TY - JOUR AB - The extent of heterogeneity among driver gene mutations present in naturally occurring metastases - that is, treatment-naive metastatic disease - is largely unknown. To address this issue, we carried out 60× whole-genome sequencing of 26 metastases from four patients with pancreatic cancer. We found that identical mutations in known driver genes were present in every metastatic lesion for each patient studied. Passenger gene mutations, which do not have known or predicted functional consequences, accounted for all intratumoral heterogeneity. Even with respect to these passenger mutations, our analysis suggests that the genetic similarity among the founding cells of metastases was higher than that expected for any two cells randomly taken from a normal tissue. The uniformity of known driver gene mutations among metastases in the same patient has critical and encouraging implications for the success of future targeted therapies in advanced-stage disease. AU - Makohon Moore, Alvin AU - Zhang, Ming AU - Reiter, Johannes AU - Božić, Ivana AU - Allen, Benjamin AU - Kundu, Deepanjan AU - Chatterjee, Krishnendu AU - Wong, Fay AU - Jiao, Yuchen AU - Kohutek, Zachary AU - Hong, Jungeui AU - Attiyeh, Marc AU - Javier, Breanna AU - Wood, Laura AU - Hruban, Ralph AU - Nowak, Martin AU - Papadopoulos, Nickolas AU - Kinzler, Kenneth AU - Vogelstein, Bert AU - Iacobuzio Donahue, Christine ID - 653 IS - 3 JF - Nature Genetics SN - 10614036 TI - Limited heterogeneity of known driver gene mutations among the metastases of individual patients with pancreatic cancer VL - 49 ER - TY - CONF AB - A memory-hard function (MHF) ƒn with parameter n can be computed in sequential time and space n. Simultaneously, a high amortized parallel area-time complexity (aAT) is incurred per evaluation. In practice, MHFs are used to limit the rate at which an adversary (using a custom computational device) can evaluate a security sensitive function that still occasionally needs to be evaluated by honest users (using an off-the-shelf general purpose device). The most prevalent examples of such sensitive functions are Key Derivation Functions (KDFs) and password hashing algorithms where rate limits help mitigate off-line dictionary attacks. As the honest users' inputs to these functions are often (low-entropy) passwords special attention is given to a class of side-channel resistant MHFs called iMHFs. Essentially all iMHFs can be viewed as some mode of operation (making n calls to some round function) given by a directed acyclic graph (DAG) with very low indegree. Recently, a combinatorial property of a DAG has been identified (called "depth-robustness") which results in good provable security for an iMHF based on that DAG. Depth-robust DAGs have also proven useful in other cryptographic applications. Unfortunately, up till now, all known very depth-robust DAGs are impractically complicated and little is known about their exact (i.e. non-asymptotic) depth-robustness both in theory and in practice. In this work we build and analyze (both formally and empirically) several exceedingly simple and efficient to navigate practical DAGs for use in iMHFs and other applications. For each DAG we: *Prove that their depth-robustness is asymptotically maximal. *Prove bounds of at least 3 orders of magnitude better on their exact depth-robustness compared to known bounds for other practical iMHF. *Implement and empirically evaluate their depth-robustness and aAT against a variety of state-of-the art (and several new) depth-reduction and low aAT attacks. We find that, against all attacks, the new DAGs perform significantly better in practice than Argon2i, the most widely deployed iMHF in practice. Along the way we also improve the best known empirical attacks on the aAT of Argon2i by implementing and testing several heuristic versions of a (hitherto purely theoretical) depth-reduction attack. Finally, we demonstrate practicality of our constructions by modifying the Argon2i code base to use one of the new high aAT DAGs. Experimental benchmarks on a standard off-the-shelf CPU show that the new modifications do not adversely affect the impressive throughput of Argon2i (despite seemingly enjoying significantly higher aAT). AU - Alwen, Joel F AU - Blocki, Jeremiah AU - Harsha, Ben ID - 6527 SN - 9781450349468 T2 - Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security TI - Practical graphs for optimal side-channel resistant memory-hard functions ER - TY - JOUR AB - In November 2016, developmental biologists, synthetic biologists and engineers gathered in Paris for a meeting called ‘Engineering the embryo’. The participants shared an interest in exploring how synthetic systems can reveal new principles of embryonic development, and how the in vitro manipulation and modeling of development using stem cells can be used to integrate ideas and expertise from physics, developmental biology and tissue engineering. As we review here, the conference pinpointed some of the challenges arising at the intersection of these fields, along with great enthusiasm for finding new approaches and collaborations. AU - Kicheva, Anna AU - Rivron, Nicolas ID - 654 IS - 5 JF - Development SN - 09501991 TI - Creating to understand – developmental biology meets engineering in Paris VL - 144 ER - TY - CONF AB - This paper studies the complexity of estimating Rényi divergences of discrete distributions: p observed from samples and the baseline distribution q known a priori. Extending the results of Acharya et al. (SODA'15) on estimating Rényi entropy, we present improved estimation techniques together with upper and lower bounds on the sample complexity. We show that, contrarily to estimating Rényi entropy where a sublinear (in the alphabet size) number of samples suffices, the sample complexity is heavily dependent on events occurring unlikely in q, and is unbounded in general (no matter what an estimation technique is used). For any divergence of integer order bigger than 1, we provide upper and lower bounds on the number of samples dependent on probabilities of p and q (the lower bounds hold for non-integer orders as well). We conclude that the worst-case sample complexity is polynomial in the alphabet size if and only if the probabilities of q are non-negligible. This gives theoretical insights into heuristics used in the applied literature to handle numerical instability, which occurs for small probabilities of q. Our result shows that they should be handled with care not only because of numerical issues, but also because of a blow up in the sample complexity. AU - Skórski, Maciej ID - 6526 SN - 9781509040964 T2 - 2017 IEEE International Symposium on Information Theory (ISIT) TI - On the complexity of estimating Rènyi divergences ER - TY - JOUR AB - The bacterial flagellum is a self-assembling nanomachine. The external flagellar filament, several times longer than a bacterial cell body, is made of a few tens of thousands subunits of a single protein: flagellin. A fundamental problem concerns the molecular mechanism of how the flagellum grows outside the cell, where no discernible energy source is available. Here, we monitored the dynamic assembly of individual flagella using in situ labelling and real-time immunostaining of elongating flagellar filaments. We report that the rate of flagellum growth, initially ~1,700 amino acids per second, decreases with length and that the previously proposed chain mechanism does not contribute to the filament elongation dynamics. Inhibition of the proton motive force-dependent export apparatus revealed a major contribution of substrate injection in driving filament elongation. The combination of experimental and mathematical evidence demonstrates that a simple, injection-diffusion mechanism controls bacterial flagella growth outside the cell. AU - Renault, Thibaud AU - Abraham, Anthony AU - Bergmiller, Tobias AU - Paradis, Guillaume AU - Rainville, Simon AU - Charpentier, Emmanuelle AU - Guet, Calin C AU - Tu, Yuhai AU - Namba, Keiichi AU - Keener, James AU - Minamino, Tohru AU - Erhardt, Marc ID - 655 JF - eLife SN - 2050084X TI - Bacterial flagella grow through an injection diffusion mechanism VL - 6 ER - TY - JOUR AB - Plant organs are typically organized into three main tissue layers. The middle ground tissue layer comprises the majority of the plant body and serves a wide range of functions, including photosynthesis, selective nutrient uptake and storage, and gravity sensing. Ground tissue patterning and maintenance in Arabidopsis are controlled by a well-established gene network revolving around the key regulator SHORT-ROOT (SHR). In contrast, it is completely unknown how ground tissue identity is first specified from totipotent precursor cells in the embryo. The plant signaling molecule auxin, acting through AUXIN RESPONSE FACTOR (ARF) transcription factors, is critical for embryo patterning. The auxin effector ARF5/MONOPTEROS (MP) acts both