Simple Coding Techniques for Many-Hop Relaying

In this paper, we study the problem of relaying a single bit of information across a series of binary symmetric channels, and the associated trade-off between the number of hops <inline-formula> <tex-math notation="LaTeX">m </tex-math></inline-formula>, the transmis...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 68; no. 11; pp. 7043 - 7053
Main Authors: Ling, Yan Hao, Scarlett, Jonathan
Format: Journal Article
Language:English
Published: New York IEEE 01.11.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Codes
Delays
Encoding
Error probability
Information velocity
many-hop relaying
Maximum likelihood decoding
network information theory
Protocols
relay channels
Relaying
Relays
Scaling laws
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:In this paper, we study the problem of relaying a single bit of information across a series of binary symmetric channels, and the associated trade-off between the number of hops <inline-formula> <tex-math notation="LaTeX">m </tex-math></inline-formula>, the transmission time <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula>, and the error probability. We introduce a simple, efficient, and deterministic protocol that attains positive information velocity (i.e., a non-vanishing ratio <inline-formula> <tex-math notation="LaTeX">\frac {m}{n} </tex-math></inline-formula> and small error probability) and is significantly simpler than existing protocols that do so. In addition, we characterize the optimal low-noise and high-noise scaling laws of the information velocity, and we adapt our 1-bit protocol to transmit <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula> bits over <inline-formula> <tex-math notation="LaTeX">m </tex-math></inline-formula> hops with <inline-formula> <tex-math notation="LaTeX">\mathcal {O}(m+k) </tex-math></inline-formula> transmission time.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2022.3180001