M. Gastpar

University of California, Berkeley, Berkeley, MO, United States

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Publications (200)165.67 Total impact

  • Source
    Jingge Zhu, Michael Gastpar
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    ABSTRACT: Lattice codes used under the Compute-and-Forward paradigm suggest an alternative strategy for the standard Gaussian multiple-access channel (MAC): The receiver successively decodes integer linear combinations of the messages until it can invert and recover all messages. In this paper, this strategy is developed and analyzed. For the two-user MAC, it is shown that without time-sharing, the entire capacity region can be attained with a single-user decoder as soon as the signal-to-noise ratios are above $1+\sqrt{2}$. A partial analysis is given for more than two users. Lastly the strategy is extended to the so-called dirty MAC where two interfering signals are known non-causally to the two transmitters in a distributed fashion. Our scheme extends the previously known results and gives new achievable rate regions.
    07/2014;
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    ABSTRACT: Compute-and-Forward (CF), also known as reliable physical layer network coding, is a technique that provides the possibility of exploiting the features of broadcast and superposition in wireless networks. It has been shown that the throughput for multiple unicast traffic can be significantly boosted by CF. In this letter, the limit of such improvement is investigated by comparing the performance of CF with the traditional routing-based transmission schemes. For networks characterized by local interference and half-duplex constraints, it is proven that the throughput gain of CF over traditional routing, expressed by an improvement factor, is upper bounded by $3K$, where $K$ is the number of unicast sessions. Furthermore, a class of networks is presented for which an improvement by a factor of $K/2$ is feasible by applying CF. Hence, the throughput gain of CF is at most on the order of $K$ for any network, and a gain in that order is indeed achievable for some networks.
    IEEE Communications Letters 07/2014; 18(7):1111-1114. · 1.16 Impact Factor
  • Chien-Yi Wang, Michael Gastpar
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    ABSTRACT: The problem of successive refinement in distributed source coding and in joint source-channel coding is considered. The emphasis is placed on the case where the sources have to be recovered losslessly in the second stage. In distributed source coding, it is shown that all sources are successively refinable in sum rate, with respect to any (joint) distortion measure in the first stage. In joint source-channel coding, the sources are assumed independent and only a (per letter) function is to be recovered losslessly in the first stage. For a class of multiple access channels, it is shown that all sources are successively refinable with respect to a class of linear functions. Finally, when the sources have equal entropy, a simple sufficient condition of successive refinability is provided for partially invertible functions.
    2014 IEEE International Symposium on Information Theory (ISIT); 06/2014
  • Jingge Zhu, Michael Gastpar
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    ABSTRACT: A new achievable rate region is given for the Gaussian cognitive many-to-one interference channel. The proposed coding scheme is based on lattice codes and incorporates all key ingredients from conventional coding schemes. Using the idea of compute-and-forward to decode sums of codewords, our scheme improves considerably upon the conventional coding schemes which treat interference as noise or decode messages simultaneously. Roughly speaking, the novel scheme asks the decoder to decode "just enough" interfering signals and use it for extracting the desired information. Our strategy extends directly to the usual many-to-one interference channels without cognitive messages. For some simple channel settings, the proposed scheme gives constant gap or capacity results which are independent of the number of users in the system.
    04/2014;
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    ABSTRACT: Objective. Intracortical brain-machine interfaces (BMIs) have predominantly utilized spike activity as the control signal. However, an increasing number of studies have shown the utility of local field potentials (LFPs) for decoding motor related signals. Currently, it is unclear how well different LFP frequencies can serve as features for continuous, closed-loop BMI control. Approach. We demonstrate 2D continuous LFP-based BMI control using closed-loop decoder adaptation, which adapts decoder parameters to subject-specific LFP feature modulations during BMI control. We trained two macaque monkeys to control a 2D cursor in a center-out task by modulating LFP power in the 0-150 Hz range. Main results. While both monkeys attained control, they used different strategies involving different frequency bands. One monkey primarily utilized the low-frequency spectrum (0-80 Hz), which was highly correlated between channels, and obtained proficient performance even with a single channel. In contrast, the other monkey relied more on higher frequencies (80-150 Hz), which were less correlated between channels, and had greater difficulty with control as the number of channels decreased. We then restricted the monkeys to use only various sub-ranges (0-40, 40-80, and 80-150 Hz) of the 0-150 Hz band. Interestingly, although both monkeys performed better with some sub-ranges than others, they were able to achieve BMI control with all sub-ranges after decoder adaptation, demonstrating broad flexibility in the frequencies that could potentially be used for LFP-based BMI control. Significance. Overall, our results demonstrate proficient, continuous BMI control using LFPs and provide insight into the subject-specific spectral patterns of LFP activity modulated during control.
    Journal of Neural Engineering 02/2014; 11(2):026002. · 3.28 Impact Factor
  • Source
    Jingge Zhu, Michael Gastpar
