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This paper introduces the notion of triangulation codes, a family of non-linear codes that 1) admit efficient encoding/decoding 2) their bit error rate deteriorates gracefully as the quality of the erasure channel degrades. Some coding theoretic properties of these codes are established. In the case of transmitting data over the erasure channel, it is shown that, even with sub-optimal decoding, they can achieve lower bit error rate than uncoded transmission for any number of received output symbols.
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Optimal Learning Rate of Sending One Bit Over Arbitrary Acyclic BISO-Channel Networks
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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- Award ID(s):
- 1816013
- PAR ID:
- 10474213
- Publisher / Repository:
- IEEE
- Date Published:
- ISBN:
- 978-1-6654-7554-9
- Page Range / eLocation ID:
- 1360 to 1365
- Format(s):
- Medium: X
- Location:
- Taipei, Taiwan
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ISIT54713.2023.10206476
