{"id":"07d4082a-1a58-4669-8b9b-4dfdf7b3debe","arxiv_id":"1908.04327","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Non-adaptive transmission achieves the Shannon capacity region for injective semi-deterministic two-way channels and is asymptotically optimal for the Poisson two-way channel at high dark current.","lead":"Full-duplex two-way channels can in principle reuse received signals when transmitting, but that adaptation is complex. This paper identifies two channel families where simple non-adaptive coding already achieves the full Shannon capacity region, including a new asymptotic result for the optical Poisson two-way channel.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Poisson outer bound is self-contradictory: Theorem 5 defines π* via π0(s)→0, while Theorem 6's proof uses π*=min(σ,1/2); the O(s^-2) gap is not derived from the stated one-way capacity.","rationale":"The ISD half of the paper is sound: Theorem 1's conditions are applied correctly, and Theorem 2's injectivity argument verifies (C1) and (C2). The additive examples have index/label typos (Theorem 3's printed R_1 swaps the roles of A_1/m_2 and A_2/m_1; Theorem 4 uses undefined m_i), but the proofs contain the correct rates, so these are presentation errors. The Poisson half is where the central claim is insecure. The reader's weakest assumption (Lemma 1) is accurate but not the only problem; in fact the printed Theorem 5 is inconsistent with the asymptotics used in the Appendix. The one-way capacity formula as stated would give an exponentially small outer bound in the high-dark-current limit, while the asymptotic proof uses the physically correct π*≈min(σ,1/2) and O(1/s) rate. Thus the claimed O(s^-2) gap is not a consequence of the paper's stated outer bound; the paper needs a corrected statement of Theorem 5 (or a proof of the one-way capacity from first principles) before the Poisson result can be certified. This is fixable, so the CONDITIONAL verdict is appropriate; no change to the verdict is needed, but the revision must address the contradiction.","tokens_in":15236,"tokens_out":35286,"duration_ms":349243,"concrete_test":"Check the maximizer of the one-way binary-channel expression f(π)=π(1+s)log(1+s)+(1−π)s log s−(s+π)log(s+π) at s=10 with constraint σ=0.3: compute f(0.3), f(0.001295), and the unconstrained critical point satisfying log(s+π)=(s+1)log(s+1)−s log s−1. If f(0.3)≈0.010 A and exceeds f(0.001295)≈0.000065 A, Theorem 5's printed π0(s) is not the capacity-achieving distribution and the outer bound used in Theorem 6 must be corrected; if instead π0 is the maximizer, Theorem 6's Appendix uses the wrong π* and its O(s^-2) gap calculation does not apply to the stated R_OWC_o.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central Poisson claim is not supported by the paper as written because of an internal contradiction in the one-way outer bound. Theorem 5 (Sec. V-C) states that the one-way capacity-achieving input has p*(1)=π*=min(σ,π0(s)) with π0(s)=((1+s)^{1+s}/s^s)e^{-s}. For large s, π0(s)≈s e^{1-s}→0, so the stated outer bound R_OWC_o would decay exponentially in s. The paragraph immediately before Theorem 6 and the Appendix instead set π*_i=min(σ_i,1/2), which is the correct large-s optimizer of the same binary-channel expression, and then prove the gap GAP1=Aπ*_1(1−π*_1)π*_2/(2s^2)+O(s^-3). These two definitions cannot both describe C_OWC(σ): for s=10 and σ=0.3, the printed π0 gives a one-way rate about 1.5e-4 A, while min(σ,1/2)=0.3 gives about 0.010 A. Consequently the Appendix's gap computation is not a comparison with the outer bound stated in Theorem 5; Theorem 6's proof would have to re-derive C_OWC from a corrected Theorem 5. This is the load-bearing step because the Poisson asymptotic-optimality result is exactly the claim that Ri meets R_OWC_o to O(s^-2). Lemma 1 is also only a proof sketch, but the formula contradiction is already decisive and independently testable.