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We study communication models for channels with erasures in which the erasure pattern can be controlled by an adversary with partial knowledge of the transmitted codeword. In particular, we design block codes for channels with binary inputs with an adversary who can erase a fraction p of the transmitted bits. We consider causal adversaries, who must choose to erase an input bit using knowledge of that bit and previously transmitted bits, and myopic adversaries, who can choose an erasure pattern based on observing the transmitted codeword through a binary erasure channel with random erasures. For both settings we design efficient (polynomial time) encoding and decoding algorithms that use randomization at the encoder only. Our constructions achieve capacity for the causal and “sufficiently myopic” models. For the “insufficiently myopic” adversary, the capacity is unknown, but existing converses show the capacity is zero for a range of parameters. For all parameters outside of that range, our construction achieves positive rates.
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Channel Capacity for Adversaries With Computationally Bounded Observations
We study reliable communication over point-to-point adversarial channels in which the adversary can observe the transmitted codeword via some function that takes the n-bit codeword as input and computes an r*n-bit output for some given r in [0,1]. We consider the scenario where the r*n -bit observation is computationally bounded - the adversary is free to choose an arbitrary observation function as long as the function can be computed using a polynomial amount of computational resources. This observation-based restriction differs from conventional channel-based computational limitations, where in the later case, the resource limitation applies to the computation of the (adversarial) channel error/corruption. For all r in [0,1−H(p)] where H(.) is the binary entropy function and p is the adversary’s error budget, we characterize the capacity of the above channel and find that the capacity is identical to the completely oblivious setting (r=0). This result can be viewed as a generalization of known results on myopic adversaries and on channels with active eavesdroppers for which the observation process depends on a fixed distribution and fixed-linear structure, respectively, that cannot be chosen arbitrarily by the adversary.
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- Award ID(s):
- 2309887
- PAR ID:
- 10524882
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- IEEE Transactions on Information Theory
- Volume:
- 70
- Issue:
- 1
- ISSN:
- 0018-9448
- Page Range / eLocation ID:
- 75 to 92
- Subject(s) / Keyword(s):
- Adversarial channels capacity arbitrarily varying channels
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1109/TIT.2023.3330811
