Ensemble-Tight Second-Order Asymptotics and Exponents for Guessing-Based Decoding with Abandonment

Hamdi Joudeh; Vincent Y. F. Tan

REVIEW 1 major objections 3 minor 1 cited by

Ensemble-Tight Second-Order Asymptotics and Exponents for Guessing-Based Decoding with Abandonment

T0 review · 1 major / 3 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read The paper proves that for a guessing-based decoder with abandonment, the ensemble error probability in the second-order, error-exponent, and strong-converse regimes is governed by a single scalar: the minimum or maximum of the code-rate…

desk verdict A genuinely useful paper on guessing-based decoding: Theorems 2 and 3 are solid, and Theorem 4 is likely true but its printed proof has a reversed bound that must be fixed. read the letter →

arxiv 2502.05959 v2 pith:GS3H55TK submitted 2025-02-09 cs.IT math.IT

Vincent Y. F. Tan , Hamdi Joudeh This is my paper · ORCID

classification cs.ITmath.IT MSC 94A1594A2960F05

keywords guessing-baseddecodingabandonmentsecond-orderasymptoticserrorexponentsstrongconversediscretememorylesschannelsconstant-compositioncodesepsilon-dispersion

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper derives exact asymptotic limits for a decoder that, given a channel output, guesses input sequences in order of decreasing closeness and stops after a fixed number of guesses. For discrete memoryless channels with positive $\epsilon$-dispersion, it proves that the second-order region is a quadrant: $(s,t)$ is achievable exactly when $s \wedge t \ge \sqrt{V_{\epsilon}(W)} Q^{-1}(\epsilon)$, and the limiting ensemble error probability is $Q((s \wedge t)/\sqrt{V_{\epsilon}(W)})$. It also proves the error exponent is $\min\{E_r(R,P_X), E_a(r,P_X)\}$ and the strong converse exponent is $K_{\mathrm{sp}}(\max\{R, H(P_X)-r\}, P_X)$. The unifying message is that one scalar---the bottleneck between the code-rate backoff and the abandonment-rate backoff---controls the ensemble error in all three regimes. These results make precise when a guessing decoder can query exponentially fewer sequences than the codebook size without losing near-capacity performance.

What carries the argument

The argument is carried by the modified rank function $G(x|y)$, which counts all input sequences in the codebook's type class whose empirical conditional entropy is no larger than that of $x$; equation (5) pins this rank to $e^{n\hat{H}(x|y)}$ up to polynomial factors. Lemma 1 similarly pins the probability $\Psi(x,y)$ that an independent codeword outranks the transmitted pair to $e^{-n\hat{I}(x\wedge y)}$ up to polynomial factors. These two bounds turn both the incorrect-decoding event and the abandonment event into threshold crossings of the single scalar random variable $\hat{I}(X\wedge Y)$, so the central limit theorem and large-deviation estimates for empirical mutual information close the proofs in all three asymptotic regimes.

What would settle it

Fix a binary asymmetric channel with positive $\epsilon$-dispersion, choose $s>t>0$, and simulate random constant-composition codes with $M_n=e^{nC-s\sqrt{n}}$ codewords and abandonment budget $m_n=e^{nH_{P_X\times W}(X|Y)+t\sqrt{n}}$. The theorem predicts the ensemble error tends to $Q(t/\sqrt{V_{\epsilon}(W)})$, independent of $s$; observing instead a dependence on $s$, or a limit different from $Q(t/\sqrt{V_{\epsilon}(W)})$, would falsify the second-order characterization.

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Extended reading notes

Core claim

For a discrete memoryless channel with positive $\epsilon$-dispersion, the set of ensemble-tight second-order rates is exactly $L^*_{\epsilon}(P_X,W) = \{(s,t): s \wedge t \ge \sqrt{V_{\epsilon}(W)} Q^{-1}(\epsilon)\}$. Parametrized as $R_n \approx C(W) - s/\sqrt{n}$ and $r_n \approx H_{P_X\times W}(X|Y) + t/\sqrt{n}$, the ensemble average error probability converges to $Q((s \wedge t)/\sqrt{V_{\epsilon}(W)})$, with $V_{\min}(W)$ when $s \wedge t \ge 0$ and $V_{\max}(W)$ when $s \wedge t < 0$. In the exponent regimes, the ensemble error exponent is $\min\{E_r(R,P_X), E_a(r,P_X)\}$, which reduces to $E_r(\max\{R, H(P_X)-r\}, P_X)$ above the critical rate, and the strong converse exponent is $K_{\mathrm{sp}}(\max\{R, H(P_X)-r\}, P_X)$. These characterizations are ensemble-tight in the sense that achievability and converse bounds on the average error over random constant-composition codebooks coincide for the fixed guessing rule.