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    ABSTRACT: We present a modified compute-and-forward scheme which utilizes Channel State Information at the Transmitters (CSIT) in a natural way. The modified scheme allows different users to have different coding rates, and use CSIT to achieve larger rate region. This idea is applicable to all systems which use the compute-and-forward technique and can be arbitrarily better than the regular scheme in some settings.
    01/2014;
  • Source
    Sang-Woon Jeon, Chien-Yi Wang, Michael Gastpar
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    ABSTRACT: Function computation of arbitrarily correlated discrete sources over Gaussian networks with orthogonal components is studied. Two classes of functions are considered: the arithmetic sum function and the type function. The arithmetic sum function in this paper is defined as a set of multiple weighted arithmetic sums, which includes averaging of the sources and estimating each of the sources as special cases. The type or frequency histogram function counts the number of occurrences of each argument, which yields many important statistics such as mean, variance, maximum, minimum, median, and so on. The proposed computation coding first abstracts Gaussian networks into the corresponding modulo sum multiple-access channels via nested lattice codes and linear network coding and then computes the desired function by using linear Slepian-Wolf source coding. For orthogonal Gaussian networks (with no broadcast and multiple-access components), the computation capacity is characterized for a class of networks. For Gaussian networks with multiple-access components (but no broadcast), an approximate computation capacity is characterized for a class of networks.
    10/2013;
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    Chien-Yi Wang, Sang-Woon Jeon, Michael Gastpar
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    ABSTRACT: In wireless sensor networks, various applications involve learning one or multiple functions of the measurements observed by sensors, rather than the measurements themselves. This paper focuses on type-threshold functions, e.g., the maximum and indicator functions. Previous work studied this problem under the collocated collision network model and showed that under many probabilistic models for the measurements, the achievable computation rates converge to zero as the number of sensors increases. This paper considers two network models reflecting both the broadcast and superposition properties of wireless channels: the collocated linear finite field network and the collocated Gaussian network. A general multi-round coding scheme exploiting not only the broadcast property but particularly also the superposition property of the networks is developed. Through careful scheduling of concurrent transmissions to reduce redundancy, it is shown that given any independent measurement distribution, all type-threshold functions can be computed reliably with a non-vanishing rate in the collocated Gaussian network, even if the number of sensors tends to infinity.
    10/2013;
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    ABSTRACT: Recent progress in brain-machine interfaces (BMIs) has shown tremendous improvements in task complexity and degree of control. In particular, closed-loop decoder adaptation (CLDA) has emerged as an effective paradigm for both improving and maintaining the performance of BMI systems. Here, we demonstrate the first reported use of a CLDA algorithm to rapidly achieve high-performance control of a BMI based on local field potentials (LFPs). We trained a non-human primate to control a 2-D computer cursor by modulating LFP activity to perform a center-out reaching task, while applying CLDA to adaptively update the decoder. We show that the subject is quickly able to readily reach and hold at all 8 targets with an average success rate of 74% ± 7% (sustained peak rate of 85%), with rapid convergence in the decoder parameters. Moreover, the subject is able to maintain high performance across 4 days with minimal adaptations to the decoder. Our results indicate that CLDA can be used to facilitate LFP-based BMI systems, allowing for both rapid improvement and maintenance of performance.
    Conference proceedings: ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Conference 07/2013; 2013:285-288.
  • S.Kartik Buddha, Kelvin So, Jose M. Carmena, Michael C. Gastpar
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    ABSTRACT: It is plausible to hypothesize that the spiking responses of certain neurons represent functions of the spiking signals of other neurons. A natural ensuing question concerns how to use experimental data to infer what kind of a function is being computed. Model-based approaches typically require assumptions on how information is represented. By contrast, information measures are sensitive only to relative behavior: information is unchanged by applying arbitrary invertible transformations to the involved random variables. This paper develops an approach based on the information bottleneck method that attempts to find such functional relationships in a neuron population. Specifically, the information bottleneck method is used to provide appropriate compact representations which can then be parsed to infer functional relationships. In the present paper, the parsing step is specialized to the case of remapped-linear functions. The approach is validated on artificial data and then applied to recordings from the motor cortex of a macaque monkey performing an arm-reaching task. Functional relationships are identified and shown to exhibit some degree of persistence across multiple trials of the same experiment.
    Entropy 05/2013; 5(5). · 1.35 Impact Factor
  • Source
    Naveen Goela, Emmanuel Abbe, Michael Gastpar
