Journal article
Multilevel Diversity Coding Systems: Rate Regions, Codes, Computation, & Forbidden Minors
IEEE transactions on information theory, v 63(1), pp 230-251
Jan 2017
Abstract
The rate regions of multilevel diversity coding systems (MDCSs), a sub-class of the broader family of multi-source multi-sink networks with special structure, are investigated in a systematic way. We enumerate all non-isomorphic MDCS instances with at most three sources and four encoders. Then, the exact rate region of every one of these more than 7000 instances is proven via computations showing that the Shannon outer bound matches with a custom constructed linear code-based inner bound. Results gained from these computations are summarized in key statistics involving aspects, such as the sufficiency of scalar binary codes, the necessary size of vector binary codes, and so on. Also, it is shown how to construct the codes for an achievability proof. Based on this large repository of rate regions, a series of results about general MDCS cases of arbitrary size that they inspired is introduced and proved. In particular, a series of embedding operations that preserve the property of sufficiency of scalar or vector codes is presented. The utility of these operations is demonstrated by boiling the thousands of MDCS instances for which scalar binary (superposition) codes are insufficient down to 12 (26) forbidden the smallest embedded MDCS instances.instances.
Metrics
Details
- Title
- Multilevel Diversity Coding Systems: Rate Regions, Codes, Computation, & Forbidden Minors
- Creators
- Congduan Li - Drexel UniversitySteven Weber - Drexel UniversityJohn MacLaren Walsh - Drexel University
- Publication Details
- IEEE transactions on information theory, v 63(1), pp 230-251
- Publisher
- IEEE
- Grant note
- CCF-1016580 / National Science Foundation (10.13039/100000001)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Electrical and Computer Engineering
- Web of Science ID
- WOS:000391740000018
- Scopus ID
- 2-s2.0-85008473070
- Other Identifier
- 991019167604704721
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Computer Science, Information Systems
- Computer Science, Theory & Methods
- Engineering, Electrical & Electronic
- Mathematics, Applied