Load-bearing premise

The second-order characterization assumes the channel's $\epsilon$-dispersion is strictly positive; if it is zero, the Gaussian limits on which the $\sqrt{n}$ backoff result rests fail and Theorem 2 does not apply.

Editorial extensions

If this is right

At the optimal first-order pair $(R,r)=(C(W), H_{P_X\times W}(X|Y))$, a guessing decoder achieves vanishing error with about $e^{nH_{P_X\times W}(X|Y)}$ guesses, which is exponentially fewer than the $e^{nC(W)}$ codewords exactly when $C(W) > H(P_X)/2$.
The second-order region is rectangular: once $s \wedge t$ is fixed, the larger of the two backoffs can be increased without changing the limiting ensemble error probability.
In the error-exponent regime, whenever both $R$ and $H(P_X)-r$ lie above the critical rate, lowering the abandonment rate $r$ and raising the code rate $R$ have exactly the same effect, since the exponent depends only on $\max\{R, H(P_X)-r\}$.
In the strong-converse regime, the correct-decoding probability decays at exponential rate $K_{\mathrm{sp}}(\max\{R, H(P_X)-r\}, P_X)$ whenever $R > C(W)$ or $r < H_{P_X\times W}(X|Y)$, making the guessing decoder's strong converse exponent a special case of the conditional almost-lossless source coding exponent.
The abandonment exponent $E_a(r,P_X)$ equals the sphere-packing exponent at rate $H(P_X)-r$, which means guessing-based decoding with abandonment inherits the error-exponent behavior of universal conditional source coding.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the paper is right, the rectangular second-order region implies an engineering tradeoff: even when the code rate is held at capacity, the entire second-order backoff can be moved into the abandonment budget without changing the asymptotic error probability, so the decoder's search complexity can be tuned independently of the code rate in the $\sqrt{n}$ regime.
The paper's explicit restriction to positive $\epsilon$-dispersion suggests a direct follow-up: for zero-dispersion channels, the Gaussian limits on $\hat{I}(X\wedge Y)$ fail, and the second-order region should instead be described by a non-$\sqrt{n}$ speed or by large-deviation thresholds rather than the $Q$-function.
The paper leaves Gaussian channels and optimized ranking metrics open; a natural testable extension is that the min/max scalar structure survives whenever the ranking metric is a sufficient statistic for the channel, with the appropriate per-symbol variance replacing $V_{\epsilon}(W)$.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Bottom line: this is a strong, carefully written paper that gives the first ensemble-tight second-order and exponent characterizations for guessing-based decoding with abandonment over general DMCs. Theorems 2 and 3 hold up under scrutiny, and the unified picture they produce—where the code-rate backoff and abandonment-rate backoff interact through a single min or max—is a real step beyond the symmetric additive-channel GRAND results. The proofs are mostly clean: Lemma 1 is explicit, the Fn/Gn decomposition is sensible, and the self-citations are standard background, not circular support.

The one place I would not let the current text stand is the achievability proof of Theorem 4. At equation (45), the text says it uses the lower bound on Ψ from Lemma 1, but the event being lower-bounded contains Ψ(X,Y) ≤ 1/(M_n−1). A lower bound on Ψ cannot imply an upper bound on Ψ, so the printed implication is backwards. The fix is straightforward: use the upper bound Ψ(x,y) ≤ (n+1)^{3|X||Y|} e^{-nI(x∧y)} together with the upper bound on G(x|y); then for I(P_X,V) ≥ max{R, H(P_X)−r} + 2δ_n both conditions hold. I believe the theorem is true, but the argument as written does not establish it. Since the paper itself acknowledges that an earlier proof of Theorem 4 was wrong, the referee should ask for a clean corrected derivation.

Other soft spots are minor. Theorem 1's achievability is written for a single rate pair rather than the full region, and the sign-split case (s > t) in the Theorem 2 converse is compressed—though it follows from the abandonment-event lower bound. The positive-dispersion assumption in Theorem 2 is a stated scope restriction, not a hidden flaw.