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    ABSTRACT: Polar codes are introduced for discrete memoryless broadcast channels. For $m$-user deterministic broadcast channels, polarization is applied to map uniformly random message bits from $m$ independent messages to one codeword while satisfying broadcast constraints. The polarization-based codes achieve rates on the boundary of the private-message capacity region. For two-user noisy broadcast channels, polar implementations are presented for two information-theoretic schemes: i) Cover's superposition codes; ii) Marton's codes. Due to the structure of polarization, constraints on the auxiliary and channel-input distributions are identified to ensure proper alignment of polarization indices in the multi-user setting. The codes achieve rates on the capacity boundary of a few classes of broadcast channels (e.g., binary-input stochastically degraded). The complexity of encoding and decoding is $O(n*log n)$ where $n$ is the block length. In addition, polar code sequences obtain a stretched-exponential decay of $O(2^{-n^{\beta}})$ of the average block error probability where $0 < \beta < 0.5$.
    01/2013;
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    ABSTRACT: Previous research has shown that postnatal exposure to simple, synthetic sounds can affect the sound representation in the auditory cortex as reflected by changes in the tonotopic map or other relatively simple tuning properties, such as AM tuning. However, their functional implications for neural processing in the generation of ethologically-based perception remain unexplored. Here we examined the effects of noise-rearing and social isolation on the neural processing of communication sounds such as species-specific song, in the primary auditory cortex analog of adult zebra finches. Our electrophysiological recordings reveal that neural tuning to simple frequency-based synthetic sounds is initially established in all the laminae independent of patterned acoustic experience; however, we provide the first evidence that early exposure to patterned sound statistics, such as those found in native sounds, is required for the subsequent emergence of neural selectivity for complex vocalizations and for shaping neural spiking precision in superficial and deep cortical laminae, and for creating efficient neural representations of song and a less redundant ensemble code in all the laminae. Our study also provides the first causal evidence for 'sparse coding', such that when the statistics of the stimuli were changed during rearing, as in noise-rearing, that the sparse or optimal representation for species-specific vocalizations disappeared. Taken together, these results imply that a layer-specific differential development of the auditory cortex requires patterned acoustic input, and a specialized and robust sensory representation of complex communication sounds in the auditory cortex requires a rich acoustic and social environment.
    PLoS ONE 01/2013; 8(4):e61417. · 3.53 Impact Factor
  • Jingge Zhu, M. Gastpar
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    ABSTRACT: In this work we consider the cognitive many-to-one interference network. We first extend existing coding schemes from the two-user case to this network scenario. Then we present a novel coding scheme using compute-and-forward and show it can enlarge the achievable rate region considerably for a wide range of parameters. Numerical evaluations are given to compare the performance of different schemes. Specializing the results to symmetric settings, for a range of parameters, our achievable rate region is shown to be within a constant gap from capacity, regardless of the number of cognitive users.
    Information Theory Proceedings (ISIT), 2013 IEEE International Symposium on; 01/2013
  • Changho Suh, M. Gastpar
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    ABSTRACT: We investigate the role of interaction for computation problem settings where nodes intend to compute functions of the raw messages generated at other nodes. In this work, we make some progress on a more elementary research component: feedback. Specifically we characterize the feedback computing capacity of a two-transmitter two-receiver linear deterministic network in which both receivers wish to decode a linear function (modulo-2 sum) of Bernoulli sources generated at the transmitters. Inspired by the concept of interference alignment and compute-and-forward, we develop a new achievable scheme called interactive function alignment. A new converse theorem is established that is tighter than cut-set based and genie-aided bounds. As a consequence of this result, we show that interaction can provide an arbitrarily large gain for computation, as in classical communication settings.
    Information Theory Proceedings (ISIT), 2013 IEEE International Symposium on; 01/2013
  • Changho Suh, M. Gastpar
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    ABSTRACT: We develop a network-decomposition framework to provide elementary parallel subnetworks that can constitute an original network without loss of optimality. In our earlier work, a network decomposition is constructed for the Avestimehr-Diggavi-Tse deterministic network which well captures key properties of wireless Gaussian networks. In this work, we apply this decomposition framework to general problem settings where receivers intend to compute functions of the messages generated at transmitters. Depending on functions, these settings include a variety of network problems, ranging from classical communication problems (such as multiple-unicast and multicast problems) to function computation problems. For many of these problems, we show that coding separately over the decomposed orthogonal subnetworks provides optimal performances, thus establishing a separation principle.
    Signal Processing Advances in Wireless Communications (SPAWC), 2013 IEEE 14th Workshop on; 01/2013
  • Sang-Woon Jeon, M. Gastpar
