121 research outputs found
Nonasymptotic noisy lossy source coding
This paper shows new general nonasymptotic achievability and converse bounds
and performs their dispersion analysis for the lossy compression problem in
which the compressor observes the source through a noisy channel. While this
problem is asymptotically equivalent to a noiseless lossy source coding problem
with a modified distortion function, nonasymptotically there is a noticeable
gap in how fast their minimum achievable coding rates approach the common
rate-distortion function, as evidenced both by the refined asymptotic analysis
(dispersion) and the numerical results. The size of the gap between the
dispersions of the noisy problem and the asymptotically equivalent noiseless
problem depends on the stochastic variability of the channel through which the
compressor observes the source.Comment: IEEE Transactions on Information Theory, 201
Quantized Estimation of Gaussian Sequence Models in Euclidean Balls
A central result in statistical theory is Pinsker's theorem, which
characterizes the minimax rate in the normal means model of nonparametric
estimation. In this paper, we present an extension to Pinsker's theorem where
estimation is carried out under storage or communication constraints. In
particular, we place limits on the number of bits used to encode an estimator,
and analyze the excess risk in terms of this constraint, the signal size, and
the noise level. We give sharp upper and lower bounds for the case of a
Euclidean ball, which establishes the Pareto-optimal minimax tradeoff between
storage and risk in this setting.Comment: Appearing at NIPS 201
Joint source-channel coding with feedback
This paper quantifies the fundamental limits of variable-length transmission
of a general (possibly analog) source over a memoryless channel with noiseless
feedback, under a distortion constraint. We consider excess distortion, average
distortion and guaranteed distortion (-semifaithful codes). In contrast to
the asymptotic fundamental limit, a general conclusion is that allowing
variable-length codes and feedback leads to a sizable improvement in the
fundamental delay-distortion tradeoff. In addition, we investigate the minimum
energy required to reproduce source samples with a given fidelity after
transmission over a memoryless Gaussian channel, and we show that the required
minimum energy is reduced with feedback and an average (rather than maximal)
power constraint.Comment: To appear in IEEE Transactions on Information Theor
Successive Refinement of Shannon Cipher System Under Maximal Leakage
We study the successive refinement setting of Shannon cipher system (SCS)
under the maximal leakage constraint for discrete memoryless sources under
bounded distortion measures. Specifically, we generalize the threat model for
the point-to-point rate-distortion setting of Issa, Wagner and Kamath (T-IT
2020) to the multiterminal successive refinement setting. Under mild conditions
that correspond to partial secrecy, we characterize the asymptotically optimal
normalized maximal leakage region for both the joint excess-distortion
probability (JEP) and the expected distortion reliability constraints. Under
JEP, in the achievability part, we propose a type-based coding scheme, analyze
the reliability guarantee for JEP and bound the leakage of the information
source through compressed versions. In the converse part, by analyzing a
guessing scheme of the eavesdropper, we prove the optimality of our
achievability result. Under expected distortion, the achievability part is
established similarly to the JEP counterpart. The converse proof proceeds by
generalizing the corresponding results for the rate-distortion setting of SCS
by Schieler and Cuff (T-IT 2014) to the successive refinement setting. Somewhat
surprisingly, the normalized maximal leakage regions under both JEP and
expected distortion constraints are identical under certain conditions,
although JEP appears to be a stronger reliability constraint
Joint source-channel coding with feedback
This paper quantifies the fundamental limits of variable-length transmission of a general (possibly analog) source over a memoryless channel with noiseless feedback, under a distortion constraint. We consider excess distortion, average distortion and guaranteed distortion (d-semifaithful codes). In contrast to the asymptotic fundamental limit, a general conclusion is that allowing variable-length codes and feedback leads to a sizable improvement in the fundamental delay-distortion tradeoff
Causal Sampling, Compressing, and Channel Coding of Streaming Data
With the emergence of the Internet of Things, communication systems, such as those employed in distributed control and tracking scenarios, are becoming increasingly dynamic, interactive, and delay-sensitive. The data in such real-time systems arrive at the encoder progressively in a streaming fashion. An intriguing question is: what codes can transmit streaming data with both high reliability and low latency? Classical non-causal (block) encoding schemes can transmit data reliably but under the assumption that the encoder knows the entire data block before the transmission. While this is a realistic assumption in delay-tolerant systems, it is ill-suited to real-time systems due to the delay introduced by collecting data into a block. This thesis studies causal encoding: the encoder transmits information based on the causally received data while the data is still streaming in and immediately incorporates the newly received data into a continuing transmission on the fly.
This thesis investigates causal encoding of streaming data in three scenarios: causal sampling, causal lossy compressing, and causal joint source-channel coding (JSCC). In the causal sampling scenario, a sampler observes a continuous-time source process and causally decides when to transmit real-valued samples of it under a constraint on the average number of samples per second; an estimator uses the causally received samples to approximate the source process in real time. We propose a causal sampling policy that achieves the best tradeoff between the sampling frequency and the end-to-end real-time estimation distortion for a class of continuous Markov processes. In the causal lossy compressing scenario, the sampling frequency constraint in the causal sampling scenario is replaced by a rate constraint on the average number of bits per second. We propose a causal code that achieves the best causal distortion-rate tradeoff for the same class of processes. In the causal JSCC scenario, the noiseless channel and the continuous-time process in the previous scenarios are replaced by a discrete memoryless channel with feedback and a sequence of streaming symbols, respectively. We propose a causal joint sourcechannel code that achieves the maximum exponentially decaying rate of the error probability compatible with a given rate. Remarkably, the fundamental limits in the causal lossy compressing and the causal JSCC scenarios achieved by our causal codes are no worse than those achieved by the best non-causal codes. In addition to deriving the fundamental limits and presenting the causal codes that achieve the limits, we also show that our codes apply to control systems, are resilient to system deficiencies such as channel delay and noise, and have low complexities.</p
Modulation and Estimation with a Helper
The problem of transmitting a parameter value over an additive white Gaussian
noise (AWGN) channel is considered, where, in addition to the transmitter and
the receiver, there is a helper that observes the noise non-causally and
provides a description of limited rate to the transmitter and/or
the receiver. We derive upper and lower bounds on the optimal achievable
-th moment of the estimation error and show that they coincide for
small values of and for low SNR values. The upper bound relies on a
recently proposed channel-coding scheme that effectively conveys
bits essentially error-free and the rest of the rate - over the same AWGN
channel without help, with the error-free bits allocated to the most
significant bits of the quantized parameter. We then concentrate on the setting
with a total transmit energy constraint, for which we derive achievability
results for both channel coding and parameter modulation for several scenarios:
when the helper assists only the transmitter or only the receiver and knows the
noise, and when the helper assists the transmitter and/or the receiver and
knows both the noise and the message. In particular, for the message-informed
helper that assists both the receiver and the transmitter, it is shown that the
error probability in the channel-coding task decays doubly exponentially.
Finally, we translate these results to those for continuous-time power-limited
AWGN channels with unconstrained bandwidth. As a byproduct, we show that the
capacity with a message-informed helper that is available only at the
transmitter can exceed the capacity of the same scenario when the helper knows
only the noise but not the message.Comment: This work has been submitted to the IEEE for possible publication.
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