Overall: the central contributions are valuable, the mathematics is mostly sound, and the flaw in Theorem 4 looks repairable rather than load-bearing. This paper deserves a serious peer review, but the referee should require a fixed proof of Theorem 4 before publication.

Recommendation: send it out, with the Theorem 4 proof as the main requested revision.

Referee Report

1 major / 3 minor

Summary. This paper analyzes a fixed ensemble of constant-composition random codebooks for discrete memoryless channels, used with a universal guessing-based decoder that rank-orders input sequences by empirical conditional entropy and abandons after e^{n r_n} guesses. The central claims are exact ensemble asymptotics for this scheme: Theorem 1 characterizes the first-order region of code rate and abandonment rate; Theorem 2 gives the second-order region under a positive-dispersion assumption, with the asymptotic error probability governed by Q((s∧t)/√V_ε(W)); Theorem 3 characterizes the error exponent as min{E_r(R,P_X), E_a(r,P_X)}; and Theorem 4 characterizes the strong converse exponent as K_{sp}(max{R, H(P_X)−r}, P_X). The unifying structural conclusion is that either the code-rate backoff or the abandonment-rate backoff dominates, so the three asymptotic regimes are determined by a scalar minimum or maximum of the two rate penalties.

Significance. The results are significant if they hold: they extend GRAND-style guessing decoding beyond symmetric additive channels and provide ensemble-tight first-order, second-order, exponent, and strong-converse characterizations for the memoryless case. The paper is careful in several respects: the proofs are detailed and follow standard large-deviation and CLT techniques; Lemma 1 gives explicit two-sided bounds on the rank probability; the decomposition into the incorrect-decoding event E_1 and the abandonment event A_1 is transparent; and the authors explicitly acknowledge a previously flawed proof of Theorem 4, which invites extra scrutiny. There are no fitted constants or circular arguments. The main caveat is a wrong bound direction in the achievability proof of Theorem 4, which must be corrected before that theorem is established.

major comments (1)

[VI-A, Eq. (45)] The step leading to (45) is invalid as stated. The event being lower-bounded contains {Ψ(X,Y) ≤ 1/(M_n−1)}, so to convert that indicator into a lower bound on the probability, one needs the upper bound Ψ(x,y) ≤ (n+1)^{3|X||Y|} e^{−n\hat I(x∧y)} from Lemma 1. A lower bound on Ψ cannot imply Ψ ≤ 1/(M_n−1); it implies the opposite direction of control. With the correct upper bound, the sufficient condition becomes \hat I(P_X,V) ≥ R + 3δ_n (up to subexponential factors), and the claimed exponent K_{sp}(max{R, H(P_X)−r}, P_X) is recovered after the usual δ_n→0 argument. The text at (45) should be revised accordingly; as printed, the proof of Theorem 4's achievability does not go through.

minor comments (3)

[VI-A] After defining the set H_n, the chain of inequalities writes P[(X,Y) ∈ S_r ∩ F_n]; F_n was defined in Section IV with a different threshold. This should read H_n.
[IV-B] The converse lower bound on (♣) is only meaningful when s ≤ t; for s > t the displayed Gaussian difference Q(s/√V) − Q(t/√V) is negative. The desired converse in that case follows from the abandonment term (♠) alone, but the proof should state this explicitly rather than leaving it implicit.
[III-A] The achievability proof treats only the choices R = I(P_X,W) − δ and r = H_{P_X×W}(X|Y) + δ. The full region in Theorem 1 follows by monotonicity of the error probability in M_n and m_n, but this should be said so that the proof covers every stated rate pair.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the asymptotic results are derived from the fixed guessing rule via type-class and CLT/large-deviation arguments; the flagged Theorem 4 proof gap is a correctness issue, not a self-referential one.