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    ABSTRACT: The capacity scaling laws of two overlaid networks sharing the same wireless resources with different priorities are investigated. The primary network is assumed to operate in an order-optimal fashion to achieve its standalone capacity scaling law. The secondary “cognitive” network must keep its interference to the primary network below a certain threshold while at the same time maximizing its own throughput scaling law based on cognition information. The existing scaling results for cognitive networks inherently assume multihop communication treating all other signals except from a single intended transmitter as noise. By contrast, in this paper, a general coding model is considered without any specific physical layer coding assumptions. Therefore, this paper provides a general framework for comprehensive understanding of fundamental limits on the capacity scaling laws of cognitive networks. For the extended network model, the capacity scaling laws of both the primary and secondary networks are completely characterized. For the dense network model, an improved throughput scaling law is achieved by inducing cooperation within the secondary network. In both cases, it turns out that the conventional multihop approach is in general quite suboptimal.
    INFOCOM, 2013 Proceedings IEEE; 01/2013
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    ABSTRACT: In wireless sensor networks, various applications involve learning one or multiple functions of the measurements observed by sensors, rather than the measurements themselves. This paper focuses on the computation of type-threshold functions which include the maximum, minimum, and indicator functions as special cases. Previous work studied this problem under the collocated collision network model and showed that under many probabilistic models for the measurements, the achievable computation rates tend to zero as the number of sensors increases. In this paper, wireless sensor networks are modeled as fully connected Gaussian networks with equal channel gains, which are termed collocated Gaussian networks. A general multi-round coding scheme exploiting not only the broadcast property but also the superposition property of Gaussian networks is developed. Through careful scheduling of concurrent transmissions to reduce redundancy, it is shown that given any independent measurement distribution, all type-threshold functions can be computed reliably with a non-vanishing rate even if the number of sensors tends to infinity.
    Information Theory Proceedings (ISIT), 2013 IEEE International Symposium on; 01/2013
  • K. Eswaran, M. Gastpar
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    ABSTRACT: This paper explores the problem of feedback coding for a channel whose output is simultaneously used for two purposes: it is decoded to establish reliable communication, and it is used to control a dynamical system. In general, there is a tradeoff between the rate of communication and the accuracy of control. An intuitive communication and control strategy is analyzed and shown to be optimal in several cases of interest. Using methods from stochastic control, a corresponding upper bound is derived on the rate for a given cost, and this bound can be applied to find the capacity for an interesting class of channels. Under certain regularity conditions, the capacity has a simple characterization, and a series of examples is provided to demonstrate how it can be calculated.
    IEEE Transactions on Information Theory 01/2013; 59(10):6243-6257. · 2.62 Impact Factor
  • J. Goseling, M. Gastpar, J.H. Weber
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    ABSTRACT: We consider a physical-layer network coding strategy for the random-access channel, based on compute-and-forward. When packets collide, it is possible to reliably recover a linear combination of the packets at the receiver. Over many rounds of transmission, the receiver can thus obtain many linear combinations and eventually recover all original packets. This is by contrast to slotted ALOHA where packet collisions lead to complete erasures. In previous work we introduced a compute-and-forward strategy for the two-user random-access channel. In the current work we consider an arbitrary number of users. The strategy is shown to be significantly superior to the best known strategies, including multipacket reception.
    Information Theory Proceedings (ISIT), 2013 IEEE International Symposium on; 01/2013
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    ABSTRACT: Signal superposition and broadcast are important features of the wireless medium. Compute-and-Forward, also known as Physical Layer Network Coding, is a technique exploiting these features in order to improve performance of wireless networks. In this paper, the possible benefits for the line network with multiple bi-directional sessions and local interference are investigated. Four different modes, indicating whether or not broadcast and/or superposition are exploited, are considered. In particular, expressions for the maximum achievable common rate are derived for each of the four different modes. Scheduling and coding schemes achieving these rates are presented. From the results it follows that, in most cases, the common rate is improved by a factor close to two by using Compute-and-Forward. However, it is also found that the benefit may be smaller for particular session configurations.
    Information Theory Proceedings (ISIT), 2013 IEEE International Symposium on; 01/2013

Publication Stats

5k Citations
165.67 Total Impact Points

Institutions

  • 2–2012
    • University of California, Berkeley
      • Department of Electrical Engineering and Computer Sciences
      Berkeley, MO, United States
  • 2011
    • Boston University
      • Department of Electrical and Computer Engineering
      Boston, MA, United States
  • 2010
    • San Jose State University
      • Department of Electrical Engineering
      San Jose, CA, United States
    • University of Wisconsin, Madison
      • Department of Electrical and Computer Engineering
      Madison, Wisconsin, United States
    • University of California, San Diego
      San Diego, California, United States
  • 2009–2010
    • Delft University of Technology
      • Faculty of Electrical Engineering, Mathematics and Computer Sciences (EEMCS)
      Delft, South Holland, Netherlands
    • Qualcomm
      San Diego, California, United States
  • 2002
    • École Polytechnique Fédérale de Lausanne
      Lausanne, Vaud, Switzerland
  • 2001
    • Eawag: Das Wasserforschungs-Institut des ETH-Bereichs
      Duebendorf, Zurich, Switzerland