cell-autonomously and noncell-autonomously to control embryonic vascular tissue formation and root initiation, respectively. Here we show that auxin response and ARF activity cell-autonomously control the asymmetric division of the first ground tissue cells. By identifying embryonic target genes, we show that MP transcriptionally initiates the ground tissue lineage and acts upstream of the regulatory network that controls ground tissue patterning and maintenance. Strikingly, whereas the SHR network depends on MP, this MP function is, at least in part, SHR independent. Our study therefore identifies auxin response as a regulator of ground tissue specification in the embryonic root, and reveals that ground tissue initiation and maintenance use different regulators and mechanisms. Moreover, our data provide a framework for the simultaneous formation of multiple cell types by the same transcriptional regulator. AU - Möller, Barbara AU - Ten Hove, Colette AU - Xiang, Daoquan AU - Williams, Nerys AU - López, Lorena AU - Yoshida, Saiko AU - Smit, Margot AU - Datla, Raju AU - Weijers, Dolf ID - 657 IS - 12 JF - PNAS SN - 00278424 TI - Auxin response cell autonomously controls ground tissue initiation in the early arabidopsis embryo VL - 114 ER - TY - JOUR AB - With the accelerated development of robot technologies, control becomes one of the central themes of research. In traditional approaches, the controller, by its internal functionality, finds appropriate actions on the basis of specific objectives for the task at hand. While very successful in many applications, self-organized control schemes seem to be favored in large complex systems with unknown dynamics or which are difficult to model. Reasons are the expected scalability, robustness, and resilience of self-organizing systems. The paper presents a self-learning neurocontroller based on extrinsic differential plasticity introduced recently, applying it to an anthropomorphic musculoskeletal robot arm with attached objects of unknown physical dynamics. The central finding of the paper is the following effect: by the mere feedback through the internal dynamics of the object, the robot is learning to relate each of the objects with a very specific sensorimotor pattern. Specifically, an attached pendulum pilots the arm into a circular motion, a half-filled bottle produces axis oriented shaking behavior, a wheel is getting rotated, and wiping patterns emerge automatically in a table-plus-brush setting. By these object-specific dynamical patterns, the robot may be said to recognize the object's identity, or in other words, it discovers dynamical affordances of objects. Furthermore, when including hand coordinates obtained from a camera, a dedicated hand-eye coordination self-organizes spontaneously. These phenomena are discussed from a specific dynamical system perspective. Central is the dedicated working regime at the border to instability with its potentially infinite reservoir of (limit cycle) attractors "waiting" to be excited. Besides converging toward one of these attractors, variate behavior is also arising from a self-induced attractor morphing driven by the learning rule. We claim that experimental investigations with this anthropomorphic, self-learning robot not only generate interesting and potentially useful behaviors, but may also help to better understand what subjective human muscle feelings are, how they can be rooted in sensorimotor patterns, and how these concepts may feed back on robotics. AU - Der, Ralf AU - Martius, Georg S ID - 658 IS - MAR JF - Frontiers in Neurorobotics SN - 16625218 TI - Self organized behavior generation for musculoskeletal robots VL - 11 ER - TY - JOUR AB - Migration frequently involves Rac-mediated protrusion of lamellipodia, formed by Arp2/3 complex-dependent branching thought to be crucial for force generation and stability of these networks. The formins FMNL2 and FMNL3 are Cdc42 effectors targeting to the lamellipodium tip and shown here to nucleate and elongate actin filaments with complementary activities in vitro. In migrating B16-F1 melanoma cells, both formins contribute to the velocity of lamellipodium protrusion. Loss of FMNL2/3 function in melanoma cells and fibroblasts reduces lamellipodial width, actin filament density and -bundling, without changing patterns of Arp2/3 complex incorporation. Strikingly, in melanoma cells, FMNL2/3 gene inactivation almost completely abolishes protrusion forces exerted by lamellipodia