RESEARCH STATEMENT SHIRIN SAEEDI BIDOKHTI

Transcription

1 RESEARCH STATEMENT SHIRIN SAEEDI BIDOKHTI The emerging technology of Internet of Things (IoT) has raised fundamental challenges in the design of practical and high performance data transmission and storage systems. Current network architectures and communication schemes are incapable of supporting the massive data, high rate, low latency, and large number of users that are envisioned in the applications of IoT. I am interested in novel cloud-based and cache-aided network architectures, and the opportunities they can provide to fundamentally boost the performance of communication networks. In particular, I seek to answer questions such as: How much coordination is needed in a network to support a desired rate and how to establish this coordination among the network nodes? How to utilize local storage units at network nodes to improve rate and latency? What is the tradeoff between communication and computation in distributed systems? How to compress data using minimum storage cost such that the important features of the data are preserved in the compressed domain? To approach these questions, I use tools from information theory, network theory, optimization, and algorithms to develop coding strategies that are efficient with respect to rate, energy, memory, complexity, latency, and cost. In the long term, I aim to develop a mathematical understanding of information extraction, storage and communication for data analysis, where the challenge is to learn certain information, rather than to reconstruct the entire data exactly. In the following, I present some of my past research contributions and future research directions. 1. Cloud Radio Access Networks Virtual BBU Pool BBU BBU BBU Centralized Baseband Pool Cloud Computing Fronthaul Network Collaborative Radio Interference Management Fig 1 A Cloud Radio Access Network Cloud Radio Access Networks (C-RANs) are among the most promising proposed technologies for the next generation of mobile networks. They combine advances in both wireless networks and cloud distributed processing to improve spectral efficiency and energy efficiency. By aggregating all processing units (BBUs) into a central cloud and distributing the radio heads (s) in desired areas, the C-RAN architecture creates novel opportunities for coordination, advanced interference management, and multi-cell processing. This architecture is shown in Fig. 1 and consists of a cloud processor, a fronthaul network, and an interference network. One of the main challenges in exploiting the above mentioned opportunities is due to the inherent interplay between coordination and rate. On the one hand, we would like to design and harness the interference to the benefit of the users, rather than avoid it. To this end, we need to jointly design the code accross the s and thus fully coordinate them. On the other hand, the fronthaul links are costly and scarce; therefore, they can not support the communication overhead that having full coordination imposes. To overcome these challenges in a single-user C-RAN, we proposed a coordinated coding scheme [1, 2, 3, 4] that utilizes the fronthaul network to send not only information bits, but also coordination bits. We could thus establish partial coordination among the s depending on the available fronthaul bandwidth and the interference network. In particular, we provided a fundamental interplay between coordination and rate, as explained below. We study the behavior of any coding scheme across network cuts. While the cut-set bound has remained the upper bound of choice in networks due to its simplicity, it is well known that it is not tight. In particular, in the context of C-RAN downlinks, we show in [1] that the cut-set bound does not well capture

2 the tradeoff between efficiency of communication on the fronthaul links and the desired coordination among the s. For example for the network of Fig. 2, the simplest cut-set bound is given by (1) R max min{c 1 + C 2, I(X p(x 1,x 2 ) }{{} 1 X 2 ; Y )} }{{} Cut #1 Cut #2 where R is the rate with which the user is served and I(X 1 X 2 ; Y ) captures the amount of information passing through the second cut. Suppose we Fig 2 Cut-set bound have a scheme that performs with a rate close to the first term in (1). This means that the fronthaul links carry independent information. However, by transmitting independent information to the two s, one cannot establish coordination between them (i.e., we can only establish product distributions p(x 1 )p(x 2 ), rather than general joint distributions p(x 1, x 2 ) which is allowed in the maximization in (1)). So the tradeoff between rate and coordination is not well-captured through the cutset bound. In a series of works [5, 3, 4, 1, 2], we developed a new technique to better capture and quantify this tradeoff. This is done by introducing an auxiliary