Low-Density Parity-Check Codes From Transversal Designs With Improved Stopping Set Distributions

This paper examines the construction of low-density parity-check (LDPC) codes from transversal designs based on sets of mutually orthogonal Latin squares (MOLS). By transferring the concept of configurations in combinatorial designs to the level of Latin squares, we thoroughly investigate the occurrence and avoidance of stopping sets for the arising codes. Stopping sets are known to determine the decoding performance over the binary erasure channel and should be avoided for small sizes. Based on large sets of simple-structured MOLS, we derive powerful constraints for the choice of suitable subsets, leading to improved stopping set distributions for the corresponding codes. We focus on LDPC codes with column weight 4, but the results are also applicable for the construction of codes with higher column weights. Finally, we show that a subclass of the presented codes has quasi-cyclic structure which allows low-complexity encoding.Comment: 11 pages; to appear in "IEEE Transactions on Communications

Spherical and Hyperbolic Toric Topology-Based Codes On Graph Embedding for Ising MRF Models: Classical and Quantum Topology Machine Learning

The paper introduces the application of information geometry to describe the ground states of Ising models by utilizing parity-check matrices of cyclic and quasi-cyclic codes on toric and spherical topologies. The approach establishes a connection between machine learning and error-correcting coding. This proposed approach has implications for the development of new embedding methods based on trapping sets. Statistical physics and number geometry applied for optimize error-correcting codes, leading to these embedding and sparse factorization methods. The paper establishes a direct connection between DNN architecture and error-correcting coding by demonstrating how state-of-the-art architectures (ChordMixer, Mega, Mega-chunk, CDIL, ...) from the long-range arena can be equivalent to of block and convolutional LDPC codes (Cage-graph, Repeat Accumulate). QC codes correspond to certain types of chemical elements, with the carbon element being represented by the mixed automorphism Shu-Lin-Fossorier QC-LDPC code. The connections between Belief Propagation and the Permanent, Bethe-Permanent, Nishimori Temperature, and Bethe-Hessian Matrix are elaborated upon in detail. The Quantum Approximate Optimization Algorithm (QAOA) used in the Sherrington-Kirkpatrick Ising model can be seen as analogous to the back-propagation loss function landscape in training DNNs. This similarity creates a comparable problem with TS pseudo-codeword, resembling the belief propagation method. Additionally, the layer depth in QAOA correlates to the number of decoding belief propagation iterations in the Wiberg decoding tree. Overall, this work has the potential to advance multiple fields, from Information Theory, DNN architecture design (sparse and structured prior graph topology), efficient hardware design for Quantum and Classical DPU/TPU (graph, quantize and shift register architect.) to Materials Science and beyond.Comment: 71 pages, 42 Figures, 1 Table, 1 Appendix. arXiv admin note: text overlap with arXiv:2109.08184 by other author

Advanced constellation and demapper schemes for next generation digital terrestrial television broadcasting systems

206 p.Esta tesis presenta un nuevo tipo de constelaciones llamadas no uniformes. Estos esquemas presentan una eficacia de hasta 1,8 dB superior a las utilizadas en los últimos sistemas de comunicaciones de televisión digital terrestre y son extrapolables a cualquier otro sistema de comunicaciones (satélite, móvil, cable¿). Además, este trabajo contribuye al diseño de constelaciones con una nueva metodología que reduce el tiempo de optimización de días/horas (metodologías actuales) a horas/minutos con la misma eficiencia. Todas las constelaciones diseñadas se testean bajo una plataforma creada en esta tesis que simula el estándar de radiodifusión terrestre más avanzado hasta la fecha (ATSC 3.0) bajo condiciones reales de funcionamiento.Por otro lado, para disminuir la latencia de decodificación de estas constelaciones esta tesis propone dos técnicas de detección/demapeo. Una es para constelaciones no uniformes de dos dimensiones la cual disminuye hasta en un 99,7% la complejidad del demapeo sin empeorar el funcionamiento del sistema. La segunda técnica de detección se centra en las constelaciones no uniformes de una dimensión y presenta hasta un 87,5% de reducción de la complejidad del receptor sin pérdidas en el rendimiento.Por último, este trabajo expone un completo estado del arte sobre tipos de constelaciones, modelos de sistema, y diseño/demapeo de constelaciones. Este estudio es el primero realizado en este campo