and modifies their ultrastructural organization. Consistently, CRISPR/Cas-mediated depletion of FMNL2/3 in fibroblasts reduces both migration and capability of cells to move against viscous media. Together, we conclude that force generation in lamellipodia strongly depends on FMNL formin activity, operating in addition to Arp2/3 complex-dependent filament branching. AU - Kage, Frieda AU - Winterhoff, Moritz AU - Dimchev, Vanessa AU - Müller, Jan AU - Thalheim, Tobias AU - Freise, Anika AU - Brühmann, Stefan AU - Kollasser, Jana AU - Block, Jennifer AU - Dimchev, Georgi A AU - Geyer, Matthias AU - Schnittler, Hams AU - Brakebusch, Cord AU - Stradal, Theresia AU - Carlier, Marie AU - Sixt, Michael K AU - Käs, Josef AU - Faix, Jan AU - Rottner, Klemens ID - 659 JF - Nature Communications SN - 20411723 TI - FMNL formins boost lamellipodial force generation VL - 8 ER - TY - JOUR AB - Growing microtubules are protected from depolymerization by the presence of a GTP or GDP/Pi cap. End-binding proteins of the EB1 family bind to the stabilizing cap, allowing monitoring of its size in real time. The cap size has been shown to correlate with instantaneous microtubule stability. Here we have quantitatively characterized the properties of cap size fluctuations during steadystate growth and have developed a theory predicting their timescale and amplitude from the kinetics of microtubule growth and cap maturation. In contrast to growth speed fluctuations, cap size fluctuations show a characteristic timescale, which is defined by the lifetime of the cap sites. Growth fluctuations affect the amplitude of cap size fluctuations; however, cap size does not affect growth speed, indicating that microtubules are far from instability during most of their time of growth. Our theory provides the basis for a quantitative understanding of microtubule stability fluctuations during steady-state growth. AU - Rickman, Jamie AU - Düllberg, Christian F AU - Cade, Nicholas AU - Griffin, Lewis AU - Surrey, Thomas ID - 660 IS - 13 JF - PNAS SN - 00278424 TI - Steady state EB cap size fluctuations are determined by stochastic microtubule growth and maturation VL - 114 ER - TY - JOUR AB - We report a direct-numerical-simulation study of the Taylor-Couette flow in the quasi-Keplerian regime at shear Reynolds numbers up to (105). Quasi-Keplerian rotating flow has been investigated for decades as a simplified model system to study the origin of turbulence in accretion disks that is not fully understood. The flow in this study is axially periodic and thus the experimental end-wall effects on the stability of the flow are avoided. Using optimal linear perturbations as initial conditions, our simulations find no sustained turbulence: the strong initial perturbations distort the velocity profile and trigger turbulence that eventually decays. AU - Shi, Liang AU - Hof, Björn AU - Rampp, Markus AU - Avila, Marc ID - 662 IS - 4 JF - Physics of Fluids SN - 10706631 TI - Hydrodynamic turbulence in quasi Keplerian rotating flows VL - 29 ER - TY - CONF AB - In this paper, we propose an approach to automatically compute invariant clusters for nonlinear semialgebraic hybrid systems. An invariant cluster for an ordinary differential equation (ODE) is a multivariate polynomial invariant g(u→, x→) = 0, parametric in u→, which can yield an infinite number of concrete invariants by assigning different values to u→ so that every trajectory of the system can be overapproximated precisely by the intersection of a group of concrete invariants. For semialgebraic systems, which involve ODEs with multivariate polynomial right-hand sides, given a template multivariate polynomial g(u→, x→), an invariant cluster can be obtained by first computing the remainder of the Lie derivative of g(u→, x→) divided by g(u→, x→) and then solving the system of polynomial equations obtained from the coefficients of the remainder. Based on invariant clusters and sum-of-squares (SOS) programming, we present a new method for the safety verification of hybrid systems. Experiments on nonlinear benchmark systems from biology and control theory show that our approach is efficient. AU - Kong, Hui AU - Bogomolov, Sergiy AU - Schilling, Christian AU - Jiang, Yu AU - Henzinger, Thomas A ID - 663 SN - 978-145034590-3 T2 - Proceedings of the 20th International Conference on Hybrid Systems TI - Safety verification of nonlinear hybrid systems based on invariant clusters ER - TY - JOUR AB - Macrophage