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies two-way channels (TWCs) and asks when Shannon's inner bound, which is achievable by non-adaptive coding, coincides with the general outer bound. It introduces the class of injective semi-deterministic (ISD) TWCs, proves that for this class the Shannon inner and outer bounds coincide, and derives an explicit rectangular capacity region (Theorems 1-2, Corollary 1). Examples include multiplicative channels, additive channels with exponential and Cauchy noise, and an input-dependent Gaussian noise model. The second contribution is a continuous-time Poisson TWC. The authors discretize it into a binary TWC (Lemma 1), define Shannon inner and one-way outer bounds, and claim in Theorem 6 that the inner bound asymptotically meets the one-way outer bound as the dark current grows, with an O(s^{-2}) gap; the proof is an asymptotic expansion in the Appendix. The ISD part is clean and checkable. The Poisson part currently contains a serious internal inconsistency in the statement of the one-way capacity formula and its use in the asymptotic proof.","tokens_in":15382,"tokens_out":25877,"duration_ms":244739,"significance":"If the ISD results stand, they provide a broad and useful sufficient condition under which adaptation is unnecessary, together with closed-form capacity expressions for realistic full-duplex channel models; this part is a genuine contribution. The Poisson TWC result, if proved with a correct one-way capacity statement and a rigorous discretization, would be an interesting first continuous-time full-duplex capacity characterization and would show that adaptation is asymptotically useless in the high-dark-current regime. The paper contains no fitted parameters and the asymptotic expansions are explicit and testable. However, the Poisson claim is not currently supported as written because of the contradiction described below, so the significance of the paper depends on a fixable but nontrivial revision.","major_comments":[{"comment":"The one-way capacity formula in Theorem 5 defines pi* = min(sigma, pi0(s)) with pi0(s) = ((1+s)^{1+s}/s^s)e^{-s}. For large s this pi0(s) decays as s e^{1-s}, so the printed C_OWC(sigma) would decay exponentially in s for every fixed sigma>0. The unconstrained maximizer of the displayed expression is actually ((1+s)^{1+s}/s^s)e^{-1} - s, which tends to 1/2; the printed pi0(s) also exceeds 1 for some s (for example at s=1 it is 4/e). Yet the paragraph immediately before Theorem 6 and the entire Appendix set pi*_i = min(sigma_i,1/2) and derive the gap A pi*_1(1-pi*_1)pi*_2/(2s^2) + O(s^{-3}). Thus the asymptotic proof is not comparing against the outer bound stated in Theorem 5. Theorem 6 needs to be re-derived from a corrected, consistently stated one-way capacity expression, with the optimizer used in the Appendix matching the optimizer in Theorem 5.","section":"Section V-C, Theorem 5 and Appendix"},{"comment":"Lemma 1 is the bridge from the continuous-time Poisson TWC to the discrete-time binary channel in (6), but its proof is only a sketch asserting that Wyner's one-way discretization carries over 'without significant changes.' In a two-way channel the two transmitted waveforms interact in both received Poisson processes, and each terminal's encoder may in general depend on its past received signal; it is not automatic that both waveforms can simultaneously be made slot-constant 0/A and that slot-wise photon-count thresholding is optimal without changing the rate region. Both the inner bound Ri and the equivalent channel used in the asymptotic computation rely on this lemma. A complete proof of the two-way discretization, or a precise citation establishing it, is needed before the Poisson capacity claim is fully supported.","section":"Section V-B, Lemma 1"},{"comment":"The proof says it is sufficient to show that at least one point of C lies within an O(1/lambda_0^2) ball centered at the outer-bound corner. For a general convex region this would not imply that the boundaries are close; however, the subsequent computation in fact gives both coordinates of the inner-bound rectangle for the fixed product distribution (p*_1,p*_2), and for fixed product inputs the inner bound contains the rectangle [0,I_1] x [0,I_2]. The proof should state this explicitly, since the boundary-gap conclusion follows from the rectangle, not from the single-point formulation as written.","section":"Appendix, first paragraph"}],"minor_comments":[{"comment":"Theorem 4 uses m1 and m2 in the capacity expressions, but the Cauchy model is parameterized by dispersions gamma_1 and gamma_2 and no m_i is defined in that section; the theorem should read log(A1/gamma_2) and log(A2/gamma_1), consistent with the proof.","section":"Section IV-B.2, Theorem 4"},{"comment":"Definition 2 calls Ri the 'Shannon inner bound' but omits the convex-hull operation that appears