Emrah Akyol

On Zero-Delay Source-Channel Coding

This paper studies the zero-delay source-channel coding problem, and specifically the problem of obtaining the vector transformations that optimally map between the m-dimensional source space and k-dimensional channel space, under a given transmission power constraint and for the mean square error distortion. The functional properties of the cost are studied and the necessary conditions for the optimality of the encoder and decoder mappings are derived. An optimization algorithm that imposes these conditions iteratively, in conjunction with the noisy channel relaxation method to mitigate poor local minima, is proposed. The numerical results show strict improvement over prior methods. The numerical approach is extended to the scenario of source-channel coding with decoder side information. The resulting encoding mappings are shown to be continuous relatives of, and in fact subsume as special case, the Wyner-Ziv mappings encountered in digital distributed source coding systems. A well-known result in information theory pertains to the linearity of optimal encoding and decoding mappings in the scalar Gaussian source and channel setting, at all channel signal-to-noise ratios (CSNRs). In this paper, the linearity of optimal coding, beyond the Gaussian source and channel, is considered and the necessary and sufficient condition for linearity of optimal mappings, given a noise (or source) distribution, and a specified a total power constraint are derived. It is shown that the Gaussian source-channel pair is unique in the sense that it is the only source-channel pair for which the optimal mappings are linear at more than one CSNR values. Moreover, the asymptotic linearity of optimal mappings is shown for low CSNR if the channel is Gaussian regardless of the source and, at the other extreme, for high CSNR if the source is Gaussian, regardless of the channel. The extension to the vector settings is also considered where besides the conditions inherited from the scalar case, additional constraints must be satisfied to ensure linearity of the optimal mappings.

A Deterministic Annealing Approach to Witsenhausen's Counterexample

This paper proposes an optimization method, based on information theoretic ideas, to a class of distributed control problems. As a particular test case, the well-known and numerically “over-mined” problem of decentralized control and implicit communication, commonly referred to as Witsenhausens counterexample, is considered. The key idea is to randomize the zero-delay mappings. which become “soft”, probabilistic mappings to be optimized in a deterministic annealing process, by incorporating a Shannon entropy constraint in the problem formulation. The entropy of the mapping is controlled and gradually lowered to zero to obtain deterministic mappings, while avoiding poor local minima. For the particular test case, our approach obtains new mappings that shed light on the structure of the optimal solution, as well as achieving a small improvement in total cost over the state of the art in numerical approaches to this problem. Proposed method is general and applicable to any problem of similar nature.

The Lossy Common Information of Correlated Sources

The two most prevalent notions of common information (CI) are due to Wyner and Gács-Körner and both the notions can be stated as two different characteristic points in the lossless Gray-Wyner region. Although the information theoretic characterizations for these two CI quantities can be easily evaluated for random variables with infinite entropy (e.g., continuous random variables), their operational significance is applicable only to the lossless framework. The primary objective of this paper is to generalize these two CI notions to the lossy Gray-Wyner network, which hence extends the theoretical foundation to general sources and distortion measures. We begin by deriving a single letter characterization for the lossy generalization of Wyners CI, defined as the minimum rate on the shared branch of the Gray-Wyner network, maintaining minimum sum transmit rate when the two decoders reconstruct the sources subject to individual distortion constraints. To demonstrate its use, we compute the CI of bivariate Gaussian random variables for the entire regime of distortions. We then similarly generalize Gács and Körners definition to the lossy framework. The latter half of this paper focuses on studying the tradeoff between the total transmit rate and receive rate in the Gray-Wyner network. We show that this tradeoff yields a contour of points on the surface of the Gray-Wyner region, which passes through both the Wyner and Gács-Körner operating points, and thereby provides a unified framework to understand the different notions of CI. We further show that this tradeoff generalizes the two notions of CI to the excess sum transmit rate and receive rate regimes, respectively.

A deterministic annealing approach to optimization of zero-delay source-channel codes

This paper studies optimization of zero-delay source-channel codes, and specifically the problem of obtaining globally optimal transformations that map between the source space and the channel space, under a given transmission power constraint and for the mean square error distortion. Particularly, we focus on the setting where the decoder has access to side information, whose cost surface is known to be riddled with local minima. Prior work derived the necessary conditions for optimality of the encoder and decoder mappings, along with a greedy optimization algorithm that imposes these conditions iteratively, in conjunction with the heuristic “noisy channel relaxation” method to mitigate poor local minima. While noisy channel relaxation is arguably effective in simple settings, it fails to provide accurate global optimization results in more complicated settings including the decoder with side information as considered in this paper. We propose a global optimization algorithm based on the ideas of “deterministic annealing” - a non-convex optimization method, derived from information theoretic principles with analogies to statistical physics, and successfully employed in several problems including clustering, vector quantization and regression. We present comparative numerical results that show strict superiority of the proposed algorithm over greedy optimization methods as well as over the noisy channel relaxation.

On optimum communication cost for joint compression and dispersive information routing

In this paper, we consider the problem of minimum cost joint compression and routing for networks with multiple-sinks and correlated sources. We introduce a routing paradigm, called dispersive information routing, wherein the intermediate nodes are allowed to forward a subset of the received bits on subsequent paths. This paradigm opens up a rich class of research problems which focus on the interplay between encoding and routing in a network. What makes it particularly interesting is the challenge in encoding sources such that, exactly the required information is routed to each sink, to reconstruct the sources they are interested in. We demonstrate using simple examples that our approach offers better asymptotic performance than conventional routing techniques. We also introduce a variant of the well known random binning technique, called ‘power binning’, to encode and decode sources that are dispersively transmitted, and which asymptotically achieves the minimum communication cost within this routing paradigm.

On Optimal Jamming Over an Additive Noise Channel

This paper considers the problem of optimal zero-delay jamming over an additive noise channel. Early work had solved this problem for a Gaussian source and a Gaussian channel. Building on a sequence of recent results on conditions for linearity of optimal estimation, and of optimal mappings in source-channel coding, we derive the saddle-point solution to the jamming problem for general sources and channels, without recourse to Gaussianness assumptions. We show that linearity conditions play a pivotal role in jamming, in the sense that the optimal jamming strategy is to effectively force both the transmitter and the receiver to default to linear mappings, i.e., the jammer ensures, whenever possible, that the transmitter and the receiver cannot benefit from non-linear strategies. This result is shown to subsume the known result for Gaussian source and channel. We analyze conditions and general settings where such unbeatable strategy can indeed be achieved by the jammer. Moreover, we provide a procedure to approximate optimal jamming in the remaining (source-channel) cases where the jammer cannot impose linearity on the transmitter and the receiver.

A strictly improved achievable region for multiple descriptions using combinatorial message sharing

We recently proposed a new coding scheme for the L-channel multiple descriptions (MD) problem for general sources and distortion measures involving ‘Combinatorial Message Sharing’ (CMS) [7] leading to a new achievable rate-distortion region. Our objective in this paper is to establish that this coding scheme strictly subsumes the most popular region for this problem due to Venkataramani, Kramer and Goyal (VKG) [3]. In particular, we show that for a binary symmetric source under Hamming distortion measure, the CMS scheme provides a strictly larger region for all L> 2. The principle of the CMS coding scheme is to include a common message in every subset of the descriptions, unlike the VKG scheme which sends a single common message in all the descriptions. In essence, we show that allowing for a common codeword in every subset of descriptions provides better freedom in coordinating the messages which can be exploited constructively to achieve points outside the VKG region.

Optimization of zero-delay mappings for distributed coding by deterministic annealing

This paper studies the optimization of zero-delay analog mappings in a network setting that involves distributed coding. The cost surface is known to be non-convex, and known greedy methods tend to get trapped in poor locally optimal solutions that depend heavily on initialization. We derive an optimization algorithm based on the principles of “deterministic annealing”, a powerful global optimization framework that has been successfully employed in several disciplines, including, in our recent work, to a simple zero-delay analog communications problem. We demonstrate strict superiority over the descent based methods, as well as present example mappings whose properties lend insights on the workings of the solution and relations with digital distributed coding.

Gaussian sensor networks with adversarial nodes

This paper studies a particular sensor network model which involves one single Gaussian source observed by many sensors, subject to additive independent Gaussian observation noise. Sensors communicate with the receiver over an additive Gaussian multiple access channel. The aim of the receiver is to reconstruct the underlying source with minimum mean squared error. The scenario of interest here is one where some of the sensors act as adversary (jammer): they strive to maximize distortion. We show that the ability of transmitter sensors to secretly agree on a random event, that is “coordination”, plays a key role in the analysis. Depending on the coordination capability of sensors and the receiver, we consider two problem settings. The first setting involves transmitters with “coordination” capabilities in the sense that all transmitters can use identical realization of randomized encoding for each transmission. In this case, the optimal strategy for the adversary sensors also requires coordination, where they all generate the same realization of independent and identically distributed Gaussian noise. In the second setting, the transmitter sensors are restricted to use fixed, deterministic encoders and this setting, which corresponds to a Stackelberg game, does not admit a saddle-point solution. We show that the the optimal strategy for all sensors is uncoded communications where encoding functions of adversaries and transmitters are in opposite directions. For both settings, digital compression and communication is strictly suboptimal.

On Constrained Randomized Quantization

Randomized (dithered) quantization is a method capable of achieving white reconstruction error independent of the source. Dithered quantizers have traditionally been considered within their natural setting of uniform quantization. In this paper we extend conventional dithered quantization to nonuniform quantization, via a subterfage: dithering is performed in the companded domain. Closed form necessary conditions for optimality of the compressor and expander mappings are derived for both fixed and variable rate randomized quantization. Numerically, mappings are optimized by iteratively imposing these necessary conditions. The resulting quantizer renders the reconstruction error white with negligible performance loss compared to the optimal quantizer. The framework is extended to include an explicit constraint that deterministic or randomized quantizers yield reconstruction error that is uncorrelated with the source. Surprising theoretical results show direct and simple connection between the optimal constrained quantizers and their unconstrained counterparts. Numerical results for the Gaussian source provide strong evidence that the proposed constrained randomized quantizer outperforms the conventional dithered quantizer, as well as the constrained deterministic quantizer.