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arXiv · 2208.02003

Multi-Bit Relaying over a Tandem of Channels

Yan Hao Ling·Jonathan Scarlett
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Abstract

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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Yan Hao Ling, Jonathan Scarlett. 2022-08-03. Multi-Bit Relaying over a Tandem of Channels. https://arxiv.org/abs/2208.02003

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