arXiv subjects

Pau Colomer

Publications and source records attributed to Pau Colomer.

10 recordsLinked to original sources

arXiv2026

Deterministic identification for Bernoulli channels and related channels with continuous input

For memoryless channels with continuous input alphabets, deterministic identification (DI) typically exhibits a linearithmic ($n\log n$) message growth. However, the exact DI capacity has long remained open due to a persistent gap between the best known achievability and converse bounds. This gap was recently closed for AWGN channels via a novel code construction optimising the "galaxy" codes. Here, we extend this approach to the Bernoulli channel and subsequently to any channel $W$ whose image contains a continuous curve of output probability distributions, and hence admits a reduction to the Bernoulli channel restricted to a subinterval of inputs. As a consequence, we prove that the converse bound is tight and establish $\dot{C}_{\text{DI}}(W) = \frac 12$ for this broad class of channels, thereby closing the long-standing capacity gap. A similar gap was also observed for the DI rate-reliability tradeoff. We analyse the tradeoff between rate and error of the proposed code and derive improved lower bounds on the reliability function, approaching the converse at leading order in the regime of small error exponents.

cs.IT↗

arXiv2026

Optimal Codes for Deterministic Identification over Gaussian Channels: Closing the Capacity Gap

Deterministic identification (DI) has emerged as a promising paradigm for large-scale and goal-oriented communication systems. Despite significant progress, a fundamental open problem has remained unresolved: a persistent gap between the best known lower and upper bounds on the DI capacity, as well as on the corresponding rate-reliability tradeoff bounds. In this paper, we finally close this gap for Gaussian channels $\mathcal{G}$ by constructing an optimised code that achieves the known upper bound. This allows us to establish that the linearithmic capacity for deterministic identification is $\dot{C}_{\text{DI}}(\mathcal{G})=\frac{1}{2}$. Furthermore, we analyse the rate-reliability tradeoff and show that the proposed scheme matches the known upper bounds to first order, thereby closing the existing gap in reliability performance for all admissible error decay regimes. Finally, we demonstrate the existence of an optimum universal code, which does not require knowledge of the channel parameters and yet achieves capacity.

cs.IT↗

arXiv2026

Scientific Rigor and Human Warmth: Remembering Vladimir Sidorenko (1949-2025)

During the Foundations of Future Communication Systems (FFCS) conference in Braunschweig, a dedicated memorial session was held in honor of Dr. Vladimir (Volodya) Sidorenko (1949-2025). The session, chaired by Minglai Cai, brought together colleagues, collaborators, and former students to commemorate his scientific achievements and his exceptional human qualities. This report summarizes the biographical tribute, the personal recollections shared by speakers, and the broader impact of Volodya's work in coding theory, cryptography, telecommunications, and quantum error correction. Beyond his more than 150 publications and substantial technical contributions, the session highlighted his intellectual rigor, mentorship, humor, generosity, and lasting influence on the international research community.

cs.IT↗

arXiv2026

Rate-Reliability Tradeoff for Deterministic Identification over Gaussian Channels

We extend the recent analysis of the rate-reliability tradeoff in deterministic identification (DI) to general linear Gaussian channels, marking the first such analysis for channels with continuous output. Because DI provides a framework that can substantially enhance communication efficiency, and since the linear Gaussian model underlies a broad range of physical communication systems, our results offer both theoretical insights and practical relevance for the performance evaluation of DI in future networks. Moreover, the structural parallels observed between the Gaussian and discrete-output cases suggest that similar rate-reliability behaviour may extend to wider classes of continuous channels.

cs.IT↗

arXiv2025

Identification over Poisson ISI Channels: Feedback and Molecular Applications

Molecular communication (MC) enables information transfer via molecules, making it ideal for biomedical applications where traditional methods fall short. In many such scenarios, identifying specific events is more critical than decoding full messages, motivating the use of deterministic identification (DI). This paper investigates DI over discrete-time Poisson channels (DTPCs) with inter-symbol interference (ISI), a realistic setting due to channel memory effects. We improve the known upper bound on DI capacity under power constraints from $\frac{3}{2} + \kappa$ to $\frac{1 + \kappa}{2}$. Additionally, we present the first results on deterministic identification with feedback (DIF) in this context, providing a constructive lower bound. These findings enhance the theoretical understanding of MC and support more efficient, feedback-driven biomedical systems.

cs.IT↗

arXiv2025

Quantum Hypothesis Testing Lemma for Deterministic Identification over Quantum Channels

In our previous work, we presented the \emph{Hypothesis Testing Lemma}, a key tool that establishes sufficient conditions for the existence of good deterministic identification (DI) codes for memoryless channels with finite output, but arbitrary input alphabets. In this work, we provide a full quantum analogue of this lemma, which shows that the existence of a DI code in the quantum setting follows from a suitable packing in a modified space of output quantum states. Specifically, we demonstrate that such a code can be constructed using product states derived from this packing. This result enables us to tighten the capacity lower bound for DI over quantum channels beyond the simultaneous decoding approach. In particular, we can now express these bounds solely in terms of the Minkowski dimension of a certain state space, giving us new insights to better understand the nature of the protocol, and the separation between simultaneous and non-simultaneous codes. We extend the discussion with a particular channel example for which we can construct an optimum code.

