Capacity regions of two-user broadcast erasure channels with feedback and hidden memory

• Published in: Proceedings / IEEE International Symposium on Information Theory pp. 406 - 410
• Main Authors: Heindlmaier, Michael, Bidokhti, Shirin Saeedi
• Format: Conference Proceeding Journal Article
• Language: English
• Published: IEEE 01.06.2015
• Subjects: Algorithms; Approximation algorithms; Approximation methods; Broadcasting; Channels; Coding; Encoding; Feedback; Hidden Markov models; Markov chains; Optimization; Probabilistic logic; Receivers; Transmitters
• ISSN: 2157-8095; 2157-8117
• DOI: 10.1109/ISIT.2015.7282486

The two-receiver broadcast packet erasure channel with feedback and memory is studied. Memory is modelled using a finite-state Markov chain representing a channel state. The channel state is unknown at the transmitter, but observations of this hidden Markov chain are available at the transmitter through feedback. Matching outer and inner bounds are derived and the capacity region is determined. The capacity region does not have a single-letter characterization and is, in this sense, uncomputable. Approximations of the capacity region are provided and two optimal coding algorithms are outlined. The first algorithm is a probabilistic coding scheme that bases its decisions on the past L feedback sequences. Its achievable rate-region approaches the capacity region exponentially fast in L. The second algorithm is a backpressure-like algorithm that performs optimally in the long run.