Compute-and-Forward Relay Networks with Asynchronous, Mobile, and Delay-Sensitive Users

We consider a wireless network consisting of multiple source nodes, a set of relays and a destination node. Suppose the sources transmit their messages simultaneously to the relays and the destination aims to decode all the messages. At the physical layer, a conventional approach would be for the relay to decode the individual message one at a time while treating rest of the messages as interference. Compute-and-forward is a novel strategy which attempts to turn the situation around by treating the interference as a constructive phenomenon. In compute-and-forward, each relay attempts to directly compute a combination of the transmitted messages and then forwards it to the destination. Upon receiving the combinations of messages from the relays, the destination can recover all the messages by solving the received equations. When identical lattice codes are employed at the sources, error correction to integer combination of messages is a viable option by exploiting the algebraic structure of lattice codes. Therefore, compute-and-forward with lattice codes enables the relay to manage interference and perform error correction concurrently. It is shown that compute-and-forward exhibits substantial improvement in the achievable rate compared with other state-of-the-art schemes for medium to high signal-to-noise ratio regime. Despite several results that show the excellent performance of compute-and-forward, there are still important challenges to overcome before we can utilize compute-and- forward in practice. Some important challenges include the assumptions of \perfect timing synchronization "and \quasi-static fading", since these assumptions rarely hold in realistic wireless channels. So far, there are no conclusive answers to whether compute-and-forward can still provide substantial gains even when these assumptions are removed. When lattice codewords are misaligned and mixed up, decoding integer combination of messages is not straightforward since the linearity of lattice codes is generally not invariant to time shift. When channel exhibits time selectivity, it brings challenges to compute-and-forward since the linearity of lattice codes does not suit the time varying nature of the channel. Another challenge comes from the emerging technologies for future 5G communication, e.g., autonomous driving and virtual reality, where low-latency communication with high reliability is necessary. In this regard, powerful short channel codes with reasonable encoding/decoding complexity are indispensable. Although there are fruitful results on designing short channel codes for point-to-point communication, studies on short code design specifically for compute-and-forward are rarely found. The objective of this dissertation is threefold. First, we study compute-and-forward with timing-asynchronous users. Second, we consider the problem of compute-and- forward over block-fading channels. Finally, the problem of compute-and-forward for low-latency communication is studied. Throughout the dissertation, the research methods and proposed remedies will center around the design of lattice codes in order to facilitate the use of compute-and-forward in the presence of these challenges

Constellation design for future communication systems: a comprehensive survey

[EN] The choice of modulation schemes is a fundamental building block of wireless communication systems. As a key component of physical layer design, they critically impact the expected communication capacity and wireless signal robustness. Their design is also critical for the successful roll-out of wireless standards that require a compromise between performance, efficiency, latency, and hardware requirements. This paper presents a survey of constellation design strategies and associated outcomes for wireless communication systems. The survey discusses their performance and complexity to address the need for some desirable properties, including consistency, channel capacity, system performance, required demapping architecture, flexibility, and independence. Existing approaches for constellation designs are investigated using appropriate metrics and categorized based on their theoretical algorithm design. Next, their application to different communication standards is analyzed in context, aiming at distilling general guidelines applicable to the wireless building block design. Finally, the survey provides a discussion on design directions for future communication system standardization processes.This work was supported in part by the Basque Government under Grant IT1234-19, in part by the PREDOC under Program PRE_2020_2_0105, and in part by the Spanish Government through the Project PHANTOM (MCIU/AEI/FEDER, UE) under Gran