Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE International Symposium on Information Theory (ISIT)

Approximation Theory of Output Statistics

Te Sun Han, S. Verdu

Published Aug 24, 2005• 1 citation
Publisher

Abstract

Given a channel and an input process we study the minimum randomness of those input processes whose output statistics approximate the original output statistics with arbitrary accuracy. We introduce the notion of resolvability of a channel, defined as the number of random bits required per channel use in order to generate an input that achieves arbitrarily accurate approximation of the output statistics for any given input process. We obtain a general formula for resolvability which holds regardless of the channel memory structure. We show that, for most channels, resolvability is equal to Shannon capacity. By-products of our analysis are a general formula for the minimum achievable (fixed-length) source coding rate of any finite-alphabet source, and a strong converse of the identification coding theorem, which holds for any channel that satisfies the strong converse of the channel coding theorem.

DOI
10.1109/isit.1993.748468

Related papers

Resolvability theory for the multiple-access channel

Yossef Steinberg

We study the randomness needed for approximating the output distribution of a multiple-access channel, where the original input processes are independent of each other. The approximation is achieved by simulating (possibly alternative) input processes at each of the entries, where the sources of randomness available for the simulators are independent of each other, and the simulators do not cooperate. The resolvability region of a multiple-access channel is defined as the set of all random-bit rate pairs at which accurate output approximation is possible, where the simulation accuracy is measured by the variational distance between finite-dimensional output distributions. Inner and outer bounds on the resolvability region are derived, and close relations between the concepts of resolvability region and capacity region are demonstrated.

IEEE Transactions on Information Theory•Mar 1, 1998•33 citations

The resolvability and the capacity of AWGN channels are equal

Te Sun Han, Sergio Verdú

The authors have introduced the new notion of resolvability of a channel, as the dual of the capacity, which is defined as the minimum complexity per input letter needed to generate an input process whose output distribution via the channel arbitrarily accurately approximates any prescribed achievable output distribution. The resolvability thus introduced has revealed a deep relationship between the minimum achievable rate for source coding, the channel capacity, the identification capacity and the problem of random number generation. However, the validity of the proof of the converse for the resolvability formula established by Han and Verdu (see IEEE Trans. on Inform. Theory, vol.39, no.3, p.379, 1993) hinged heavily on the assumption that the input alphabet of the channel is finite. Our main purpose in this paper is to show that we can relax this restriction and to show that the resolvability formula of Han and Verdu continues to hold also for a wide class of channels with continuous input alphabet, including as a special case, additive white Gaussian noise (AWGN) channels with power constraint.>

IEEE International Symposium on Information Theory (ISIT)•Dec 17, 2002•8 citations

Variable-Length Resolvability for General Sources and Channels

Hideki Yagi, Te Sun Han

We introduce the problem of variable-length (VL) source resolvability, in which a given target probability distribution is approximated by encoding a VL uniform random number, and the asymptotically minimum average length rate of the uniform random number, called the VL resolvability, is investigated. We first analyze the VL resolvability with the variational distance as an approximation measure. Next, we investigate the case under the divergence as an approximation measure. When the asymptotically exact approximation is required, it is shown that the resolvability under two kinds of approximation measures coincides. We then extend the analysis to the case of channel resolvability, where the target distribution is the output distribution via a general channel due to a fixed general source as an input. The obtained characterization of channel resolvability is fully general in the sense that, when the channel is just an identity mapping, it reduces to general formulas for source resolvability. We also analyze the second-order VL resolvability.

arXiv:1701.08712•Entropy•Oct 19, 2023•7 citations

Variable-Length Channel Resolvability for Discrete Memoryless Sources and Channels

Hideki Yagi, Te Sun Han

The problem of channel resolvability, where a given output probability distribution over a channel is approximated by encoding uniform random number as a channel input, is addressed. The channel resolvability has recently been generalized to the variable-length setting, where the variable-length uniform random number instead of the fixed-length one is encoded. Though the optimum resolvability rate can be reduced compared with the fixed-length resolvability, it is not yet clear how much resolvability rate can be saved even when the given source and channel are stationary and memoryless. Given a stationary memoryless source and a discrete memoryless channel, this paper establishes a single-letter formula for the variable-length resolvability under the variational distance as an approximation measure. When the channel is a full-rank discrete memoryless channel, the established formula reduces to a further simpler formula characterized by the mutual information between the source and the channel. The established formula also recovers a known formula for the variable-length source resolvability.

IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2018•0 citations

Resolvability of Classical-Quantum Channels

Masahito Hayashi, Hao–Chung Cheng, Li Gao

Channel resolvability concerns the minimum resolution for approximating the channel output. We study the resolvability of classical-quantum channels in two settings, for the channel output generated from the worst input, and from the fixed independent and identically distributed (i.i.d.) input. The direct part of the worst-input setting is derived from sequential hypothesis testing as it involves non-i.i.d. inputs. The strong converse of the worst-input setting is obtained via the connection to identification codes. For the fixed-input setting, while the direct part follows from the known quantum soft covering result, we exploit the recent alternative quantum Sanov theorem to prove the strong converse.

arXiv:2410.16704•IEEE Transactions on Information Theory•May 15, 2025•6 citations

Separation of random number generation and resolvability

Karthik Visweswariah, Sanjeev R. Kulkarni, Sergio Verdú

We consider the problem of determining when a given source can be used to approximate the output due to any input to a given channel. We provide achievability and converse results for a general source and channel. For the special case of a full-rank discrete memoryless channel we give a stronger converse result than we can give for a general channel.

IEEE Transactions on Information Theory•Jan 1, 2000•12 citations
Given a channel and an input process we study the minimum randomness of those input processes whose output statistics approximate the original output statistics with arbitrary accuracy. We introduce the notion of resolvability of a channel, defined as the number of random bits required per channel use in order to generate an input that achieves arbitrarily accurate approximation of the output statistics for any given input process. We obtain a general formula for resolvability which holds regardless of the channel memory structure. We show that, for most channels, resolvability is equal to Shannon capacity. By-products of our analysis are a general formula for the minimum achievable (fixed-length) source coding rate of any finite-alphabet source, and a strong converse of the identification coding theorem, which holds for any channel that satisfies the strong converse of the channel coding theorem.
We study the randomness needed for approximating the output distribution of a multiple-access channel, where the original input processes are independent of each other. The approximation is achieved by simulating (possibly alternative) input processes at each of the entries, where the sources of randomness available for the simulators are independent of each other, and the simulators do not cooperate. The resolvability region of a multiple-access channel is defined as the set of all random-bit rate pairs at which accurate output approximation is possible, where the simulation accuracy is measured by the variational distance between finite-dimensional output distributions. Inner and outer bounds on the resolvability region are derived, and close relations between the concepts of resolvability region and capacity region are demonstrated.
The authors have introduced the new notion of resolvability of a channel, as the dual of the capacity, which is defined as the minimum complexity per input letter needed to generate an input process whose output distribution via the channel arbitrarily accurately approximates any prescribed achievable output distribution. The resolvability thus introduced has revealed a deep relationship between the minimum achievable rate for source coding, the channel capacity, the identification capacity and the problem of random number generation. However, the validity of the proof of the converse for the resolvability formula established by Han and Verdu (see IEEE Trans. on Inform. Theory, vol.39, no.3, p.379, 1993) hinged heavily on the assumption that the input alphabet of the channel is finite. Our main purpose in this paper is to show that we can relax this restriction and to show that the resolvability formula of Han and Verdu continues to hold also for a wide class of channels with continuous input alphabet, including as a special case, additive white Gaussian noise (AWGN) channels with power constraint.>
We introduce the problem of variable-length (VL) source resolvability, in which a given target probability distribution is approximated by encoding a VL uniform random number, and the asymptotically minimum average length rate of the uniform random number, called the VL resolvability, is investigated. We first analyze the VL resolvability with the variational distance as an approximation measure. Next, we investigate the case under the divergence as an approximation measure. When the asymptotically exact approximation is required, it is shown that the resolvability under two kinds of approximation measures coincides. We then extend the analysis to the case of channel resolvability, where the target distribution is the output distribution via a general channel due to a fixed general source as an input. The obtained characterization of channel resolvability is fully general in the sense that, when the channel is just an identity mapping, it reduces to general formulas for source resolvability. We also analyze the second-order VL resolvability.
The problem of channel resolvability, where a given output probability distribution over a channel is approximated by encoding uniform random number as a channel input, is addressed. The channel resolvability has recently been generalized to the variable-length setting, where the variable-length uniform random number instead of the fixed-length one is encoded. Though the optimum resolvability rate can be reduced compared with the fixed-length resolvability, it is not yet clear how much resolvability rate can be saved even when the given source and channel are stationary and memoryless. Given a stationary memoryless source and a discrete memoryless channel, this paper establishes a single-letter formula for the variable-length resolvability under the variational distance as an approximation measure. When the channel is a full-rank discrete memoryless channel, the established formula reduces to a further simpler formula characterized by the mutual information between the source and the channel. The established formula also recovers a known formula for the variable-length source resolvability.
Channel resolvability concerns the minimum resolution for approximating the channel output. We study the resolvability of classical-quantum channels in two settings, for the channel output generated from the worst input, and from the fixed independent and identically distributed (i.i.d.) input. The direct part of the worst-input setting is derived from sequential hypothesis testing as it involves non-i.i.d. inputs. The strong converse of the worst-input setting is obtained via the connection to identification codes. For the fixed-input setting, while the direct part follows from the known quantum soft covering result, we exploit the recent alternative quantum Sanov theorem to prove the strong converse.