15 research outputs found
Neural Distributed Compressor Discovers Binning
We consider lossy compression of an information source when the decoder has
lossless access to a correlated one. This setup, also known as the Wyner-Ziv
problem, is a special case of distributed source coding. To this day, practical
approaches for the Wyner-Ziv problem have neither been fully developed nor
heavily investigated. We propose a data-driven method based on machine learning
that leverages the universal function approximation capability of artificial
neural networks. We find that our neural network-based compression scheme,
based on variational vector quantization, recovers some principles of the
optimum theoretical solution of the Wyner-Ziv setup, such as binning in the
source space as well as optimal combination of the quantization index and side
information, for exemplary sources. These behaviors emerge although no
structure exploiting knowledge of the source distributions was imposed. Binning
is a widely used tool in information theoretic proofs and methods, and to our
knowledge, this is the first time it has been explicitly observed to emerge
from data-driven learning.Comment: draft of a journal version of our previous ISIT 2023 paper (available
at: arXiv:2305.04380). arXiv admin note: substantial text overlap with
arXiv:2305.0438
REGION-BASED ADAPTIVE DISTRIBUTED VIDEO CODING CODEC
The recently developed Distributed Video Coding (DVC) is typically suitable for the
applications where the conventional video coding is not feasible because of its
inherent high-complexity encoding. Examples include video surveillance usmg
wireless/wired video sensor network and applications using mobile cameras etc. With
DVC, the complexity is shifted from the encoder to the decoder.
The practical application of DVC is referred to as Wyner-Ziv video coding (WZ)
where an estimate of the original frame called "side information" is generated using
motion compensation at the decoder. The compression is achieved by sending only
that extra information that is needed to correct this estimation. An error-correcting
code is used with the assumption that the estimate is a noisy version of the original
frame and the rate needed is certain amount of the parity bits. The side information is
assumed to have become available at the decoder through a virtual channel. Due to
the limitation of compensation method, the predicted frame, or the side information, is
expected to have varying degrees of success. These limitations stem from locationspecific
non-stationary estimation noise. In order to avoid these, the conventional
video coders, like MPEG, make use of frame partitioning to allocate optimum coder
for each partition and hence achieve better rate-distortion performance. The same,
however, has not been used in DVC as it increases the encoder complexity.
This work proposes partitioning the considered frame into many coding units
(region) where each unit is encoded differently. This partitioning is, however, done at
the decoder while generating the side-information and the region map is sent over to
encoder at very little rate penalty. The partitioning allows allocation of appropriate
DVC coding parameters (virtual channel, rate, and quantizer) to each region. The
resulting regions map is compressed by employing quadtree algorithm and
communicated to the encoder via the feedback channel. The rate control in DVC is
performed by channel coding techniques (turbo codes, LDPC, etc.). The performance
of the channel code depends heavily on the accuracy of virtual channel model that models estimation error for each region. In this work, a turbo code has been used and
an adaptive WZ DVC is designed both in transform domain and in pixel domain. The
transform domain WZ video coding (TDWZ) has distinct superior performance as
compared to the normal Pixel Domain Wyner-Ziv (PDWZ), since it exploits the
'
spatial redundancy during the encoding. The performance evaluations show that the
proposed system is superior to the existing distributed video coding solutions.
Although the, proposed system requires extra bits representing the "regions map" to be
transmitted, fuut still the rate gain is noticeable and it outperforms the state-of-the-art
frame based DVC by 0.6-1.9 dB.
The feedback channel (FC) has the role to adapt the bit rate to the changing
'
statistics between the side infonmation and the frame to be encoded. In the
unidirectional scenario, the encoder must perform the rate control. To correctly
estimate the rate, the encoder must calculate typical side information. However, the
rate cannot be exactly calculated at the encoder, instead it can only be estimated. This
work also prbposes a feedback-free region-based adaptive DVC solution in pixel
domain based on machine learning approach to estimate the side information.
Although the performance evaluations show rate-penalty but it is acceptable
considering the simplicity of the proposed algorithm.
vii
REGION-BASED ADAPTIVE DISTRIBUTED VIDEO CODING CODEC
The recently developed Distributed Video Coding (DVC) is typically suitable for the
applications where the conventional video coding is not feasible because of its
inherent high-complexity encoding. Examples include video surveillance usmg
wireless/wired video sensor network and applications using mobile cameras etc. With
DVC, the complexity is shifted from the encoder to the decoder.