channel from the output of the channel Y with the goal of making X 1 and X 2 conditionally independent. In other words, we find the common information between the s signals and relate it to the overhead that is needed on the fronthaul network to establish the desired coordination among the s. Future Work. Our previous work points to the fact that the component of coordination is missing from the existing frameworks for wireless network information flow and it lays a clear and promising path to capture the essence of coordination in general networks. To see why coordination bits (in addition to the actual information bits) need to flow in a network (in an efficient code design), we proceed as follows: Make a cut in the network, disconnecting the source and the destination into two layers (see Fig. 3). We ask two questions that are inter-related: (i) For a given rate to be feasible on the second layer, how much coordination is needed among the involved nodes? (ii) How should coordination be established on the nodes of the second layer, and what is its associated communication cost on the first layer? Many interesting questions remain open and timely to pursue: How can we develop a general framework to explain how information and coordination flow on wireless networks? How does coordination among network nodes provide new opportunities and techniques in interference management for multi-user C-RANs? When is coordination necessary and what is its cost? How can we trade rate with complexity of code design in order to come up with low complexity and near-optimal schemes? 2. Cache-Aided Networks Fig 3 Interplay between coordination and fronthaul link capacities Caching is an idea from content delivery networks to replicate and store information across networks to balance traffic load and improve accessibility/latency. Recently, caching has found its way into wireless networks and promised new opportunities that build on the inherent features of wireless networks, namely the broadcast nature of transmission and the superposition nature of reception. In cache-aided systems, communication takes place in two phases: a caching phase (typically done in low-traffic periods) in which the server stores parts of its data in local storage units of the users before knowing their demands, and a delivery phase (typically done in peak hours) in which users are served based on their actual demands. Prior work showed that in a noise-free system, a smart design of the caching scheme offers global caching gains that scale with the number of users [6]. To investigate the gains of caching in wireless networks, we initiated a study on the role of caching in 2

3 broadcast networks, where a noisy version of the sent signal is overheard at every user (see Fig 4). A common approach, which was believed to be near-optimal, is to combine caching and channel coding using separate cachechannel architectures (see Fig 5). Separation is however suboptimal, as we explain below. In [7, 8], we proposed a joint cache-channel coding architecture where the cache content is not only helpful in conveying desired information bits, but Fig 4 A cache-aided broadcast network is also essential for channel decoding. The role of caches is thus two-fold: to store information and to help with the decoding. This approach significantly improves on state-of-the-art schemes in terms of rate and latency and offers new global caching gains. In particular, it provides a scheme where weaker users are not rate bottlenecks in the network. Joint cache-channel coding is particularly beneficial in heterogeneous networks. Consequently, we have developed coding schemes for broadcast networks (including Gaussian networks) with heterogeneous cache sizes and asked the following question: Given a total amount of cache memory, how should one allocate it to individual users in order to maximize the overall communication rate? We answered this question in a series of works [9, 10, 11] and proposed a cache allocation that carefully assigns larger cache memories to weaker receivers to best utilize the dual role of the caches. An interesting application of this coding scheme is in (virtual) state-adaptive cache allocation in time-varying channels. In particular, we showed the benefits of the scheme in terms of rate and decoding latency in [12]. We have further proved performance guarantees for the scheme in [7, 13, 14]. Our bounds are tighter than all previously known bounds in noisy and noiseless broadcast networks and provide good approximations on the rate-memory tradeoffs. Caching Encoder Channel Encoder Encoding Channel Decoder Caching Decoder Decoding Fig 5 Separate cachechannel architecture is not optimal Arguably, there is a close connection between the problems of caching, index coding, network coding, and feedback in broadcast networks. For example, the coding technique proposed in [6] is a