Abstract:Consider a point-to-point communication system in which the transmitter holds a binary message of length $m$ and transmits a corresponding codeword of length $n$. The receiver's goal is to recover a Boolean function of that message, where the function is unknown to the transmitter, but chosen from a known class $F$. We are interested in the asymptotic relationship of $m$ and $n$: given $n$, how large can $m$ be (asymptotically), such that the value of the Boolean function can be recovered reliably? This problem generalizes the identification-via-channels framework introduced by Ahlswede and Dueck. We formulate the notion of computation capacity, and derive achievability and converse results for selected classes of functions $F$, characterized by the Hamming weight of functions. Our obtained results are tight in the sense of the scaling behavior for all cases of $F$ considered in the paper.
From: Jingge Zhu [view email]
[v1]
Mon, 19 Jan 2026 01:07:09 UTC (86 KB)
[v2]
Thu, 16 Apr 2026 01:04:40 UTC (87 KB)
[v3]
Wed, 12 Aug 2026 06:00:42 UTC (87 KB)
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