full rationale

The derivation chain is self-contained rather than circular. The second-order result is proved by writing the ensemble error as P[E1 union A1], splitting on the rank set S_r, using the two-sided rank bounds (5) and Lemma 1's two-sided bounds on Psi, and then applying the CLT for the empirical mutual information to a scalar event; the ensemble converse mirrors the same scalar event in (18) and (28). No equation is equal to the theorem by construction: Definition 2 only fixes the limiting capacity-achieving input distribution according to the sign of s and t, while the threshold sqrt(V_epsilon) Q^{-1}(epsilon) emerges from the Gaussian limit rather than being inserted into the definition. The error-exponent and strong-converse-exponent results are likewise reductions to the standard random-coding and sphere-packing exponents via union bounds, the RCU bound, and type-shell sums; the identity Ea(r,PX)=Esp(H(PX)-r,PX) is used as an algebraic observation, while the achievability and converse proofs bound the abandonment probability directly through Ea. Self-citations such as [5], [18], [21], and [23] are used for background, continuity bounds, or proof techniques, not as assumptions of the target theorems, so they are not load-bearing. The only flagged issue is a correctness gap rather than circularity: in the achievability proof of Theorem 4, Eq. (45) says it uses 'the lower bound on Psi(x,y) stated in Lemma 1' to pass from the event Psi(X,Y) <= 1/(M_n-1) to a mutual-information lower bound, but a lower bound on Psi cannot imply an upper bound on Psi; the paper itself acknowledges that 'Prof. Nakiboglu identified an error in the proof of Theorem 4 in an earlier version of this paper.' This concern affects whether Theorem 4 is established as printed, but it does not make the claimed result an input to itself. Accordingly, the circularity score is 0.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The proofs rest on standard method-of-types bounds, the CLT for empirical mutual information, and the RCU tightness lemma. These are external theorems, not fitted parameters. The only scope-specific input is the fixed random ensemble with constant-composition codebooks and the guessed rank function, which is stated as a design choice rather than an assumption with independent evidence. No free parameters are fitted to data.

assumptions (6)

standard math Type class enumeration bounds and conditional type shell bounds (Csiszar-Korner Lemma 2.5) are valid.
Used throughout to bound G(x|y), Psi(x,y), and to convert sums over sequences to sums over conditional types (Lemma 1, Appendix A).
standard math The empirical mutual information satisfies a central limit theorem with variance V(P,W) for i.i.d. or type-uniform inputs.
Invoked in the second-order proof around (18) and (28); cited to [19]. This is a standard CLT result for empirical information measures.
standard math The random coding union bound and the 1/2-tightness lemma for independent events [35, Lemma A.2] hold.
Used in the error exponent converse (38) to lower bound P[E1] by half the RCU expression.
domain assumption The channel W has positive epsilon-dispersion, V_epsilon(W) > 0.
Theorem 2 is stated only under this condition; without it the sqrt(n) scaling need not apply.
domain assumption Codewords are drawn independently and uniformly from a single type class, and the decoder uses the modified rank function G with ties declared as errors.
Defines the ensemble analyzed; the whole paper is scoped to this fixed scheme (Section II-A).
domain assumption Known equivalences: Ea(r,P_X) = Esp(H(P_X)-r,P_X), and the strong converse exponent for conditional source coding equals Ksp/Kr under the conditions in [32].
Used to interpret and simplify Theorems 3 and 4; these are standard results in source coding.

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Cite this review

Pith. "Pith review of Ensemble-Tight Second-Order Asymptotics and Exponents for Guessing-Based Decoding with Abandonment." pith.science (2026). https://pith.science/paper/GS3H55TK

@misc{pith2026250205959,
  author       = {Pith},
  title        = {Pith review of: Ensemble-Tight Second-Order Asymptotics and Exponents for Guessing-Based Decoding with Abandonment},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GS3H55TK}},
  note         = {Machine review of arXiv:2502.05959}
}

read the original abstract

This paper considers guessing-based decoders with abandonment for discrete memoryless channels in which all codewords have the same composition. This class of decoders rank-orders all input sequences in the codebook's composition class from ``closest'' to ``farthest'' from the channel output and then queries them sequentially in that order for codebook membership. Decoding terminates when a codeword is encountered or when a predetermined number of guesses is reached, and decoding is abandoned. We derive ensemble-tight first-order asymptotics for the code rate and abandonment rate, which shows that guessing-based decoding is more efficient than conventional testing-based decoding whenever the capacity of the channel exceeds half the entropy of the capacity-achieving input distribution. The main focus of this paper is on refined asymptotics, specifically, second-order asymptotics, error exponents, and strong converse exponents. The optimal second-order region is characterized in terms of the minimum of the second-order code and abandonment rates. The error (resp.\ strong converse) exponent is characterized in terms of the minimum (resp.\ maximum) of the usual channel coding exponent and an abandonment exponent, which turns out to be a special case of the exponent of conditional almost-lossless source coding.