cs.IT↗

arXiv2025

Rate-reliability tradeoff for deterministic identification

We investigate deterministic identification over arbitrary memoryless channels under the constraint that the error probabilities of first and second kind are exponentially small in the block length $\mathbf{n}$, controlled by reliability exponents $\mathbf{E_1,E_2 \geq 0}$. In contrast to the regime of slowly vanishing errors, where the identifiable message length scales linearithmically as $\mathbf{\Theta(n\log n)}$, here we find that for positive exponents linear scaling is restored, now with a rate that is a function of the reliability exponents. We give upper and lower bounds on the ensuing rate-reliability function in terms of (the logarithm of) the packing and covering numbers of the channel output set, which for small error exponents $\mathbf{E_1,E_2>0}$ can be expanded in leading order as the product of the Minkowski dimension of a certain parametrisation the channel output set and $\mathbf{\log\min\{E_1,E_2\}}$. These allow us to recover the previously observed slightly superlinear identification rates, and offer a different perspective for understanding them in more traditional information theory terms. We also show that even if only one of the two errors is required to be exponentially small, the linearithmic scaling is lost. We further illustrate our results with a discussion of the case of dimension zero, and extend them to classical-quantum channels and quantum channels with tensor product input restriction.

cs.IT↗

arXiv2024

Zero-entropy encoders and simultaneous decoders in identification via quantum channels

Motivated by deterministic identification via classical channels, where the encoder is not allowed to use randomization, we revisit the problem of identification via quantum channels but now with the additional restriction that the message encoding must use pure quantum states, rather than general mixed states. Together with the previously considered distinction between simultaneous and general decoders, this suggests a two-dimensional spectrum of different identification capacities, whose behaviour could a priori be very different. We demonstrate two new results as our main findings: first, we show that all four combinations (pure/mixed encoder, simultaneous/general decoder) have a double-exponentially growing code size, and that indeed the corresponding identification capacities are lower bounded by the classical transmission capacity for a general quantum channel, which is given by the Holevo-Schumacher-Westmoreland Theorem. Secondly, we show that the simultaneous identification capacity of a quantum channel equals the simultaneous identification capacity with pure state encodings, thus leaving three linearly ordered identification capacities. By considering some simple examples, we finally show that these three are all different: general identification capacity can be larger than pure-state-encoded identification capacity, which in turn can be larger than pure-state-encoded simultaneous identification capacity.

quant-ph↗

arXiv2024

Deterministic identification over channels with finite output: a dimensional perspective on superlinear rates

Following initial work by JaJa, Ahlswede and Cai, and inspired by a recent renewed surge in interest in deterministic identification (DI) via noisy channels, we consider the problem in its generality for memoryless channels with finite output, but arbitrary input alphabets. Such a channel is essentially given by its output distributions as a subset in the probability simplex. Our main findings are that the maximum length of messages thus identifiable scales superlinearly as $R\,n\log n$ with the block length $n$, and that the optimal rate $R$ is bounded in terms of the covering (aka Minkowski, or Kolmogorov, or entropy) dimension $d$ of a certain algebraic transformation of the output set: $\frac14 d \leq R \leq \frac12 d$. Remarkably, both the lower and upper Minkowski dimensions play a role in this result. Along the way, we present a "Hypothesis Testing Lemma" showing that it is sufficient to ensure pairwise reliable distinguishability of the output distributions to construct a DI code. Although we do not know the exact capacity formula, we can conclude that the DI capacity exhibits superactivation: there exist channels whose capacities individually are zero, but whose product has positive capacity. We also generalise these results to classical-quantum channels with finite-dimensional output quantum system, in particular to quantum channels on finite-dimensional quantum systems under the constraint that the identification code can only use tensor product inputs.

cs.IT↗

arXiv2023

Decoupling by local random unitaries without simultaneous smoothing, and applications to multi-user quantum information tasks

We show that a simple telescoping sum trick, together with the triangle inequality and a tensorisation property of expected-contractive coefficients of random channels, allow us to achieve general simultaneous decoupling for multiple users via local actions. Employing both old [Dupuis et al. Commun. Math. Phys. 328:251-284 (2014)] and new methods [Dupuis, arXiv:2105.05342], we obtain bounds on the expected deviation from ideal decoupling either in the one-shot setting in terms of smooth min-entropies, or the finite block length setting in terms of R\'enyi entropies. These bounds are essentially optimal without the need to address the simultaneous smoothing conjecture, which remains unresolved. This leads to one-shot, finite block length, and asymptotic achievability results for several tasks in quantum Shannon theory, including local randomness extraction of multiple parties, multi-party assisted entanglement concentration, multi-party quantum state merging, and quantum coding for the quantum multiple access channel. Because of the one-shot nature of our protocols, we obtain achievability results without the need for time-sharing, which at the same time leads to easy proofs of the asymptotic coding theorems. We show that our one-shot decoupling bounds furthermore yield achievable rates (so far only conjectured) for all four tasks in compound settings, that is for only partially known i.i.d. source or channel, which are furthermore optimal for entanglement of assistance and state merging.

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