arXiv subjects

Angelos Gkekas

Publications and source records attributed to Angelos Gkekas.

2 recordsLinked to original sources

arXiv2026

Geometry-Informed Optimization of Binary RIS Configurations for Communication and Sensing

Practical Reconfigurable Intelligent Surfaces (RISs) often support only a small number of phase states, making their configuration inherently discrete. For a 1-bit RIS with $N$ elements, direct optimization requires searching among $2^N$ binary configurations. This work shows that this exponential configuration space is not unstructured. By reformulating 1-bit RIS optimization as the maximization of the norm of a signed sum of channel-dependent vectors, we prove that every globally optimal configuration must be induced by the signs of their projections onto a common direction. This geometric characterization restricts the class of configurations that can contain global optima and leads to different algorithmic consequences depending on the signal-space dimension. For general Multiple-Input-Multiple-Output (MIMO) systems, we develop a geometry-informed sampling method that evaluates only structurally admissible configurations. For Single-Input-Single-Output (SISO) systems, the same principle reduces to a two-dimensional angular partition, allowing the complete candidate set to be characterized and the global optimum to be recovered through polynomial-time enumeration, by evaluating at most $N+1$ out of the $2^N$ configurations. Finally, we apply the same binary optimization principle to an Integrated Sensing and Communication (ISAC) scenario, where communication enhancement and target localization reduce to the same underlying geometric problem. The proposed framework therefore provides a unified approach for exploiting the structure of practical 1-bit RIS configurations across communication and sensing functionalities.

cs.IT↗

arXiv2025

On the Computability of Finding Capacity-Achieving Codes

This work studies the problem of constructing capacity-achieving codes from an algorithmic perspective. Specifically, we prove that there exists a Turing machine which, given a discrete memoryless channel $p_{Y|X}$, a target rate $R$ less than the channel capacity $C(p_{Y|X})$, and an error tolerance $ε> 0$, outputs a block code $\mathcal{C}$ achieving a rate at least $R$ and a maximum block error probability below $ε$. The machine operates in the general case where all transition probabilities of $p_{Y|X}$ are computable real numbers, and the parameters $R$ and $ε$ are rational. The proof builds on Shannon's channel coding theorem and relies on an exhaustive search approach that systematically enumerates all codes of increasing block length until a valid code is found. This construction is formalized using the theory of recursive functions, yielding a $μ$-recursive function $\mathrm{FindCode} : \mathbb{N}^3 \rightharpoonup \mathbb{N}$ that takes as input appropriate encodings of $p_{Y|X}$, $R$, and $ε$, and, whenever $R < C(p_{Y|X})$, outputs an encoding of a valid code. By Kleene's normal form theorem, which establishes the computational equivalence between Turing machines and $μ$-recursive functions, we conclude that the problem is solvable by a Turing machine. This result can also be extended to the case where $ε$ is a computable real number, while we further discuss an analogous generalization of our analysis when $R$ is computable as well. We note that the assumptions that the probabilities of $p_{Y|X}$, as well as $ε$ and $R$, are computable real numbers cannot be further weakened, since computable reals constitute the largest subset of $\mathbb{R}$ representable by algorithmic means.

cs.IT↗