filopodia, finger-like membrane protrusions, were first implicated in phagocytosis more than 100 years ago, but little is still known about the involvement of these actin-dependent structures in particle clearance. Using spinning disk confocal microscopy to image filopodial dynamics in mouse resident Lifeact-EGFP macrophages, we show that filopodia, or filopodia-like structures, support pathogen clearance by multiple means. Filopodia supported the phagocytic uptake of bacterial (Escherichia coli) particles by (i) capturing along the filopodial shaft and surfing toward the cell body, the most common mode of capture; (ii) capturing via the tip followed by retraction; (iii) combinations of surfing and retraction; or (iv) sweeping actions. In addition, filopodia supported the uptake of zymosan (Saccharomyces cerevisiae) particles by (i) providing fixation, (ii) capturing at the tip and filopodia-guided actin anterograde flow with phagocytic cup formation, and (iii) the rapid growth of new protrusions. To explore the role of filopodia-inducing Cdc42, we generated myeloid-restricted Cdc42 knock-out mice. Cdc42-deficient macrophages exhibited rapid phagocytic cup kinetics, but reduced particle clearance, which could be explained by the marked rounded-up morphology of these cells. Macrophages lacking Myo10, thought to act downstream of Cdc42, had normal morphology, motility, and phagocytic cup formation, but displayed markedly reduced filopodia formation. In conclusion, live-cell imaging revealed multiple mechanisms involving macrophage filopodia in particle capture and engulfment. Cdc42 is not critical for filopodia or phagocytic cup formation, but plays a key role in driving macrophage lamellipodial spreading. AU - Horsthemke, Markus AU - Bachg, Anne AU - Groll, Katharina AU - Moyzio, Sven AU - Müther, Barbara AU - Hemkemeyer, Sandra AU - Wedlich Söldner, Roland AU - Sixt, Michael K AU - Tacke, Sebastian AU - Bähler, Martin AU - Hanley, Peter ID - 668 IS - 17 JF - Journal of Biological Chemistry SN - 00219258 TI - Multiple roles of filopodial dynamics in particle capture and phagocytosis and phenotypes of Cdc42 and Myo10 deletion VL - 292 ER - TY - JOUR AB - The exocyst, a eukaryotic tethering complex, coregulates targeted exocytosis as an effector of small GTPases in polarized cell growth. In land plants, several exocyst subunits are encoded by double or triple paralogs, culminating in tens of EXO70 paralogs. Out of 23 Arabidopsis thaliana EXO70 isoforms, we analyzed seven isoforms expressed in pollen. Genetic and microscopic analyses of single mutants in EXO70A2, EXO70C1, EXO70C2, EXO70F1, EXO70H3, EXO70H5, and EXO70H6 genes revealed that only a loss-of-function EXO70C2 allele resulted in a significant male-specific transmission defect (segregation 40%:51%:9%) due to aberrant pollen tube growth. Mutant pollen tubes grown in vitro exhibited an enhanced growth rate and a decreased thickness of the tip cell wall, causing tip bursts. However, exo70C2 pollen tubes could frequently recover and restart their speedy elongation, resulting in a repetitive stop-and-go growth dynamics. A pollenspecific depletion of the closest paralog, EXO70C1, using artificial microRNA in the exo70C2 mutant background, resulted in a complete pollen-specific transmission defect, suggesting redundant functions of EXO70C1 and EXO70C2. Both EXO70C1 and EXO70C2, GFP tagged and expressed under the control of their native promoters, localized in the cytoplasm of pollen grains, pollen tubes, and also root trichoblast cells. The expression of EXO70C2-GFP complemented the aberrant growth of exo70C2 pollen tubes. The absent EXO70C2 interactions with core exocyst subunits in the yeast two-hybrid assay, cytoplasmic localization, and genetic effect suggest an unconventional EXO70 function possibly as a regulator of exocytosis outside the exocyst complex. In conclusion, EXO70C2 is a novel factor contributing to the regulation of optimal tip growth of Arabidopsis pollen tubes. AU - Synek, Lukáš AU - Vukašinović, Nemanja AU - Kulich, Ivan AU - Hála, Michal AU - Aldorfová, Klára AU - Fendrych, Matyas AU - Žárský, Viktor ID - 669 IS - 1 JF - Plant Physiology SN - 00320889 TI - EXO70C2 is a key regulatory factor for optimal tip growth of pollen VL - 174 ER - TY - CONF AB - Polar codes represent one of the major recent breakthroughs in coding theory and, because of their attractive features, they have been selected for the incoming 5G standard. As such, a lot of attention