17 research outputs found
Sign-Compute-Resolve for Random Access
We present an approach to random access that is based on three elements:
physical-layer network coding, signature codes and tree splitting. Upon
occurrence of a collision, physical-layer network coding enables the receiver
to decode the sum of the information that was transmitted by the individual
users. For each user this information consists of the data that the user wants
to communicate as well as the user's signature. As long as no more than
users collide, their identities can be recovered from the sum of their
signatures. A splitting protocol is used to deal with the case that more than
users collide. We measure the performance of the proposed method in terms
of user resolution rate as well as overall throughput of the system. The
results show that our approach significantly increases the performance of the
system even compared to coded random access, where collisions are not wasted,
but are reused in successive interference cancellation.Comment: Accepted for presentation at 52nd Annual Allerton Conference on
Communication, Control, and Computin
A Note on the Probability of Rectangles for Correlated Binary Strings
Consider two sequences of independent and identically distributed fair
coin tosses, and , which are
-correlated for each , i.e. .
We study the question of how large (small) the probability can be among all sets of a given cardinality.
For sets it is well known that the largest (smallest)
probability is approximately attained by concentric (anti-concentric) Hamming
balls, and this can be proved via the hypercontractive inequality (reverse
hypercontractivity). Here we consider the case of . By
applying a recent extension of the hypercontractive inequality of
Polyanskiy-Samorodnitsky (J. Functional Analysis, 2019), we show that Hamming
balls of the same size approximately maximize in
the regime of . We also prove a similar tight lower bound, i.e.
show that for the pair of opposite Hamming balls approximately
minimizes the probability