reminiscent of the feedback algorithm in [15] and both use ideas from network coding and index coding. The idea is to treat any information that is stored and/or overheard by a user as side information in later stages. This becomes challenging in practical systems where the environment is dynamic; e.g. channels with memory. In a series of works, we considered broadcast packet erasure channels and investigated the role of feedback when channels have memory. This problem was brought to our attention by Munich Aerospace (DLR) in a joint project, and our results were published in [16, 17, 18]. We modeled the channel memory using a finite-state machine and considered the following scenarios: (i) the channel state is visible to the transmitter, (ii) the channel state is not observable. In both scenarios, we used tools from network coding and queuing theory and developed max-weight backpressure algorithms that are rate-optimal and implementable. Moreover, we provided an analytic framework for our algorithms by devising their probabilistic counterparts which have a similar performance. We showed that in this probabilistic paradigm, analyzing the performance of an algorithm is equivalent to solving a max-flow min-cut problem. Future Work. Caching and feedback will be key components in future wireless networks as a solution to the rapidly growing number of users and demands. They both create novel opportunities for broadcasting and thus rate efficiency. In current code designs, rate-efficiency usually comes at the expense of complex code designs, and complexity of code design often manifests itself in decoding delay. Motivated by the importance of decoding delay in streaming applications, I am interested in developing a new understanding of the fundamental tradeoffs between rate and decoding delay and studying the role of feedback and caching in this regard. While these questions, in their general forms, are challenging open problems, I believe that they could be approached and fundamentally understood in the class of network codes. In particular, given a network coding scheme, one could develop an equivalent network of queues where different queues store 3

4 and represent different classes of coded symbols (depending on how many information bits they encode). Using tools from information theory, network coding, queuing theory, and graph theory, we can then analyze the behavior of the code with respect to network stability, rate-performance, decoding latency, etc. Many interesting research directions are also unpaved in dynamic environments and under practical constraints (noisy feedback, cache failure, etc.). Although these constraints are often well captured and dealt with on the network layer, a separate treatment of the network layer and the physical layer is oftentimes suboptimal compared to what information theoretical limits promise. How can we design cache/delivery schemes in networks where users demands depend on their browsing history? When should we use the network to cache and when should we use it to deliver messages in a dynamic network environment? How can we devise robust caching and feedback algorithms that allow reliable storage and transmission even when local storage units fail or when the network dynamics are unknown? 3. Data Compression for Data Analysis In the era of big data, the high rate at which data is acquired and the high dimensional nature of it makes its storage, processing, and analysis a grand challenge in terms of accuracy as well as computational feasibility. Conventional data compression techniques, such as the Lempel-Ziv algorithm, are used in practice to reduce the space required for storing data. Unfortunately, many important features of the data are inaccessible in the compressed domain. For example, in genomic data analysis, we may need to access certain positions of the genome sequence (i.e., random access) across several individuals. To access the data and analyze it, under the common existing architectures, one has to fully decompress the data and work with the original dataset from scratch. Existing solutions in the computer science literature include succinct data structures that allow certain types of query in the compressed domain [19] and heuristic hashing methods for similarity search. Previous work on this topic is limited [20, 21] but suggests that information theory is a complementary aspect that is missing from current literature. Two of my recent and ongoing works are on developing compression techniques for similarity search and random access query. In [22], we have developed and analyzed compressors that encode two independent sources for similarity query. Here, the goal of compression is not to recover the source sequences, but to ensure a reliable answer to the following question: Are the source sequences similar with respect to a given distance measure?. The outputs of such