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Michèle Wigger

Publications and source records attributed to Michèle Wigger.

64 records · Page 4Linked to original sources
arXiv2016

Noisy Broadcast Networks with Receiver Caching

We study noisy broadcast networks with local cache memories at the receivers, where the transmitter can pre-store information even before learning the receivers' requests. We mostly focus on packet-erasure broadcast networks with two disjoint sets of receivers: a set of weak receivers with all-equal erasure probabilities and equal cache sizes and a set of strong receivers with all-equal erasure probabilities and no cache memories. We present lower and upper bounds on the capacity-memory tradeoff of this network. The lower bound is achieved by a new joint cache-channel coding idea and significantly improves on schemes that are based on separate cache-channel coding. We discuss how this coding idea could be extended to more general discrete memoryless broadcast channels and to unequal cache sizes. Our upper bound holds for all stochastically degraded broadcast channels. For the described packet-erasure broadcast network, our lower and upper bounds are tight when there is a single weak receiver (and any number of strong receivers) and the cache memory size does not exceed a given threshold. When there are a single weak receiver, a single strong receiver, and two files, then we can strengthen our upper and lower bounds so as they coincide over a wide regime of cache sizes. Finally, we completely characterise the rate-memory tradeoff for general discrete-memoryless broadcast channels with arbitrary cache memory sizes and arbitrary (asymmetric) rates when all receivers always demand exactly the same file.

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arXiv2016

Conferencing in Wyner's Asymmetric Interference Network: Effect of Number of Rounds

Our goal is to study the effect of the number of conferencing rounds on the capacity of large interference networks. We do this at hand of the per-user multiplexing gain (MG) of Wyner's soft-handoff model with dedicated conferencing links between neighbouring transmitters and receivers. We present upper and lower bounds on the per-user MG of this network, which depend on the capacities of the transmitter- and receiver-conferencing links and on the number of allowed conferencing rounds. The bounds are tight when: the prelogs of the conferencing links are small or high; there is only transmitter conferencing or only receiver conferencing; or some symmetry conditions between transmitter-conferencing and receiver-conferencing hold. We also determine the per-user MG of the network when the number of conferencing rounds is unlimited. Our results show that for small conferencing prelogs around 1/6, a single conferencing round suffices to attain the maximum per-user MG when the number of conferencing rounds is unconstrained. In contrast, when the prelogs are large, then every additional conferencing round increases the maximum per-user MG.

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arXiv2016

Coding Schemes with Rate-Limited Feedback that Improve over the Nofeedback Capacity for a Large Class of Broadcast Channels

We propose two coding schemes for the two-receiver discrete memoryless broadcast channel (BC) with rate-limited feedback from one or both receivers. They improve over the nofeedback capacity region for a large class of channels, including the class of \emph{strictly essentially less-noisy BCs} that we introduce in this article. Examples of strictly essentially less-noisy BCs are the binary symmetric BC (BSBC) or the binary erasure BC (BEBC) with unequal cross-over or erasure probabilities at the two receivers. When the feedback rates are sufficiently large, our schemes recover all previously known capacity results for discrete memoryless BCs with feedback. In both our schemes, we let the receivers feed back quantization messages about their receive signals. In the first scheme, the transmitter simply \emph{relays} the quantization information obtained from Receiver 1 to Receiver 2, and vice versa. This provides each receiver with a second observation of the input signal and can thus improve its decoding performance unless the BC is physically degraded. Moreover, each receiver uses its knowledge of the quantization message describing its own outputs so as to attain the same performance as if this message had not been transmitted at all. In our second scheme the transmitter first \emph{reconstructs and processes} the quantized output signals, and then sends the outcome as a common update information to both receivers. A special case of our second scheme applies also to memoryless BCs without feedback but with strictly-causal state-information at the transmitter and causal state-information at the receivers. It recovers all previous achievable regions also for this setup with state-information.

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arXiv2015

Coordination in State-Dependent Distributed Networks: The Two-Agent Case

This paper addresses a coordination problem between two agents (Agents $1$ and $2$) in the presence of a noisy communication channel which depends on an external system state $\{x_{0,t}\}$. The channel takes as inputs both agents' actions, $\{x_{1,t}\}$ and $\{x_{2,t}\}$ and produces outputs that are observed strictly causally at Agent $2$ but not at Agent $1$. The system state is available either causally or non-causally at Agent $1$ but unknown at Agent $2$. Necessary and sufficient conditions on a joint distribution $\bar{Q}(x_0,x_1,x_2)$ to be implementable asymptotically (i.e, when the number of taken actions grows large) are provided for both causal and non-causal state information at Agent $1$. Since the coordination degree between the agents' actions, $x_{1,t}$ and $x_{2,t}$, and the system state $x_{0,t}$ is measured in terms of an average payoff function, feasible payoffs are fully characterized by implementable joint distributions. In this sense, our results allow us to derive the performance of optimal power control policies on an interference channel and to assess the gain provided by non-causal knowledge of the system state at Agent $1$. The derived proofs readily yield new results also for the problem of state-amplification under a causality constraint at the decoder.