The practical application of DVC is referred to as Wyner-Ziv video coding (WZ)
where an estimate of the original frame called "side information" is generated using
motion compensation at the decoder. The compression is achieved by sending only
that extra information that is needed to correct this estimation. An error-correcting
code is used with the assumption that the estimate is a noisy version of the original
frame and the rate needed is certain amount of the parity bits. The side information is
assumed to have become available at the decoder through a virtual channel. Due to
the limitation of compensation method, the predicted frame, or the side information, is
expected to have varying degrees of success. These limitations stem from locationspecific
non-stationary estimation noise. In order to avoid these, the conventional
video coders, like MPEG, make use of frame partitioning to allocate optimum coder
for each partition and hence achieve better rate-distortion performance. The same,
however, has not been used in DVC as it increases the encoder complexity.
This work proposes partitioning the considered frame into many coding units
(region) where each unit is encoded differently. This partitioning is, however, done at
the decoder while generating the side-information and the region map is sent over to
encoder at very little rate penalty. The partitioning allows allocation of appropriate
DVC coding parameters (virtual channel, rate, and quantizer) to each region. The
resulting regions map is compressed by employing quadtree algorithm and
communicated to the encoder via the feedback channel. The rate control in DVC is
performed by channel coding techniques (turbo codes, LDPC, etc.). The performance
of the channel code depends heavily on the accuracy of virtual channel model that models estimation error for each region. In this work, a turbo code has been used and
an adaptive WZ DVC is designed both in transform domain and in pixel domain. The
transform domain WZ video coding (TDWZ) has distinct superior performance as
compared to the normal Pixel Domain Wyner-Ziv (PDWZ), since it exploits the
'
spatial redundancy during the encoding. The performance evaluations show that the
proposed system is superior to the existing distributed video coding solutions.
Although the, proposed system requires extra bits representing the "regions map" to be
transmitted, fuut still the rate gain is noticeable and it outperforms the state-of-the-art
frame based DVC by 0.6-1.9 dB.
The feedback channel (FC) has the role to adapt the bit rate to the changing
'
statistics between the side infonmation and the frame to be encoded. In the
unidirectional scenario, the encoder must perform the rate control. To correctly
estimate the rate, the encoder must calculate typical side information. However, the
rate cannot be exactly calculated at the encoder, instead it can only be estimated. This
work also prbposes a feedback-free region-based adaptive DVC solution in pixel
domain based on machine learning approach to estimate the side information.
Although the performance evaluations show rate-penalty but it is acceptable
considering the simplicity of the proposed algorithm.
vii
Rate-cost tradeoffs in control
Consider a distributed control problem with a communication channel connecting the observer of a linear stochastic system to the controller. The goal of the controller is minimize a quadratic cost function. The most basic special case of that cost function is the mean-square deviation of the system state from the desired state. We study the fundamental tradeoff between the communication rate r bits/sec and the limsup of the expected cost b, and show a lower bound on the rate necessary to attain b. The bound applies as long as the system noise has a probability density function. If target cost b is not too large, that bound can be closely approached by a simple lattice quantization scheme that only quantizes the innovation, that is, the difference between the controller's belief about the current state and the true state
Rate-Cost Tradeoffs in Control
Consider a control problem with a communication channel connecting the observer of a linear stochastic system to the controller. The goal of the controller is to minimize a quadratic cost function in the state variables and control signal, known as the linear quadratic regulator (LQR). We study the fundamental tradeoff between the communication rate r bits/sec and the expected cost b. We obtain a lower bound on a certain rate-cost function, which quantifies the minimum directed mutual information between the channel input and output that is compatible with a target LQR cost. The rate-cost function has operational significance in multiple scenarios of interest: among others, it allows us to lower-bound the minimum communication rate for fixed and variable length quantization, and for control over noisy channels. We derive an explicit lower bound to the rate-cost function, which applies to the vector, non-Gaussian, and partially observed systems, thereby extending and generalizing an earlier explicit expression for the scalar Gaussian system, due to Tatikonda el al. [2]. The bound applies as long as the differential entropy of the system noise is not ââ . It can be closely approached by a simple lattice quantization scheme that only quantizes the innovation, that is, the difference between the controller's belief about the current state and the true state. Via a separation principle between control and communication, similar results hold for causal lossy compression of additive noise Markov sources. Apart from standard dynamic programming arguments, our technical approach leverages the Shannon lower bound, develops new estimates for data compression with coding memory, and uses some recent results on high resolution variablelength vector quantization to prove that the new converse bounds are tight