has been devoted to the development of decoding algorithms with good error performance and efficient hardware implementation. One of the leading candidates in this regard is represented by successive-cancellation list (SCL) decoding. However, its hardware implementation requires a large amount of memory. Recently, a partitioned SCL (PSCL) decoder has been proposed to significantly reduce the memory consumption [1]. In this paper, we examine the paradigm of PSCL decoding from both theoretical and practical standpoints: (i) by changing the construction of the code, we are able to improve the performance at no additional computational, latency or memory cost, (ii) we present an optimal scheme to allocate cyclic redundancy checks (CRCs), and (iii) we provide an upper bound on the list size that allows MAP performance. AU - Hashemi, Seyyed Ali AU - Mondelli, Marco AU - Hassani, Hamed AU - Urbanke, Ruediger AU - Gross, Warren ID - 6679 T2 - 2017 IEEE Global Communications Conference TI - Partitioned list decoding of polar codes: Analysis and improvement of finite length performance ER - TY - JOUR AB - Humans routinely use conditionally cooperative strategies when interacting in repeated social dilemmas. They are more likely to cooperate if others cooperated before, and are ready to retaliate if others defected. To capture the emergence of reciprocity, most previous models consider subjects who can only choose from a restricted set of representative strategies, or who react to the outcome of the very last round only. As players memorize more rounds, the dimension of the strategy space increases exponentially. This increasing computational complexity renders simulations for individuals with higher cognitive abilities infeasible, especially if multiplayer interactions are taken into account. Here, we take an axiomatic approach instead. We propose several properties that a robust cooperative strategy for a repeated multiplayer dilemma should have. These properties naturally lead to a unique class of cooperative strategies, which contains the classical Win-Stay Lose-Shift rule as a special case. A comprehensive numerical analysis for the prisoner's dilemma and for the public goods game suggests that strategies of this class readily evolve across various memory-n spaces. Our results reveal that successful strategies depend not only on how cooperative others were in the past but also on the respective context of cooperation. AU - Hilbe, Christian AU - Martinez, Vaquero AU - Chatterjee, Krishnendu AU - Nowak, Martin ID - 671 IS - 18 JF - PNAS SN - 00278424 TI - Memory-n strategies of direct reciprocity VL - 114 ER - TY - JOUR AB - We propose an efficient method to model paper tearing in the context of interactive modeling. The method uses geometrical information to automatically detect potential starting points of tears. We further introduce a new hybrid geometrical and physical-based method to compute the trajectory of tears while procedurally synthesizing high resolution details of the tearing path using a texture based approach. The results obtained are compared with real paper and with previous studies on the expected geometric paths of paper that tears. AU - Schreck, Camille AU - Rohmer, Damien AU - Hahmann, Stefanie ID - 670 IS - 2 JF - Computer Graphics Forum SN - 01677055 TI - Interactive paper tearing VL - 36 ER - TY - JOUR AB - Trafficking cells frequently transmigrate through epithelial and endothelial monolayers. How monolayers cooperate with the penetrating cells to support their transit is poorly understood. We studied dendritic cell (DC) entry into lymphatic capillaries as a model system for transendothelial migration. We find that the chemokine CCL21, which is the decisive guidance cue for intravasation, mainly localizes in the trans-Golgi network and intracellular vesicles of lymphatic endothelial cells. Upon DC transmigration, these Golgi deposits disperse and CCL21 becomes extracellularly enriched at the sites of endothelial cell-cell junctions. When we reconstitute the transmigration process in vitro, we find that secretion of CCL21-positive vesicles is triggered by a DC contact-induced calcium signal, and selective calcium chelation in lymphatic endothelium attenuates transmigration. Altogether, our data demonstrate a chemokine-mediated feedback between DCs and lymphatic endothelium, which facilitates transendothelial migration. AU - Vaahtomeri, Kari AU - Brown, Markus AU - Hauschild, Robert AU - De