Channel Simulation: Finite Blocklengths and Broadcast Channels
- URL: http://arxiv.org/abs/2212.11666v2
- Date: Thu, 8 Jun 2023 08:07:55 GMT
- Title: Channel Simulation: Finite Blocklengths and Broadcast Channels
- Authors: Michael X. Cao, Navneeth Ramakrishnan, Mario Berta, Marco Tomamichel
- Abstract summary: We study channel simulation under common randomness-assistance in the finite-blocklength regime.
We identify the smooth channel max-information as a linear program one-shot converse on the minimal simulation cost for fixed error tolerance.
- Score: 20.35937589646518
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We study channel simulation under common randomness-assistance in the
finite-blocklength regime and identify the smooth channel max-information as a
linear program one-shot converse on the minimal simulation cost for fixed error
tolerance. We show that this one-shot converse can be achieved exactly using
no-signaling assisted codes, and approximately achieved using common
randomness-assisted codes. Our one-shot converse thus takes on an analogous
role to the celebrated meta-converse in the complementary problem of channel
coding, and find tight relations between these two bounds. We asymptotically
expand our bounds on the simulation cost for discrete memoryless channels,
leading to the second-order as well as the moderate deviation rate expansion,
which can be expressed in terms of the channel capacity and channel dispersion
known from noisy channel coding. Our techniques extend to discrete memoryless
broadcast channels. In stark contrast to the elusive broadcast channel capacity
problem, we show that the reverse problem of broadcast channel simulation under
common randomness-assistance allows for an efficiently computable single-letter
characterization of the asymptotic rate region in terms of the broadcast
channel's multi-partite mutual information. Finally, we present a
Blahut-Arimoto type algorithm to compute the rate region efficiently.
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