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arXiv2015

Extrinsic Jensen-Shannon Divergence: Applications to Variable-Length Coding

This paper considers the problem of variable-length coding over a discrete memoryless channel (DMC) with noiseless feedback. The paper provides a stochastic control view of the problem whose solution is analyzed via a newly proposed symmetrized divergence, termed extrinsic Jensen-Shannon (EJS) divergence. It is shown that strictly positive lower bounds on EJS divergence provide non-asymptotic upper bounds on the expected code length. The paper presents strictly positive lower bounds on EJS divergence, and hence non-asymptotic upper bounds on the expected code length, for the following two coding schemes: variable-length posterior matching and MaxEJS coding scheme which is based on a greedy maximization of the EJS divergence. As an asymptotic corollary of the main results, this paper also provides a rate-reliability test. Variable-length coding schemes that satisfy the condition(s) of the test for parameters $R$ and $E$, are guaranteed to achieve rate $R$ and error exponent $E$. The results are specialized for posterior matching and MaxEJS to obtain deterministic one-phase coding schemes achieving capacity and optimal error exponent. For the special case of symmetric binary-input channels, simpler deterministic schemes of optimal performance are proposed and analyzed.

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arXiv2014

MIMO MAC-BC Duality with Linear-Feedback Coding Schemes

We show that for the multi-antenna Gaussian multi-access channel (MAC) and broadcast channel (BC) with perfect feedback, the rate regions achieved by linear-feedback coding schemes (called linear-feedback capacity regions) coincide when the same total input-power constraint is imposed on both channels and when the MAC channel matrices are the transposes of the BC channel matrices. Such a pair of MAC and BC is called dual. We also identify sub-classes of linear-feedback coding schemes that achieve the linear-feedback capacity regions of these two channels and present multi-letter expressions for the linear-feedback capacity regions. Moreover, within the two sub-classes of coding schemes that achieve the linear-feedback capacity regions for a given MAC and its dual BC, we identify for each MAC scheme a BC scheme and for each BC scheme a MAC scheme so that the two schemes have same total input power and achieve the same rate regions.

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arXiv2013

Insufficiency of Linear-Feedback Schemes In Gaussian Broadcast Channels with Common Message

We consider the $K\geq 2$-user memoryless Gaussian broadcast channel (BC) with feedback and common message only. We show that linear-feedback schemes with a message point, in the spirit of Schalkwijk & Kailath's scheme for point-to-point channels or Ozarow & Leung's scheme for BCs with private messages, are strictly suboptimal for this setup. Even with perfect feedback, the largest rate achieved by these schemes is strictly smaller than capacity $C$ (which is the same with and without feedback). In the extreme case where the number of receivers $K\to \infty$, the largest rate achieved by linear-feedback schemes with a message point tends to 0. To contrast this negative result, we describe a scheme for \emph{rate-limited} feedback that uses the feedback in an intermittent way, i.e., the receivers send feedback signals only in few channel uses. This scheme achieves all rates $R$ up to capacity $C$ with an $L$-th order exponential decay of the probability of error if the feedback rate $R_{\textnormal{fb}}$ is at least $(L-1)R$ for some positive integer $L$.

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arXiv2013

Constrained Source Coding with Side Information

The source-coding problem with side information at the decoder is studied subject to a constraint that the encoder---to whom the side information is unavailable---be able to compute the decoder's reconstruction sequence to within some distortion. For discrete memoryless sources and finite single-letter distortion measures, an expression is given for the minimal description rate as a function of the joint law of the source and side information and of the allowed distortions at the encoder and at the decoder. The minimal description rate is also computed for a memoryless Gaussian source with squared-error distortion measures. A solution is also provided to a more general problem where there are more than two distortion constraints and each distortion function may be a function of three arguments: the source symbol, the encoder's reconstruction symbol, and the decoder's reconstruction symbol.

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arXiv2012

Source Coding Problems with Conditionally Less Noisy Side Information

A computable expression for the rate-distortion (RD) function proposed by Heegard and Berger has eluded information theory for nearly three decades. Heegard and Berger's single-letter achievability bound is well known to be optimal for \emph{physically degraded} side information; however, it is not known whether the bound is optimal for arbitrarily correlated side information (general discrete memoryless sources). In this paper, we consider a new setup in which the side information at one receiver is \emph{conditionally less noisy} than the side information at the other. The new setup includes degraded side information as a special case, and it is motivated by the literature on degraded and less noisy broadcast channels. Our key contribution is a converse proving the optimality of Heegard and Berger's achievability bound in a new setting. The converse rests upon a certain \emph{single-letterization} lemma, which we prove using an information theoretic telescoping identity {recently presented by Kramer}. We also generalise the above ideas to two different successive-refinement problems.

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