Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2501.12548

Galaxy Codes: Advancing Achievability for Deterministic Identification via Gaussian Channels

Holger Boche·Christian Deppe·Safieh Mahmoodi·Golamreza Omidi
View original source ↗Read source document ↗Export metadata ↓

Abstract

Deterministic identification offers an efficient solution for scenarios where decoding entire messages is unnecessary. It is commonly used in alarm systems and control systems. A key advantage of this approach is that the capacity for deterministic identification in Gaussian channels with power constraints grows superexponentially, unlike Shannon's transmission capacity. This allows for a significantly higher number of messages to be transmitted using this event-driven method. So far, only upper and lower bounds for deterministic identification capacity have been established. Our work introduces a novel construction: galaxy codes for deterministic identification. Using these codes, we demonstrate an improvement in the achievability bound of 1/4 to 3/8, representing a previously unknown advance that opens new possibilities for efficient communication.

Explore related subjects

cs.ITmath.IT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Holger Boche, Christian Deppe, Safieh Mahmoodi, Golamreza Omidi. 2025-01-22. Galaxy Codes: Advancing Achievability for Deterministic Identification via Gaussian Channels. https://arxiv.org/abs/2501.12548

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Efficient and rate-optimal list-decoding in the presence of minimal feedback

Given a channel with length-$n$ inputs and outputs over the alphabet $\{0,1,\ldots,q-1\}$, and of which a fraction $\varrho \in (0,1-1/q)$ of symbols can be arbitrarily corrupted by an adversary, a fundamental problem is that of communicating at rates close to the information-theoretically optimal values, while ensuring the receiver can infer that the transmitter's message is from a ``small" set. While the existence of such codes is known, and constructions with computationally tractable encoding/decoding procedures are known for large $q$, we provide the first schemes that attain this performance for any $q \geq 2$, as long as low-rate feedback (asymptotically negligible relative to the number of transmissions) from the receiver to the transmitter is available. For any sufficiently small $\varepsilon > 0$ and $\varrho \in (1-{1}/{q}-Θ(\sqrt{\varepsilon}))$ our minimal feedback scheme has the following parameters: Rate $1-H_q(\varrho) - \varepsilon$ (i.e., $\varepsilon$-close to information-theoretically optimal -- here $H_q(\varrho)$ is the $q$-ary entropy function), list-size $\exp\left(\mathcal{O}\left(\varepsilon^{-3/2}\log^2(1/\varepsilon)\right)\right)$, computational complexity of encoding/decoding $n^{\mathcal{O}(\varepsilon^{-1}\log(1/\varepsilon))}$, storage complexity $\mathcal{O}(n^{η+1}\log n)$ for a code design parameter $η>1$ that trades off storage complexity with the probability of error. The error probability is $\mathcal{O}(n^{-η})$, and the (vanishing) feedback rate is $\mathcal{O}({1}/{\sqrt{\log(n)}})$. Our full-feedback scheme has zero probability of error and minimal storage complexity, while the other parameters are the same as the vanishing rate feedback scheme.

cs.IT↗
arXiv2026

On Cost-Aware Designs for Sequential Hypothesis Testing

We introduce Cost-Aware (CA) Sequential Hypothesis Testing (CASHT), in which an active decision-maker selects sensing actions with different, random costs to identify the true hypothesis under an average-error constraint $δ$, while minimizing the expected total cost (rather than the number of samples). For fixed costs, we prove that the optimal expected total cost scales as $Θ(\log(1/δ))$, and is achievable by Multihypothesis Sequential Probability Ratio Test-based procedures. We show that the CA design principle is to maximize the ratio of expected information gain to expected cost under the policy-induced action distribution. Guided by this principle, we adapt two classic policies to the CA setting and establish their asymptotic optimality. We then treat random costs under two revelation models: ex-post, where costs are disclosed only after a sample is obtained, and the cost-error tradeoff coincides with the fixed-cost case, and ex-ante, where costs accrue before acquisition, and the decision maker may cancel an action mid-operation. For the ex-ante model, we characterize when cancellation lowers the total cost and analyze several cost distributions in detail. Simulations confirm our findings that the CA variants consistently reduce total cost relative to their classic counterparts, and when action cancellation helps or hurts.

cs.IT↗
arXiv2026

All you need is log

How different are several probability distributions from one another? For two distributions the standard answer is the family of Rényi divergences, singled out by two natural requirements: processing the data never makes distributions easier to tell apart, and independent repetitions add. Many problems in learning and statistics compare more than two distributions at once, such as testing among several hypotheses or bounding generalization against several priors. The same two requirements leave one kind of building block, built on a coincidence probability: how unlikely it is that independent samples, one from each distribution, all show the same empirical distribution. The logarithm is forced because repetitions add, which is already visible for a single experiment repeated. This characterization is known in greater generality, and this paper is about the meaning of its building blocks. On a finite alphabet, each building block indexed by a rational point of the simplex is the exponential rate of that coincidence as the samples grow in fixed proportions. Each is also the limiting free energy of Bayesian inference over distributions. At any amount of data, the free energy of the posterior is the coincidence measure plus two costs: the expected distance from a posterior draw to the most likely distribution, and the information gained per unit of data. Both costs vanish as data accumulate. When the comparison is conditioned on side information, every kind of building block has a conditional counterpart, and the coincidence ones alone do not suffice.

cs.IT↗