Rate-cost tradeoffs in control
Consider a distributed control problem with a communication channel connecting the observer of a linear stochastic system to the controller. The goal of the controller is minimize a quadratic cost function. The most basic special case of that cost function is the mean-square deviation of the system state from the desired state. We study the fundamental tradeoff between the communication rate r bits/sec and the limsup of the expected cost b, and show a lower bound on the rate necessary to attain b. The bound applies as long as the system noise has a probability density function. If target cost b is not too large, that bound can be closely approached by a simple lattice quantization scheme that only quantizes the innovation, that is, the difference between the controller's belief about the current state and the true state
Entropy-based evaluation of context models for wavelet-transformed images
Entropy is a measure of a message uncertainty. Among others aspects, it serves to determine the minimum coding rate that practical systems may attain. This paper defines an entropy-based measure to evaluate context models employed in wavelet-based image coding. The proposed measure is defined considering the mechanisms utilized by modern coding systems. It establishes the maximum performance achievable with each context model. This helps to determine the adequateness of the model under different coding conditions and serves to predict with high precision the coding rate achieved by practical systems. Experimental results evaluate four well-known context models using different types of images, coding rates, and transform strategies. They reveal that, under specific coding conditions, some widely-spread context models may not be as adequate as it is generally thought. The hints provided by this analysis may help to design simpler and more efficient wavelet-based image codecs
Fourth Workshop on Information Theoretic Methods in Science and Engineering : Proceedings
Peer reviewe
Capacity-Achieving Coding Mechanisms: Spatial Coupling and Group Symmetries
The broad theme of this work is in constructing optimal transmission mechanisms for a wide variety of communication systems. In particular, this dissertation provides a proof of threshold saturation for spatially-coupled codes, low-complexity capacity-achieving coding schemes for side-information problems, a proof that Reed-Muller and primitive narrow-sense BCH codes achieve capacity on erasure channels, and a mathematical framework to design delay sensitive communication systems.
Spatially-coupled codes are a class of codes on graphs that are shown to achieve capacity universally over binary symmetric memoryless channels (BMS) under belief-propagation decoder. The underlying phenomenon behind spatial coupling, known as âthreshold saturation via spatial couplingâ, turns out to be general and this technique has been applied to a wide variety of systems. In this work, a proof of the threshold saturation phenomenon is provided for irregular low-density parity-check (LDPC) and low-density generator-matrix (LDGM) ensembles on BMS channels. This proof is far simpler than published alternative proofs and it remains as the only technique to handle irregular and LDGM codes. Also, low-complexity capacity-achieving codes are constructed for three coding problems via spatial coupling: 1) rate distortion with side-information, 2) channel coding with side-information, and 3) write-once memory system. All these schemes are based on spatially coupling compound LDGM/LDPC ensembles.
Reed-Muller and Bose-Chaudhuri-Hocquengham (BCH) are well-known algebraic codes introduced more than 50 years ago. While these codes are studied extensively in the literature it wasnât known whether these codes achieve capacity. This work introduces a technique to show that Reed-Muller and primitive narrow-sense BCH codes achieve capacity on erasure channels under maximum a posteriori (MAP) decoding. Instead of relying on the weight enumerators or other precise details of these codes, this technique requires that these codes have highly symmetric permutation groups. In fact, any sequence of linear codes with increasing blocklengths whose rates converge to a number between 0 and 1, and whose permutation groups are doubly transitive achieve capacity on erasure channels under bit-MAP decoding. This pro-vides a rare example in information theory where symmetry alone is suďŹcient to achieve capacity.
While the channel capacity provides a useful benchmark for practical design, communication systems of the day also demand small latency and other link layer metrics. Such delay sensitive communication systems are studied in this work, where a mathematical framework is developed to provide insights into the optimal design of these systems