{"id":"97c703a7-8b2f-4c68-95c2-9beabe2d6e5b","arxiv_id":"2411.15529","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Treating interference as noise with carefully layered QAM constellations comes close to ideal SIC performance for uplink users with heterogeneous packet lengths and reliability constraints.","lead":"This paper proposes an uplink wireless multiple access scheme where users with different packet lengths and reliability targets transmit with standard QAM constellations while the base station decodes each user by treating everyone else as noise. The authors report rates close to the idealized baseline of Gaussian signaling with perfect interference cancellation, sometimes exceeding it, while using lower transmit power.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Theorem 1's proof invokes Lemma 47 of [19] for non-i.i.d. information-density sums without stating the needed generalization; if the lemma does not extend, the finite-blocklength rate formula (44) is unsupported.","rationale":"The reader's weakest assumption is exactly the point most load-bearing for the paper's central claim: the finite-blocklength achievable rate in Theorem 1, used to generate the numerical rates in Fig. 5 and the comparison to Gaussian signaling with perfect SIC. The proof of Theorem 1 requires a bound on a tilted expectation of the information density sum; the paper cites Lemma 47 of [19] as though it applied directly to a sum of independent but non-identically distributed information densities. The manuscript does not state the assumptions of that lemma, and the surrounding equations contain a suspicious positive exponent in (55b) and an O(√N_k) first term in (59) that is dimensionally surprising for the quantity being bounded. If Lemma 47 requires i.i.d. summands or if the exponent is wrong, the derivation of (63)-(68) does not go through, so the claimed second-order term and the numerical achievable rates lack rigorous support. This does not invalidate the first-order constant-gap result of Section IV-B, which is based on the deterministic model and the minimum-distance analysis and appears plausible, nor does it undermine the practical polar-code experiments. The issue is likely fixable by supplying a Lyapunov-version of the lemma with the correct O(1/√N_k) tail bound, which is why the appropriate verdict remains CONDITIONAL rather than REJECT. The reader's conditional verdict therefore stands, and no change to the verdict is needed.","tokens_in":23011,"tokens_out":31038,"duration_ms":285075,"concrete_test":"Locate the precise statement of Lemma 47 in Polyanskiy-Poor-Verdü [19] and check whether it assumes i.i.d. summands. Then for the K=2 numerical setting (N1=128, N2=200, constellations from Table I), compute the quantity E[2^{-(S-a)}1{S>a}] with S = Σ_{j=1}^{N_2} i(X[j];Y[j]) by Monte Carlo or numerical integration, using the actual sub-block distributions. Compare the result against the claimed bound 2√(2π V_total)+4B_k/√N_k from (59) and against a corrected O(1/√N_k) bound derived from the Berry-Esseen/Lyapunov theorem. If the claimed bound fails, or if (55b) is confirmed to require 2^{-i} instead of 2^{i}, Theorem 1 needs a revised proof.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In Appendix B, the proof of Theorem 1 applies Lemma 47 of [19] (Eq. (59)) to bound a tilted information-density expectation for the sum i(X^{N_k};Y^{N_k}) = Σ_{j=1}^{N_k} i(X[j];Y[j]). The summands are independent but not identically distributed: user k's block is partitioned into k sub-blocks, each with its own constellation Λ_{k,ℓ}, so the per-symbol information density has a different distribution in each sub-block. Lemma 47 in [19] is stated for i.i.d. copies; the paper neither states nor proves a non-i.i.d. generalization. Moreover, Eq. (55b) displays 2^{i(...)} in the second term, whereas the identity for 2^{-max{0,i-log α}} requires 2^{-i(...)}; if this is not a transcription error, Lemma 47 is invoked for the wrong integrand. The bound in (59) also has a first term 2√(2π Σ(N_ℓ-N_{ℓ-1})V(...)), which scales as √N_k. For a tail expectation of the form E[2^{-(S-a)}1{S>a}] under a CLT, the natural bound is O(1/√N_k), not O(√N_k). Unless the correct non-i.i.d. version of Lemma 47 with the correct exponent and scaling is supplied, the inversion from (63)-(68) that yields Theorem 1 is not justified. This is load-bearing because the numerical rate pairs in Fig. 5 and the claimed closeness to the Gaussian-SIC benchmark are computed from Eq. (44), so the central finite-blocklength claim rests on this step.