On the Binary Adder Channel With Complete Feedback, With an Application to Quantitative Group Testing

@article{Florin2022OnTB,
  title={On the Binary Adder Channel With Complete Feedback, With an Application to Quantitative Group Testing},
  author={Samuel H. Florin and M. H. Ho and Zilin Jiang},
  journal={IEEE Transactions on Information Theory},
  year={2022},
  volume={68},
  pages={2839-2856}
}
We determine the exact value of the optimal symmetric rate point <inline-formula> <tex-math notation="LaTeX">$(r, r)$ </tex-math></inline-formula> in the Dueck zero-error capacity region of the binary adder channel with complete feedback. We proved that the average zero-error capacity <inline-formula> <tex-math notation="LaTeX">$r = h(1/2-\delta) \approx 0.78974$ </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">$h(\cdot)$ </tex-math></inline-formula> is the binary… 

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References

SHOWING 1-10 OF 21 REFERENCES
Some families of zero- error block codes for the two-user binary adder channel with feedback
TLDR
A family of zero-error codes is introduced, based on the Fibonacci recursion; these codes are readily implemented by means of a simple square-dividing strategy.
A new bound for the zero-error capacity region of the two-user binary adder channel
TLDR
It is demonstrated that the problem of finding UD code pairs for the closely related binary XOR channel is in one-to-one correspondence with a certain construction of binary one-error-correcting codes.
Source coding with side information and a converse for degraded broadcast channels
TLDR
In Section H of the paper, a characterization of the capacity region for degraded broadcast channels (DBC's) is given, which was conjectured by Bergmans and is somewhat sharper than the one obtained by Gallager.
On Capacities of the Two-User Union Channel With Complete Feedback
TLDR
For the zero-error capacity region, using superposition coding, this work provides a practical near-optimal communication scheme which improves all the previous explicit constructions and hinges on the technical lemma that concerns the maximal joint entropy of two independent random variables in terms of their probability of equality.
On multiple access channels with feedback
  • F. Willems
  • Computer Science
    IEEE Trans. Inf. Theory
  • 1984
TLDR
This work proves that the symmetrical rate pair is achievable in the ease of feedback and applies this result to demonstrate the fact that the feedback capacity region of the product of two multiple access channels can be strictly larger than the (Minkowski)sum of the feedbackcapacity regions for the separate channels.
Elements of Information Theory
TLDR
The author examines the role of entropy, inequality, and randomness in the design of codes and the construction of codes in the rapidly changing environment.
Search problems on graphs
Binary B2-Sequences : A New Upper Bound
We show that the maximum size of a B2-sequence of binary n-vectors for large enough n is at most 20.5753n, thus improving on the previous bound 20.6n due to B. Lindstrom.
The optimal procedures for quantitative group testing
Determination of two vectors from the sum
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