Identifiability for Blind Source Separation of Multiple Finite Alphabet Linear Mixtures
Behr M, Munk A (2017)
Publication Type: Journal article
Publication year: 2017
Journal
Book Volume: 63
Pages Range: 5506-5517
Article Number: 7953681
Journal Issue: 9
Abstract
We give under weak assumptions a complete combinatorial characterization of identifiability for linear mixtures of finite alphabet sources, with unknown mixing weights and unknown source signals, but known alphabet. This is based on a detailed treatment of the case of a single linear mixture. Notably, our identifiability analysis applies also to the case of unknown number of sources. We provide sufficient and necessary conditions for identifiability and give a simple sufficient criterion together with an explicit construction to determine the weights and the source signals for deterministic data by taking advantage of the hierarchical structure within the possible mixture values. We show that the probability of identifiability is related to the distribution of a hitting time and converges exponentially fast to one when the underlying sources come from a discrete Markov process. Finally, we explore our theoretical results in a simulation study. This paper extends and clarifies the scope of scenarios for which blind source separation becomes meaningful.
Involved external institutions
Germany (DE)How to cite
APA:
Behr, M., & Munk, A. (2017). Identifiability for Blind Source Separation of Multiple Finite Alphabet Linear Mixtures. IEEE Transactions on Information Theory, 63(9), 5506-5517. https://dx.doi.org/10.1109/TIT.2017.2717586
MLA:
Behr, Merle, and Axel Munk. "Identifiability for Blind Source Separation of Multiple Finite Alphabet Linear Mixtures." IEEE Transactions on Information Theory 63.9 (2017): 5506-5517.
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