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":23298,"tokens_out":13799,"duration_ms":128690,"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":[{"comment":"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.","section":"Appendix B, Eq. (55b)"},{"comment":"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.","section":"Appendix B, Eq. (59)"},{"comment":"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).","section":"Section IV-B, Eq. (38b)"},{"comment":"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.","section":"Appendix B, Eq. (54)"}],"minor_comments":[{"comment":"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.","section":"Eq. (55b) and Eq. (59)"},{"comment":"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.","section":"Section VI"},{"comment":"The caption contains a typo: 'Fig, 1' should be 'Fig. 1'.","section":"Fig. 1 caption"},{"comment":"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.","section":"Section IV-C"}],"recommendation":"major_revision","confidential_remarks":"The core idea and the deterministic-model part are credible, and the mutual-information gap can likely be repaired with a corrected Eq. (38). The main obstacle is the finite-blocklength proof: the current Appendix B contains an exponent sign error and a misapplied/mis-scaled Lemma 47, and those errors directly affect Eq. (44) and the numerical comparisons. I do not think rejection is warranted, because these are technical gaps rather than a fundamentally impossible claim, but the authors need to supply a correct non-i.i.d. version of the relevant lemma with the right scaling before the theorem can be accepted."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: this is a solid, practically motivated paper whose first-order constant-gap result is the real contribution; the finite-blocklength theorem has a proof gap that is load-bearing but probably fixable. I agree with the reader's conditional verdict, and the stress-test note is on target.\n\nWhat's new: the uplink counterpart of the authors' downlink scheme, with per-user channel gains; a cascaded deterministic model; a generator-matrix construction that achieves the whole deterministic rate region with TIN; and the translation into QAM sub-blocks using a single channel code per user. The constant-gap mutual information argument in Section IV-B is clean, and the min-distance lower bound, modulo the dropped factor in (38c), gives the right constant. The numerical section is unusually honest: the Gaussian-SIC benchmark is explicitly hypothetical, the power-saving numbers are concrete, and the polar-code BLER curves match the analytical bounds.\n\nSoft spots: (1) The proof of Theorem 1 as written is not valid. Eq. (55b) has a sign error: the identity for 2^{-max{0,i-log alpha}} requires the conditional second term to be alpha * E[2^{-i(X;Y)} 1{...}], not alpha * E[2^{i(X;Y)} 1{...}]. The bound in (59) then invokes Lemma 47 of [19] on a sum of non-i.i.d. information densities (different constellations per sub-block), and the stated bound has the wrong scaling: 2 sqrt(2 pi sum(...)) grows with N, whereas the tail expectation should decay like 1/sqrt(N). Unless the authors supply a non-i.i.d. version of Lemma 47 with the correct exponent and scaling, the second-order rate (44) is unsupported. This is a real gap, not a typo in one line, because Fig. 5 and the 'close to SIC' rate comparison use (44). That said, this is exactly the kind of gap that a careful revision can close: the summands are independent, bounded, and have separated variances, so a Lindeberg/Berry-Esseen argument plus the standard random-coding bound should go through. The first-order claim does not depend on this part.\n\n(2) Minor: (38c) drops a factor 2^{n_l/2}; the inequality direction survives, so the constant gap still holds.\n\nThe citation pattern looks fine. [30] and [32] are relevant prior work by the same group, and the extension here is substantive, not incremental self-citation.\n\nWho this is for: people working on short-packet URLLC/eMBB coexistence or non-SIC multiple access. I would send it to a serious referee, with instructions that Appendix B needs to be fixed before acceptance.","headline":"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.","tokens_in":23894,"tokens_out":5414,"would_cite":true,"duration_ms":52991,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["94A15","94A24","94A40"],"pacs":[],"model":"deepseek-v4-flash","headline":"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…","keywords":["uplink multiple access","URLLC and eMBB coexistence","treating interference as noise","discrete signaling","quadrature amplitude modulation","finite blocklength coding","heterogeneous blocklength","no successive interference cancellation"],"falsifier":"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.","tokens_in":22748,"feed_emoji":"📶","tokens_out":10771,"duration_ms":88141,"temperature":0.7,"pith_summary":"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.","feed_headline":"Treating interference as noise rivals perfect SIC in uplink","feed_subtitle":"Discrete QAM plus single-user decoding matches or beats Gaussian signaling with perfect SIC for mixed URLLC/eMBB traffic.