in the discrete-time inner bound in Section II-B and that is needed for time sharing between product distributions; the definition and Proposition 1 should be aligned on this point.","section":"Section V-B, Definition 2"},{"comment":"After correcting pi0(s), the notation pi* should be unified: Theorem 5 uses it for the one-way optimizer, while the Appendix uses pi*_i = min(sigma_i,1/2) without noting that this is the large-s limit of the corrected optimizer; a single consistent definition would remove the current ambiguity.","section":"Section V-C, Theorem 5"},{"comment":"The sentence 'Generalization does not significantly change results of this paper' about unequal peak powers/dark currents is unsupported; either give the straightforward generalization or remove the claim.","section":"Section V-A"},{"comment":"The expansion assumes sigma_i>0, since pi*_i appears in a denominator later as a factor in the leading term; this should be stated as a standing assumption in Theorem 6.","section":"Appendix"}],"recommendation":"major_revision","confidential_remarks":"To the editor: the ISD part of the paper is sound and publishable on its own. The Poisson part is the main novelty but is not currently supported as written: Theorem 5's pi0(s) is demonstrably wrong (it is not the maximizer of the displayed expression, can exceed 1, and decays exponentially), while the Appendix uses the correct large-s optimizer min(sigma,1/2). This is fixable by correcting the one-way capacity formula and re-deriving the asymptotics. The second load-bearing issue, Lemma 1, is a proof sketch for a nontrivial two-way discretization; the authors should provide a complete proof or a precise reference. I recommend major revision rather than rejection because the fixes appear feasible and the ISD contribution alone is substantial."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"I agree with the reader's positive assessment of the ISD part, but the reader missed a sharper problem in the Poisson section. The novel ISD material is clean: Theorem 1 gives a simple sufficient condition, Theorem 2 and Corollary 1 prove capacity without adaptation for injective semi-deterministic channels, and the examples (exponential, Cauchy, multiplicative, input-dependent Gaussian) are genuinely useful. The Poisson TWC is a good problem choice, and the appendix's O(s^-2) gap calculation is correct—but only if you use the right one-way capacity.\n\nThe problem is that Theorem 5 states the one-way capacity with π0(s) = ((1+s)^(1+s)/s^s)e^{-s}, which decays like e·s·e^{-s} as s→∞. That would make C_OWC(σ) collapse exponentially. But the paragraph before Theorem 6 and the appendix silently use π*_i = min(σ_i, 1/2), which is the correct large-s optimizer of the binary channel expression. These are not asymptotically equivalent: for s=10, σ=0.3, the printed π0 gives a one-way rate around 0.003A, while min(σ,1/2)=0.3 gives about 0.011A. So the proof's comparison is not with the outer bound stated in Theorem 5. The fix is likely small—the stationarity condition gives π0(s) = e^{-1}(1+s)^(1+s)/s^s - s, which tends to 1/2—but as written, Theorem 6 is not proven.\n\nOther soft spots: Lemma 1 is only a proof sketch, and carrying Wyner's discretization to the two-way channel deserves more than 'without significant changes.' Theorem 3 swaps indices against its own proof, Theorem 4 uses undefined m_i, and Section IV-C writes an equality for h(Y2|X2) that only holds under independence. These are minor by comparison, and they don't affect the ISD part.\n\nThe Poisson section, as printed, is internally contradictory in its load-bearing step. Still, this is a paper worth engaging: the ISD results stand, and the Poisson result is probably true with a corrected Theorem 5. I would not desk-reject it, but I would send it back for major revision and ask for a corrected one-way capacity statement and a proper proof of Lemma 1. A serious referee can fix these without starting over.","headline":"Solid ISD capacity results, but the Poisson half has a load-bearing inconsistency: Theorem 5's one-way capacity is contradicted by the proof of Theorem 6.","tokens_in":16138,"tokens_out":15691,"would_cite":false,"duration_ms":144621,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":null,"created_at":"2026-08-14T13:48:27.768223+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":null,"supporting_citations":[],"review_version":1}