alleviate lag, but at the expense of doubling the reset noise power. We propose a new reset method that alleviates lag without increasing reset noise.