6 problems
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The BSGY rate-1/2 random-access expectation conjecture
Let the rate- code family constructed by the authors of BSGY24 have block dimension and random-access expectation measured by the relevant quantity . BSGY rate-1/2 c…
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Two-packet collision approximation for vulnerable-period computation in irregular repetition ALOHA
Let be the frame duration and the vulnerable-period duration, and define … as the number of disjoint vulnerable periods within one frame. For an unresolvable collision…
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The MSRA multiple-sequence conjecture on inherent code diversity
Let MSRA denote Multi-sequence Spreading Random Access, and consider the associated multiple-measurement-vector (MMV) problem for activity detection. A well-conditioned MMV problem…
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Conjecture that relaxed maximum-likelihood activity detection achieves NNLS scaling
Let be the number of active users, the number of potentially active users, and the signal dimension in the covariance-based activity-detection problem. A l…
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Pal's covariance-LASSO conjecture for sublinear activity detection
In a single-antenna unsourced random-access model, let denote the number of active users, the number of potentially active users, and the required signal d…
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Scaling-law conjecture for the low-complexity approximated ML activity-detection algorithm
Low-complexity ML scaling-law conjecture. The low-complexity approximated ML algorithm achieves the same scaling law as the rigorously analyzed NNLS and constrained ML methods, nam…