This work considers the problem of sending a 1-bit message over an acyclic network, where the “edge” connecting any two nodes is a memoryless binary-input/symmetric-output (BISO) channel. For any arbitrary acyclic network topology and constituent channel models, a min-cut-based converse of the learning rate, denoted by r^*, is derived. It is then shown that for any r < r^*, one can design a scheme with learning rate r. Capable of approaching the optimal r^*, the proposed scheme is thus the asymptotically fastest for sending one bit over any acyclic BISO-channel network. The construction is based on a new concept of Lossless Amplify-&-Forward, a sharp departure from existing multi-hop communication scheme designs.
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Efficiently Computable Converses for Finite-Blocklength Communication
This paper presents a method for computing a finite-blocklength converse for the rate of fixed-length codes with feedback used on discrete memoryless channels (DMCs). The new converse is expressed in terms of a stochastic control problem whose solution can be efficiently computed using dynamic programming and Fourier methods. For channels such as the binary symmetric channel (BSC) and binary erasure channel (BEC), the accuracy of the proposed converse is similar to that of existing special-purpose converse bounds, but the new converse technique can be applied to arbitrary DMCs. We provide example applications of the new converse technique to the binary asymmetric channel (BAC) and the quantized amplitude-constrained AWGN channel.
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- PAR ID:
- 10398504
- Date Published:
- Journal Name:
- 2022 IEEE International Symposium on Information Theory (ISIT)
- Page Range / eLocation ID:
- 2094 to 2099
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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