Figures

Figures reproduced from arXiv: 2502.05959 by the authors.

**Figure 2.** An illustration of E∗(R, r, PX) Theorem 3. For any PX ∈ P(X ) and (R, r) ∈ R 2 +, E ∗ (R, r, PX) = min Er(R, PX), Ea(r, PX) [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** An illustration of K∗(R, r, PX) the ensemble average error probability is the random coding error exponent [37]. If r < H(PX) − R (implying that the abandonment rate is dominant), then K∗ (R, r, PX) specializes to Ksp(H(PX) − r, PX), which coincides with the strong converse exponent for the conditional source coding setting with source X ∼ Unif TP (n) X and side information Y ∼ Wn(·|X). In this case, Ksp(H(PX) − … view at source ↗

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Universal Decoding over Finite-State Additive Channels via Noise Guessing
cs.IT 2025-01 conditional novelty 7.0 of 10

Noise-guessing decoders based on universal probability estimators achieve the same random-coding error exponent as maximum likelihood decoding over finite-state additive channels.

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Works this paper leans on

37 extracted references · 36 canonical work pages · cited by 1 Pith paper

[1]

R. G. Gallager, Information Theory and Reliable Communication. New York: John Wiley & Sons, Inc., 1968

work page 1968
[2]

Nonprobabilistic mutual information without memory,

V . D. Goppa, “Nonprobabilistic mutual information without memory,” Problems of Control and Information Theory , vol. 4, pp. 97–102, 1975

work page 1975
[3]

Guessing and entropy,

J. Massey, “Guessing and entropy,” in Proc. IEEE Int. Symp. Inf. Theory (ISIT), 1994, p. 204

work page 1994
[4]

An inequality on guessing and its application to sequential decoding,

E. Arikan, “An inequality on guessing and its application to sequential decoding,” IEEE Trans. Inf. Theory , vol. 42, no. 1, pp. 99–105, 1996

work page 1996
[5]

V . Y . F. Tan, Asymptotic Estimates in Information Theory with Non- Vanishing Error Probabilities. Foundations and Trends® in Commu- nications and Information Theory, NOW Publishers, 2014, vol. 11, no. 1–2

work page 2014
[6]

Information spectrum approach to second-order coding rate in channel coding,

M. Hayashi, “Information spectrum approach to second-order coding rate in channel coding,” IEEE Trans. Inf. Theory , vol. 55, no. 11, pp. 4947–4966, Nov 2009

work page 2009
[7]

Csiszár and J

I. Csiszár and J. Körner, Information Theory: Coding Theorems for Discrete Memoryless Systems . Cambridge University Press, 2011

2011
[8]

On the converse to the coding theorem for discrete memoryless channels (corresp.),

S. Arimoto, “On the converse to the coding theorem for discrete memoryless channels (corresp.),” IEEE Trans. Inf. Theory, vol. 19, no. 3, pp. 357–359, 1973

work page 1973

Show all 37 references

[9]

Reliability function of a discrete memoryless channel at rates above capacity (corresp.),

G. Dueck and J. Körner, “Reliability function of a discrete memoryless channel at rates above capacity (corresp.),” IEEE Trans. Inf. Theory , vol. 25, no. 1, pp. 82–85, 1979

1979
[10]

Capacity-achieving guessing random additive noise decoding,

K. R. Duffy, J. Li, and M. Médard, “Capacity-achieving guessing random additive noise decoding,” IEEE Trans. Inf. Theory , vol. 65, no. 7, pp. 4023–4040, 2019

2019
[11]

Soft maximum likelihood decoding using GRAND,

A. Solomon, K. R. Duffy, and M. Médard, “Soft maximum likelihood decoding using GRAND,” in Proc. IEEE Int. Conf. Commun. (ICC) , 2020, pp. 1–6

2020
[12]

Guessing random additive noise decoding with symbol reliability information (SRGRAND),

K. R. Duffy, M. Médard, and W. An, “Guessing random additive noise decoding with symbol reliability information (SRGRAND),” IEEE Trans. Commun., vol. 70, no. 1, pp. 3–18, 2021

