Multi-Bit Relaying Over a Tandem of Channels

We study error exponents for the problem of relaying a message over a tandem of two channels sharing the same transition law, in particular moving beyond the 1-bit setting studied in recent related works. Our main results show that the 1-hop and 2-hop exponents coincide in both of the following sett...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 69; no. 6; pp. 3511 - 3524
Main Authors: Ling, Yan Hao, Scarlett, Jonathan
Format: Journal Article
Language:English
Published: New York IEEE 01.06.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Channels
Decoding
Encoding
Error analysis
error exponents
Exponents
low-rate communication
Memoryless systems
Messages
Monte Carlo methods
Protocols
Relay channels
Relaying
Relays
Sufficient conditions
tandem of channels
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:We study error exponents for the problem of relaying a message over a tandem of two channels sharing the same transition law, in particular moving beyond the 1-bit setting studied in recent related works. Our main results show that the 1-hop and 2-hop exponents coincide in both of the following settings: (i) the number of messages is fixed, and the channel law satisfies a condition called pairwise reversibility, or (ii) the channel is arbitrary, and a zero-rate limit is taken from above. In addition, we provide various extensions of our results that relax the assumptions of pairwise reversibility and/or the two channels having identical transition laws, and we provide an example for which the 2-hop exponent is strictly below the 1-hop exponent.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2023.3247829