Simple Coding Techniques for Many-Hop Relaying
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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 m, the transmission time n, and the error probability. We introduce a simple and efficient protocol that attains positive information velocity (i.e., a non-vanishing ratio m/n 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 k bits over m hops with O(m+k) transmission time.
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