2021
[13]

Ordered reliability bits guessing random additive noise decoding,

K. R. Duffy, W. An, and M. Médard, “Ordered reliability bits guessing random additive noise decoding,” IEEE Trans. Signal Process., vol. 70, pp. 4528–4542, 2022

2022
[14]

Keep the bursts and ditch the interleavers,

W. An, M. Médard, and K. R. Duffy, “Keep the bursts and ditch the interleavers,” IEEE Trans. Commun. , vol. 70, no. 6, pp. 3655–3667, 2022

2022
[15]

Soft decoding without soft demapping with ORBGRAND,

W. An, M. Médard, and K. R. Duffy, “Soft decoding without soft demapping with ORBGRAND,” in Proc. IEEE Int. Symp. Inf. Theory (ISIT), 2023, pp. 1080–1084

2023
[16]

On guessing random additive noise decoding,

H. Joudeh, “On guessing random additive noise decoding,” in Proc. IEEE Int. Symp. Inf. Theory (ISIT) , 2024, pp. 1291–1296

2024
[17]

A lower bounding method for channel and source coding probabilities,

J. K. Omura, “A lower bounding method for channel and source coding probabilities,” Information and Control , vol. 27, no. 2, pp. 148–177, 1975. 13

1975
[18]

A tight upper bound for the third- order asymptotics for most discrete memoryless channels,

M. Tomamichel and V . Y . F. Tan, “A tight upper bound for the third- order asymptotics for most discrete memoryless channels,” IEEE Trans. Inf. Theory, vol. 59, no. 1, pp. 7041–7051, Nov 2013

2013
[19]

The dispersion of joint source- channel coding,

D. Wang, A. Ingber, and Y . Kochman, “The dispersion of joint source- channel coding,” in Proc. of the 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton) , 2011

2011
[20]

Channel coding rate in the finite blocklength regime,

Y . Polyanskiy, H. V . Poor, and S. Verdú, “Channel coding rate in the finite blocklength regime,” IEEE Trans. Inf. Theory , vol. 56, no. 5, pp. 2307–2359, 2010

2010
[21]

The dispersion of nearest- neighbor decoding for additive Non-Gaussian channels,

J. Scarlett, V . Y . F. Tan, and G. Durisi, “The dispersion of nearest- neighbor decoding for additive Non-Gaussian channels,” IEEE Trans. Inf. Theory, vol. 63, no. 1, pp. 81–92, 2017

2017
[22]

Refined asymptotics for rate- distortion using Gaussian codebooks for arbitrary sources,

L. Zhou, V . Y . F. Tan, and M. Motani, “Refined asymptotics for rate- distortion using Gaussian codebooks for arbitrary sources,” IEEE Trans. Inf. Theory, vol. 65, no. 5, pp. 3145–3159, 2019

2019
[23]

On the dispersions of three network information theory problems,

V . Y . F. Tan and O. Kosut, “On the dispersions of three network information theory problems,” IEEE Trans. Inf. Theory , vol. 60, no. 2, pp. 881–903, 2014

2014
[24]

Second-order Slepian–Wolf coding theorems for non-mixed and mixed sources,

R. Nomura and T. S. Han, “Second-order Slepian–Wolf coding theorems for non-mixed and mixed sources,” IEEE Trans. Inf. Theory , vol. 60, no. 9, pp. 5553–5572, 2014

2014
[25]

T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. Wiley-Interscience, 2006

2006
[26]

Second-order asymptotics for the Gaussian MAC with degraded message sets,

J. Scarlett and V . Y . F. Tan, “Second-order asymptotics for the Gaussian MAC with degraded message sets,” IEEE Trans. Inf. Theory , vol. 61, no. 12, pp. 6700–6718, 2015

2015
[27]

Dembo and O

A. Dembo and O. Zeitouni, Large Deviations Techniques and Applica- tions, 2nd ed. Springer, 1998

1998
[28]

Estimating mutual information via Kolmogorov distance,

Z. Zhang, “Estimating mutual information via Kolmogorov distance,” IEEE Trans. Inf. Theory , vol. 53, no. 9, pp. 3280–3282, 2007

2007
[29]

Estimates of the error exponent for the semi- continuous memoryless channel (in Russian),