Vries, Ingrid AU - Leithner, Alexander F AU - Mehling, Matthias AU - Kaufmann, Walter AU - Sixt, Michael K ID - 672 IS - 5 JF - Cell Reports SN - 22111247 TI - Locally triggered release of the chemokine CCL21 promotes dendritic cell transmigration across lymphatic endothelia VL - 19 ER - TY - CONF AB - Consider the problem of constructing a polar code of block length N for the transmission over a given channel W. Typically this requires to compute the reliability of all the N synthetic channels and then to include those that are sufficiently reliable. However, we know from [1], [2] that there is a partial order among the synthetic channels. Hence, it is natural to ask whether we can exploit it to reduce the computational burden of the construction problem. We show that, if we take advantage of the partial order [1], [2], we can construct a polar code by computing the reliability of roughly N/ log 3/2 N synthetic channels. Such a set of synthetic channels is universal, in the sense that it allows one to construct polar codes for any W, and it can be identified by solving a maximum matching problem on a bipartite graph. Our proof technique consists in reducing the construction problem to the problem of computing the maximum cardinality of an antichain for a suitable partially ordered set. As such, this method is general and it can be used to further improve the complexity of the construction problem in case a new partial order on the synthetic channels of polar codes is discovered. AU - Mondelli, Marco AU - Hassani, S. Hamed AU - Urbanke, Rudiger ID - 6729 SN - 9781509040964 T2 - 2017 IEEE International Symposium on Information Theory TI - Construction of polar codes with sublinear complexity ER - TY - JOUR AB - We introduce a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding. Rather than relying on the precise structure of the codes, our method exploits code symmetry. In particular, the technique applies to any sequence of linear codes where the blocklengths are strictly increasing, the code rates converge, and the permutation group of each code is doubly transitive. In other words, we show that symmetry alone implies near-optimal performance. An important consequence of this result is that a sequence of Reed-Muller codes with increasing block length and converging rate achieves capacity. This possibility has been suggested previously in the literature but it has only been proven for cases where the limiting code rate is 0 or 1. Moreover, these results extend naturally to all affine-invariant codes and, thus, to extended primitive narrow-sense BCH codes. This also resolves, in the affirmative, the existence question for capacity-achieving sequences of binary cyclic codes. The primary tools used in the proof are the sharp threshold property for symmetric monotone Boolean functions and the area theorem for extrinsic information transfer functions. AU - Kudekar, Shrinivas AU - Kumar, Santhosh AU - Mondelli, Marco AU - Pfister, Henry D. AU - Sasoglu, Eren AU - Urbanke, Ridiger L. ID - 6730 IS - 7 JF - IEEE Transactions on Information Theory SN - 0018-9448 TI - Reed–Muller codes achieve capacity on erasure channels VL - 63 ER - TY - CONF AB - We present a rate-compatible polar coding scheme that achieves the capacity of any family of channels. Our solution generalizes the previous results [1], [2] that provide capacity-achieving rate-compatible polar codes for a degraded family of channels. The motivation for our extension comes from the fact that in many practical scenarios, e.g., MIMO systems and non-Gaussian interference, the channels cannot be ordered by degradation. The main technical contribution of this paper consists in removing the degradation condition. To do so, we exploit the ideas coming from the construction of universal polar codes. Our scheme possesses the usual attractive features of polar codes: low complexity code construction, encoding, and decoding; super-polynomial scaling of the error probability with the block length; and absence of error floors. On the negative side, the scaling of the gap to capacity with the block length is slower than in standard polar codes, and we prove an upper bound on the scaling exponent. AU - Mondelli, Marco AU - Hassani, Hamed AU - Maric, Ivana AU - Hui, Dennis AU - Hong, Song-Nam ID - 6731 SN - 9781509059089 T2 - 2017 IEEE Wireless Communications and Networking Conference Workshops TI - Capacity-achieving rate-compatible polar codes for general channels ER -