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the finite-blocklength random-coding bound and Lemma 47 used in the proof of Theorem 1 to bound the tilted information-density term.","marker":"[19]"},{"why":"Provides the cascaded linear deterministic model whose component MAC capacity regions are within 1 bit/s/Hz of their Gaussian counterparts, guiding the constant-gap argument.","marker":"[33]"},{"why":"Establishes that discrete signaling with TIN achieves a constant gap for the Gaussian interference channel, a design principle adapted here to the heterogeneous MAC.","marker":"[30]"},{"why":"Gives the mutual-information lower bound for discrete signaling via minimum distance, extended in the paper to two-dimensional QAM superimposed constellations.","marker":"[35]"},{"why":"Prior downlink heterogeneous scheme whose rate expression the paper improves on, providing the baseline for the $O(1/N_k)$ versus $O(\\log N_k/N_k)$ improvement.","marker":"[32]"},{"why":"Describes the bit-interleaved coded modulation mapping that lets a single binary code feed sub-blocks with different QAM constellations.","marker":"[34]"},{"why":"Provides the 5G modulation orders and polar-code parameters used in the numerical verification of the finite-blocklength rates and error probabilities.","marker":"[28]"}],"fun_headline_variants":["TIN with QAM rivals perfect SIC in uplink","Why cancel interference? QAM TIN rivals SIC","Discrete QAM TIN: less power, same rate as SIC","No SIC needed: QAM TIN closes gap to capacity","Heterogeneous uplink: TIN without SIC matches SIC"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["TIN with QAM rivals perfect SIC in uplink","Why cancel interference? QAM TIN rivals SIC","Discrete QAM TIN: less power, same rate as SIC","No SIC needed: QAM TIN closes gap to capacity","Heterogeneous uplink: TIN without SIC matches SIC"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000277,"raw_usage":{"total_tokens":1725,"prompt_tokens":1095,"completion_tokens":630,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":711,"completion_tokens_details":{"reasoning_tokens":539}},"tokens_in":711,"tokens_out":630,"duration_ms":6165,"temperature":1.0,"reasoning_tokens":539,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T14:11:44.890131+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Wireless network information flow: A deterministic approach,","cited_arxiv_id":null,"evidence_quote":"Provides the cascaded linear deterministic model whose component MAC capacity regions are within 1 bit/s/Hz of their Gaussian counterparts, guiding the constant-gap argument."},{"cited_title":"Discrete signaling and treating interference as noise for the Gaussian interference channel,","cited_arxiv_id":null,"evidence_quote":"Establishes that discrete signaling with TIN achieves a constant gap for the Gaussian interference channel, a design principle adapted here to the heterogeneous MAC."},{"cited_title":"Interference as noise: Friend or foe?","cited_arxiv_id":null,"evidence_quote":"Gives the mutual-information lower bound for discrete signaling via minimum distance, extended in the paper to two-dimensional QAM superimposed constellations."},{"cited_title":"Downlink transmission with hetero- geneous URLLC services: Discrete signaling with single-user decoding,","cited_arxiv_id":null,"evidence_quote":"Prior downlink heterogeneous scheme whose rate expression the paper improves on, providing the baseline for the $O(1/N_k)$ versus $O(\\log N_k/N_k)$ improvement."},{"cited_title":"Bit-interleaved coded modulation,","cited_arxiv_id":null,"evidence_quote":"Describes the bit-interleaved coded modulation mapping that lets a single binary code feed sub-blocks with different QAM constellations."},{"cited_title":"5G;NR; Multiplexing and channel coding,","cited_arxiv_id":null,"evidence_quote":"Provides the 5G modulation orders and polar-code parameters used in the numerical verification of the finite-blocklength rates and error probabilities."}],"review_version":1}