E. A. Haroutunian, “Estimates of the error exponent for the semi- continuous memoryless channel (in Russian),” Probl. Pered. Inform. , vol. 4, no. 4, pp. 37–48, 1968

1968
[30]

Hypothesis testing and information theory,

R. E. Blahut, “Hypothesis testing and information theory,” IEEE Trans. Inf. Theory, vol. 20, no. 4, pp. 405–417, 1974

1974
[31]

Linear codes for sources and source networks: Error expo- nents, universal coding,

I. Csiszár, “Linear codes for sources and source networks: Error expo- nents, universal coding,” IEEE Trans. Inf. Theory , vol. 28, no. 4, pp. 585–592, 1982

1982
[32]

Universal coding for the Slepian–Wolf data compression system and the strong converse theorem,

Y . Oohama and T. S. Han, “Universal coding for the Slepian–Wolf data compression system and the strong converse theorem,” IEEE Trans. Inf. Theory, vol. 40, no. 6, pp. 1908–1919, 1994

1908
[33]

Compound conditional source coding, slepian-wolf list decoding, and applications to media coding,

S. Draper and E. Martinian, “Compound conditional source coding, slepian-wolf list decoding, and applications to media coding,” in Proc. IEEE Int. Symp. Inf. Theory (ISIT) , 2007, pp. 1511–1515

2007
[34]

Scarlett, A

J. Scarlett, A. Guillén i Fàbregas, A. Somekh-Baruch, and A. Martinez, Information-Theoretic Foundations of Mismatched Decoding . Founda- tions and Trends® in Communications and Information Theory, NOW Publishers, 2020, vol. 17, no. 2–3

2020
[35]

Communication over an unknown channel via common broadcasting,

N. Shulman, “Communication over an unknown channel via common broadcasting,” Ph.D. dissertation, Tel Aviv University, 2003

2003
[36]

On two strong converse theorems for discrete memoryless channels,

Y . Oohama, “On two strong converse theorems for discrete memoryless channels,” IEICE Transactions on Fundamentals of Electronics, Com- munications and Computer Sciences, vol. E98.A, no. 12, pp. 2471–2475, 2015

2015
[37]

The random coding bound is tight for the average code,

R. G. Gallager, “The random coding bound is tight for the average code,” IEEE Trans. Inf. Theory , vol. 19, no. 2, pp. 244–246, 1973. Vincent Y. F. Tan (Senior Member, IEEE) was born in Singapore, in 1981. He received the B.A. and M.Eng. degrees in electrical and information s...

1973

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.

[1] [1]

R. G. Gallager, Information Theory and Reliable Communication. New York: John Wiley & Sons, Inc., 1968

work page 1968

[2] [2]

Nonprobabilistic mutual information without memory,

V . D. Goppa, “Nonprobabilistic mutual information without memory,” Problems of Control and Information Theory , vol. 4, pp. 97–102, 1975

work page 1975

[3] [3]

Guessing and entropy,

J. Massey, “Guessing and entropy,” in Proc. IEEE Int. Symp. Inf. Theory (ISIT), 1994, p. 204

work page 1994

[4] [4]

An inequality on guessing and its application to sequential decoding,

E. Arikan, “An inequality on guessing and its application to sequential decoding,” IEEE Trans. Inf. Theory , vol. 42, no. 1, pp. 99–105, 1996

work page 1996

[5] [5]

V . Y . F. Tan, Asymptotic Estimates in Information Theory with Non- Vanishing Error Probabilities. Foundations and Trends® in Commu- nications and Information Theory, NOW Publishers, 2014, vol. 11, no. 1–2

work page 2014

[6] [6]

Information spectrum approach to second-order coding rate in channel coding,

M. Hayashi, “Information spectrum approach to second-order coding rate in channel coding,” IEEE Trans. Inf. Theory , vol. 55, no. 11, pp. 4947–4966, Nov 2009

work page 2009

[7] [7]

Csiszár and J

I. Csiszár and J. Körner, Information Theory: Coding Theorems for Discrete Memoryless Systems . Cambridge University Press, 2011

2011

[8] [8]

On the converse to the coding theorem for discrete memoryless channels (corresp.),

S. Arimoto, “On the converse to the coding theorem for discrete memoryless channels (corresp.),” IEEE Trans. Inf. Theory, vol. 19, no. 3, pp. 357–359, 1973

work page 1973