Π-CoLab
Director: Farhad Shirani
Assistant Professor
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Privacy, Inference,
and Communications Laboratory
Project 3: Optimal Code Structures in Network Communications
In this work we investigate the structure of optimality achieving codes in multiterminal communications. We divide these structures into two main categories: 1) randomly generated codes with algebraic structures with effective lengths which are asymptotically large such as linear codes and group codes, and 2) randomly generated codes with constant finite effective length. We show the necessity of both these categories of structured codes in various network communication settings.
Sub-optimality of Single-letter Coding in Networks
Users in multiterminal communications face an intrinsic trade-off. On the one hand, they have to transmit their respective messages efficiently and reliably (communication). On the other hand, they have to coordinate with other users to facilitate their communication tasks (cooperation). We argue that codes which are good for communication have long memory (i.e operate over large blocks), whereas codes which are good for cooperation have short memory. In this project, we introduce the concept of dependency spectrum which provides a mathematical quantification of a code's effective length or memory. We also prove the sub-optimality of the Shannon-theoretic coding schemes used in several multi-terminal communication scenarios such as distributed source coding and distributed transmission of sources over channels. This is the first such observation in our field, and an indicator that we must take a different approach to network communications than what was done in the past several decades.
New Methods for Lattice Construction and Analysis
Direct performance analysis of lattice coding techniques in general multi-terminal setups turns out to be difficult. The analysis is usually carried out for quantization of Gaussian sources with linear Gaussian test channels, and quadratic distortion, and cost constraints a.k.a LQG problems. Also, the lattices used for network communications are designed for point-to-point communications, as opposed to the linear codes in the discrete world which are tailored for specific multi-terminal problems. Hence, characterizations of performance limits of lattices in general communication problems are not available. We provide a new method for lattice generation and lattice quantization. The advantage of the new method is that it allows for ‘technology transfer’ from discrete structured coding techniques to lattice generation techniques. We construct lattices which are truly designed for multi-terminal communications.
The method proposes the following advantages:
More details can be found in the following:
Structure Codes
for Multiple-Descriptions
We proposed random coding and structured coding schemes
that improve upon the previous known achievability schemes in the
multiple descriptions problem. The schemes uses univariate, bivariate and
multi-variate common components to compress the source more
efficiently.
Our Contributions include:
