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REVIEW 4 major objections 4 minor 39 references

Uplink Multiple Access with Heterogeneous Blocklength and Reliability Constraints: Discrete Signaling with Treating Interference as Noise

T0 review · 4 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read The paper claims that an uplink scheme using one binary code per user, sub-block QAM signaling, and treating interference as noise achieves rates close to—and sometimes better than—Gaussian signaling with perfect SIC, with a capacity gap…

desk verdict A genuinely useful constant-gap uplink TIN scheme with an honest numerical study, but the finite-blocklength theorem as written has a load-bearing proof gap in Appendix B. read the letter →

arxiv 2411.15529 v1 pith:XENYJUJE submitted 2024-11-23 cs.IT eess.SPmath.IT

Min Qiu , Yu-Chih Huang , Jinhong Yuan This is my paper · ORCID
classification cs.ITeess.SPmath.IT MSC 94A1594A2494A40
keywords uplinkmultipleaccessURLLCandeMBBcoexistencetreatinginterferenceasnoisediscretesignalingquadratureamplitudemodulationfiniteblocklengthcodingheterogeneousnosuccessivecancellation
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

The paper tackles uplink multiple access when users are heterogeneous: some send short, ultra-reliable packets, others send longer blocks, and the receiver cannot use SIC because URLLC messages must be decoded without waiting. It proposes a low-complexity scheme in which each user runs a single binary channel code and maps coded bits onto sub-blocks using possibly different QAM constellations, while the receiver decodes each user treating all others as noise. The central claim is that this SIC-free scheme achieves rates very close to the idealized benchmark of Gaussian signaling with perfect SIC, and can even exceed it, with the gap to capacity bounded by a constant that does not depend on the number of users or channel coefficients. A sympathetic reader should care because the result suggests that stringent URLLC latency constraints need not force a spectral-efficiency penalty in mixed-traffic uplinks, and that off-the-shelf binary codes and QAM can realize the gain. The paper supports this with a finite-blocklength achievable-rate formula, verified numerically with 5G polar codes.

What carries the argument

The central mechanism is a staged superposition of regular QAM constellations. User $k$ splits its block into $k$ sub-blocks, and the $\ell_k$-th sub-block is transmitted with a constellation scaled by the power coefficient in Eq. (33), so that after the channel the effective sum $\sum_{i=\ell_k}^{K} h_i X_{i,\ell_k}$ is again a regular QAM with minimum distance at least $\sqrt{3}$. Lemma 2, built by recursively applying Lemma 1, shows that superimposing regular QAMs with matching minimum distances and dyadic scalings produces another regular QAM, and Eq. (38) shows the power normalization keeps the received minimum distance bounded below by $\sqrt{3}$. This minimum-distance floor drives the mutual-information lower bound $I(X_{k,\ell_k};Y_{\ell_k}) \ge m_{k,\ell_k} - \log(5\pi e/6)$, which converts the deterministic-model rate region into a constant-gap guarantee for Gaussian channels. The finite-blocklength part then models the per-symbol information density as a sum of independent terms across sub-blocks, yielding Theorem 1's rate formula with mutual information and dispersion.

What would settle it

The first place to look is Appendix B, Eq. (59): evaluate whether Lemma 47 of [19] remains valid for the sum of independent but non-identically distributed information densities $i(X_{k,\ell_k};Y_{\ell_k})$ across sub-blocks. A concrete test is to simulate the two-user setup with $(\mathrm{SNR}_1,\mathrm{SNR}_2)=(24,12)$ dB, $(N_1,N_2)=(128,200)$, and $(m_1,m_{2,1},m_{2,2})=(4,4,4)$, using 5G polar codes, and compare measured BLER against the prediction of Eq. (44); systematic excess error at low $\epsilon_k$ would indicate that the non-i.i.d. application of the lemma is unsupported.

Watch

Extended reading notes

Core claim

On its own terms, the paper establishes that on the $K$-user Gaussian multiple-access channel with ordered SNRs, unequal blocklengths $N_1 \le \dots \le N_K$, and individual error probabilities $(\epsilon_1,\dots,\epsilon_K)$, user $k$ can achieve any rate up to $$R_k \le \sum_{\ell_k=1}^{k} \frac{N_{\ell_k}-N_{\ell_k-1}}{N_k} I(X_{k,\ell_k};Y_{\ell_k}) - \frac{\sqrt{\sum_{\ell_k=1}^{k}(N_{\ell_k}-N_{\ell_k-1}) V(X_{k,\ell_k};Y_{\ell_k})}}{N_k} $Q^{{-1}}$(\epsilon_k) + O(1/N_k),$$ using one binary code per user, sub-block QAM constellations, and TIN decoding. The decisive quantitative step is the per-sub-block lower bound $I(X_{k,\ell_k};Y_{\ell_k}) \ge m_{k,\ell_k} - \log(5\pi e/6)$, obtained from a constant minimum-distance floor of the superimposed constellation at the receiver. Together with the 1-bit deterministic-model approximation, this puts the scheme within a constant gap of the Gaussian MAC capacity region, independent of $K$ and the channel coefficients. The paper further shows that the same construction can use less than the full transmit-power budget and can beat the Gaussian perfect-SIC benchmark in some finite-blocklength regimes because its dispersion is smaller.

Load-bearing premise

The finite-blocklength guarantee in Theorem 1 rests on a concentration bound for sums of independent but not identically distributed per-symbol random variables, yet the cited lemma (Lemma 47 of [19], used in Appendix B, Eq. (59)) is stated for identically distributed variables and the paper does not spell out the conditions for the mixed-constellation case; if that bound fails, the second-order term in the achievable-rate formula is not established.

Editorial extensions

If this is right

  • SIC-free decoding with single-user encoding and decoding can be near-optimal for heterogeneous uplink multiple access, removing the latency and error-propagation burden of successive cancellation.
  • The capacity gap being bounded by a constant independent of the number of users and channel coefficients means the approach scales to many users without an unbounded performance collapse.
  • The scheme can operate below the full transmit-power budget, with average power savings up to 75 percent and potentially more, without sacrificing rate.
  • The finite-blocklength formula gives a concrete design procedure: choose modulation orders satisfying the deterministic rate-region constraints, compute the achievable rate for given blocklength and error probability, then match code lengths; the numerical section confirms the predicted BLER with standard 5G polar codes.
  • Because TIN decoding is parallel, decoding of short-block URLLC messages does not have to wait for long-block users, which is the operational scenario that motivated the work.

Reading between the lines

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

  • The proof of Theorem 1's second-order term (Appendix B, Eq. (59)) applies Lemma 47 of [19] to a sum of independent but non-identically distributed per-sub-block information densities; the conditions for that extension are not stated in the paper, so this is the first place to test before relying on the $O(1/N_k)$ formula.
  • Because TIN decoding is parallel, the scheme should survive unsynchronized user arrivals and different starting times with little change to the rate analysis; the paper assumes synchronized starts but notes this does not affect the design principle.
  • The crossover where QAM-TIN beats the Gaussian perfect-SIC benchmark is driven by the dispersion gap, so a closed-form expression for that crossover as a function of $(N_k,\epsilon_k)$ would give a simple operational rule, but the paper does not derive it.
  • The same sub-block constellation-splitting philosophy could be applied to other finite alphabets, but the minimum-distance lower bound in Eq. (38) is specific to regular QAM and would need a new proof for non-QAM lattices.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper considers a K-user uplink MAC in which users have heterogeneous blocklengths and error-probability constraints, as in coexisting URLLC and eMBB traffic. The authors propose a scheme in which each user employs a single binary channel code, maps coded bits onto several sub-blocks, and uses a different QAM constellation in each sub-block, while the receiver decodes each user by treating all other users as noise (TIN), without SIC. The paper makes three main claims: (i) based on a cascaded deterministic MAC model, the corresponding rate region is achievable with TIN; (ii) for the actual Gaussian channel, the proposed QAM-TIN scheme achieves mutual information within a constant gap to the MAC capacity, with the constant independent of the number of users and channel coefficients; and (iii) a finite-blocklength second-order achievable rate (Theorem 1, Eq. (44)) shows that the scheme performs close to, and sometimes better than, a Gaussian signaling benchmark with perfect SIC. Numerical results with QAM and 5G polar codes are provided to support the finite-blocklength claims.

Significance. If the results are correct, the scheme is practically attractive: it avoids SIC and its latency/error-propagation issues, retains single-user encoding and decoding complexity, and can save transmit power. The deterministic-model design is elegant and the numerical validation with off-the-shelf polar codes is a strength. The main significance, however, rests on Theorem 1 and on the mutual-information gap bound, since the headline comparisons in Figs. 5 and 7 are computed from those formulas. The proof of Theorem 1 currently has several unaddressed technical gaps, so the significance is conditional on a repair of that proof.

major comments (4)
  1. [Appendix B, Eq. (55b)] The identity for the expected value of 2^{-max{0,i-log alpha}} is P(i<=log alpha) + alpha E[2^{-i} 1{i>log alpha}]. Eq. (55b), however, writes the second term with a positive exponent 2^{i(...)}. With a positive exponent, the term is exponentially large and cannot be bounded as in Eq. (59). This sign error is load-bearing because the inversion leading to Theorem 1 starts from this expression; it must be corrected to 2^{-i(...)} throughout Appendix B.
  2. [Appendix B, Eq. (59)] Lemma 47 of [19] is invoked for a sum of independent but non-identically distributed information-density summands: user k's block is split into sub-blocks with different constellations and different active interference sets, so the per-symbol information density is not i.i.d. The paper neither states nor proves a non-i.i.d. generalization of Lemma 47. Moreover, the first term in (59), 2*sqrt(2*pi*sum (N_l-N_{l-1})V(...)), grows as sqrt(N_k), whereas for a tail expectation of the form E[2^{-(S-a)} 1{S>a}] under a CLT the correct leading order is O(1/sqrt(N_k)). As printed, Eqs. (63)-(64) make the argument of Q^{-1} increasingly negative for large N_k, which would produce an unbounded rate in (66). A corrected version of Lemma 47, with the correct exponent and scaling, and with the required assumptions on non-identically distributed summands, is needed to justify Eq. (44) and hence the numerical claims in Figs. 5 and 7.
  3. [Section IV-B, Eq. (38b)] The minimum-distance lower bound in (38b) drops the channel and SNR-dependent factors from the expression in (38a). Starting from h_i sqrt(P_i) = sqrt(SNR_i) = 2^{log SNR_i/2} and using the normalization bound in (39e), the coefficient of F_{i,l} inside the d_min should be at least sqrt(3) 2^{(n_l - log SNR_i)/2 + sum m}, not sqrt(3/2^{n_l}) 2^{n_l + sum m}. The printed exponent 2^{n_l+sum m} is not a valid universal lower bound. The final constant-gap claim in (41) depends on (38), so this step must be corrected (the conclusion can be recovered by using n_l >= n_i >= log SNR_i, but the displayed inequality is not correct as written).
  4. [Appendix B, Eq. (54)] Theorem 17 of [19] is stated for a DMC with i.i.d. channel uses. Here the channel is a product of sub-blocks with different per-symbol conditional distributions, so the random-coding union bound is applied to a non-stationary memoryless channel. The extension is likely straightforward, but it should be stated explicitly, because the proof of Theorem 1 starts from this bound and the non-identical nature of the channel is exactly what makes the subsequent information-density sum non-i.i.d.
minor comments (4)
  1. [Eq. (55b) and Eq. (59)] The indicator inside the expectation is written with i(X[Nk];X[Nk]) in two places; it should be i(X[Nk];Y[Nk]). This appears to be a typo but should be fixed for clarity.
  2. [Section VI] The conclusion says 'coded modulation schemes with TIN decoding for the homogeneous MAC'; the paper is about the heterogeneous MAC, so this phrase should be corrected.
  3. [Fig. 1 caption] The caption contains a typo: 'Fig, 1' should be 'Fig. 1'.
  4. [Section IV-C] The proof of Theorem 1 defines B_k in terms of E[|i(X_{k,l};Y_l)-I(X_{k,l};Y_l)|^3] divided by V(...)^{3/2}. Since the summands are non-identically distributed, a Lyapunov-style condition is involved; the text should explicitly state that this quantity is finite and that the Berry-Esseen constant is uniform over the sub-block distributions, otherwise the O(1/N_k) term is not justified.

Circularity Check

0 steps flagged · score 1.0 of 10

No circular derivation: the achievable-rate proof targets an external capacity benchmark and no fitted parameter is renamed as a prediction; self-citations are contextual. Appendix B contains a proof gap (non-i.i.d. use of Lemma 47 of [19]) that is a correctness issue, not circularity.

full rationale

We walked the derivation chain. The deterministic model in Section III is borrowed from Avestimehr et al. [33] and used only as a design guide; the generator matrices (11)-(18) are explicit constructions whose rank computations (13)-(24) verify the claimed rate region directly, without invoking the conclusion. The translation to QAM in Section IV-A defines constellations and powers from channel SNRs and modulation orders satisfying (16); the mutual-information lower bound (41) follows from the constant-minimum-distance property (38) and the entropy bound (40) via the external result [35, Prop. 1], not from the benchmark. Theorem 1's finite-blocklength bound (44) is derived from Polyanskiy et al.'s random-coding bound [19, Th. 17], Berry-Esseen [39], and Shevtsova's constant [38]; the calculation of I and V in (57)-(58) is bookkeeping for the designed sub-block distributions. No parameter is fitted to the Gaussian-SIC benchmark, and the rate pairs in Fig. 5 are evaluations of the derived formula, not regression outputs. Self-citations [1], [30], [32] supply background or a comparison term (the O(1/N) improvement over [32]) and are not premises of the proof. The skeptical concern about Appendix B is real but non-circular: Eq. (59) applies Lemma 47 of [19] to the non-i.i.d. sum (56) without stating a generalization, and Eq. (55b) writes 2^{i(...)} where the lemma's identity would require 2^{-i(...)}; if these are not repaired, the second-order term in (44) is unsupported. That is an omitted-proof/correctness risk, not a reduction of the conclusion to its inputs, so it does not raise the circularity score.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central result relies on design parameters (n_k and modulation orders) rather than fitted constants, and on four mathematical building blocks from prior literature. No new physical entities, forces, or dimensions are introduced, so the invented-entity ledger is empty.

free parameters (2)
  • deterministic levels n_k = ceil(log SNR_k)^+
    Design parameter derived from the signal-to-noise ratio; it sets the power coefficients in Eq. (33), so the achievable rate depends on this integer approximation rather than the exact SNR.
  • modulation orders m_{k,l} = chosen per sub-block (e.g., Table I)
    Constellation sizes are selected to satisfy the deterministic rate constraints in Eq. (16). They are design variables, not fitted to data, but the finite-blocklength rate formula depends on them.
assumptions (4)
  • standard math The deterministic MAC approximation of Avestimehr et al. is within 1 bit/s/Hz of each Gaussian component MAC.
    Used in Section III-A to motivate the scheme and to bound the gap to the Gaussian capacity region.
  • domain assumption Lemma 47 of Polyanskiy et al. [19] extends to sums of independent non-identically distributed information densities arising from the sub-blocks.
    Invoked in Appendix B Eq. (59) without proof or stated conditions; the sub-block distributions differ, so the summands are not i.i.d.
  • standard math The Berry-Esseen central limit theorem applies to the independent but non-identical information density summands.
    Used in Appendix B Eq. (61); the theorem is standard, but its conditions for this non-i.i.d. sum are not checked in the text.
  • domain assumption The QAM mutual information lower bound from Dytso et al. [35, Prop. 1] extends from one-dimensional PAM to two-dimensional QAM.
    Used in Eq. (40a) with the phrase 'by extending the arguments'; no complete proof is given in the paper.

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Cite this review

Pith. "Pith review of Uplink Multiple Access with Heterogeneous Blocklength and Reliability Constraints: Discrete Signaling with Treating Interference as Noise." pith.science (2026). https://pith.science/paper/XENYJUJE

@misc{pith2026241115529,
  author       = {Pith},
  title        = {Pith review of: Uplink Multiple Access with Heterogeneous Blocklength and Reliability Constraints: Discrete Signaling with Treating Interference as Noise},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XENYJUJE}},
  note         = {Machine review of arXiv:2411.15529}
}
read the original abstract

We consider the uplink multiple access of heterogeneous users, e.g., ultra-reliable low-latency communications (URLLC) and enhanced mobile broadband (eMBB) users. Each user has its own reliability requirement and blocklength constraint, and users transmitting longer blocks suffer from heterogeneous interference. On top of that, the decoding of URLLC messages cannot leverage successive interference cancellation (SIC) owing to the stringent latency requirements. This can significantly degrade the spectral efficiency of all URLLC users when the interference is strong. To overcome this issue, we propose a new multiple access scheme employing discrete signaling and treating interference as noise (TIN) decoding, i.e., without SIC. Specifically, to handle heterogeneous interference while maintaining the single-user encoding and decoding complexities, each user uses a single channel code and maps its coded bits onto sub-blocks of symbols, where the underlying constellations can be different. We demonstrate theoretically and numerically that the proposed scheme employing quadrature amplitude modulations and TIN decoding can perform very close to the benchmark scheme based on Gaussian signaling with perfect SIC decoding. Interestingly, we show that the proposed scheme does not need to use all the transmit power budget, but also can sometimes even outperform the benchmark scheme.

Figures

Figures reproduced from arXiv: 2411.15529 by the authors.

Figure 1
Figure 1. K users send their packets with different lengths to the receiver. is uniformly distributed over a zero mean regular QAM Λ with cardinality |Λ| and minimum distance dmin(Λ), whose average energy is given by EΛ = d 2 min(Λ)|Λ|−1 6 . ⌈x⌉ rounds x to the nearest integer greater than or equal to x. We define the operation (x) + ≜ max{0, x}. The binary field, the collections of binary vectors of size n and binary matrice… view at source ↗
Figure 2
Figure 2. The two-user deterministic model with (n1, n2) = (10, 8) and (m1, m2,1, m2,2) = (6, 4, 8). capacities are within 1 bit/s/Hz to the capacities of their Gaussian counterparts [33], respectively. An illustration for this model is given in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Two users send their coded symbols with different lengths to the receiver. [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: The receiver performs parallel TIN decoding on two users’ transmitted [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 7
Figure 7. Figure 7: Error probability versus the finite blocklength achievable rate for both [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 6
Figure 6. Figure 6: Dispersion pairs of two users in bits2 /s/Hz. B. Numerical Results on Error Probability We evaluate the error performance of the proposed scheme by employing off-the-shelf channel codes. As in Section V-A, we consider (SNR1, SNR2) = (24, 12) dB, (N1, N2) = (128, 200), …

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.