compressors provide us with hashing of the source sequences such that similarity search can be run on the compressed (hashed) dataset rather than the original dataset. In [23], we have built on the constructions in [20] and [24], and developed a universal two-step compressor that can compress any unknown iid source to its entropy (optimal compression), while ensuring random access to the source sequence by accessing only a constant number of stored bits. The merit of such compressors is that one does not need to decompress the entire sequence (and hence access all stored bits) in order to query a single position of the sequence. Our construction is fairly general and we believe its adaptations may be capable of transforming any good source code into one with random access property. We are currently working on such universal compressors for stationary sources. Future Work. More broadly, my goal is to develop the underlying theory and algorithms for modern compressors that keep the geometric structure of the dataset accessible in the compressed domain. With this approach, I aim to create a counterpart for many of the basic analysis tools (e.g., similarity search, clustering) in the lower dimensional compressed domain. This will significantly reduce the storage/processing memory and speed up the analysis. References [1] S. Saeedi Bidokhti and G. Kramer, Capacity bounds for diamond networks with an orthogonal broadcast channel, IEEE Trans. Inf. Theory, vol. 62, pp , Dec [2] S. Saeedi Bidokhti, G. Kramer, and S. Shamai, Capacity bounds on the downlink of symmetric, multi-relay, singlereceiver C-RAN networks, Entropy, vol. 19, no. 11, [3] S. Saeedi Bidokhti and G. Kramer, Capacity bounds for a class of diamond networks, in IEEE Int. Symp. Inf. Theory, Jun

5 [4] S. Saeedi Bidokhti and G. Kramer, Capacity of two-relay diamond networks with rate-limited links to the relays and a binary adder multiple access channel, in IEEE Int. Symp. Inf. Theory, Jul [5] S. Saeedi Bidokhti and G. Kramer, An application of a wringing lemma to the multiple access channel with cooperative encoders, in Proc. Iran Workshop on Commun. and Inf. Theory, May [6] M. Maddah-Ali and U. Niesen, Fundamental limits of caching, IEEE Trans. Inf. Theory, vol. 60, pp , May [7] S. Saeedi Bidokhti, M. Wigger, and R. Timo, Noisy broadcast networks with receiver caching, submitted to IEEE Trans. Inf. Theory, May [8] S. Saeedi Bidokhti, M. Wigger, and R. Timo, Erasure broadcast networks with receiver caching, in IEEE Int. Symp. Inf. Theory, Jul [9] S. Saeedi Bidokhti, M. Wigger, and A. Yener, Cache assignment on noisy broadcast channels, to be submitted to IEEE Trans. Inf. Theory, [10] S. Saeedi Bidokhti, M. Wigger, and A. Yener, Gaussian broadcast channels with receiver cache assignment, submitted to Int. Conf. Communications, Oct [11] S. S. Bidokhti, M. Wigger, and A. Yener, Benefits of cache assignment on degraded broadcast channels, in IEEE Int. Symp. Inf. Theory, pp , June [12] S. Saeedi Bidokhti, M. Wigger, A. Yener, and A. E. Gamal, State-adaptive coded caching for symmetric broadcast channels, in Asilomar, Nov [13] S. Saeedi Bidokhti, M. Wigger, and R. Timo, An upper bound on the capacity-memory tradeoff of degraded broadcast channels, in Int. Symp. Turbo Codes & Iterative Information Processing, Sept [14] C.-Y. Wang, S. Saeedi Bidokhti, and M. Wigger, Improved converses and gap-results for coded caching, submitted to IEEE Int. Symp. Inf. Theory, [15] L. Georgiadis and L. Tassiulas, Broadcast erasure channel with feedback-capacity and algorithms, in IEEE Workshop on Network Coding, Jun [16] M. Heindelmair, N. Reyhanian, and S. Saeedi Bidokhti, On the capacity region of the two-user broadcast packet erasure channel with feedback and memory, in Allerton Conf. Comm., Control, and Computing, Oct [17] M. Heindelmair and S. Saeedi Bidokhti, Capacity regions of two-user broadcast erasure channels with feedback and hidden memory, in IEEE Int. Symp. Inf. Theory, Jun [18] M. Heindelmair and S. Saeedi Bidokhti, Capacity regions of two-user broadcast erasure channels with feedback and memory, submitted to IEEE Trans. Inf. Theory, Dec [19] G. J. Jacobson, Succinct static data structures. PhD thesis, Carnegie Mellon University, [20] A. Mazumdar, V. Chandar, and G. W. Wornell, Local recovery in data compression for general sources, in Int. Symp. Inf. Theory, [21] A. Ingber, T. Courtade, and T. Weissman, Compression for quadratic similarity queries, IEEE Trans. Inf. Theory, vol. 61, pp , May [22] K. Tatwawadi, S. Saeedi Bidokhti, and T. Weissman, Universal compression of stationary sources with constant random access, work in preparation. [23] S. Saeedi Bidokhti and T. Weissman, Compression of independent sources for similarity query, work in preparation. [24] H. Buhrman, P. B. Miltersen, J. Radhakrishnan, and S. Venkatesh, Are bitvectors optimal?, SIAM J. Comput., vol. 31, pp , June