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Mean-based reconstruction is a fundamental, natural approach to worst-case trace reconstruction over channels with synchronization errors. It is known that $exp(O(n^{1/3}))$ traces are necessary and sufficient for mean-based worst-case trace reconstruction over the deletion channel, and this result was also extended to certain channels combining deletions and geometric insertions of uniformly random bits. In this work, we use a simple extension of the original complex-analytic approach to show that these results are examples of a much more general phenomenon: $exp(O(n^{1/3}))$ traces suffice for mean-based worst-case trace reconstruction over any memoryless channel that maps each input bit to an arbitrarily distributed sequence of replications and insertions of random bits, provided the length of this sequence follows a sub-exponential distribution.
The reconfigurable intelligent surface (RIS) is considered as a promising new technology for reconfiguring wireless communication environments. To acquire the channel information accurately and efficiently, we only turn on a fraction of all the RIS e
We consider the problem of communicating over a channel that randomly tears the message block into small pieces of different sizes and shuffles them. For the binary torn-paper channel with block length $n$ and pieces of length ${rm Geometric}(p_n)$,
This work considers a communication scenario where the transmitter chooses a list of size K from a total of M messages to send over a noisy communication channel, the receiver generates a list of size L and communication is considered successful if t
We construct a joint coordination-channel polar coding scheme for strong coordination of actions between two agents $mathsf X$ and $mathsf Y$, which communicate over a discrete memoryless channel (DMC) such that the joint distribution of actions foll
Sequencing a DNA strand, as part of the read process in DNA storage, produces multiple noisy copies which can be combined to produce better estimates of the original strand; this is called trace reconstruction. One can reduce the error rate further b