Performance Analysis of Iteratively Decoded Convergent Source Mapping with Sphere Packing-Assisted Differential Space-Time Spreading Technique for Efficient Video Transmission

With the substantial growth in number of wireless devices, future communication demands overarching research to design high-throughput and efficient systems. We propose an intelligent Convergent Source Mapping (CSM) approach incorporating Differential Space-Time Spreading (DSTS) technique with Sphere Packing (SP) modulation. The crux of CSM process is assured convergence by attaining an infinitesimal Bit-Error Rate (BER). Data Partitioning (DP) H.264 video codec is deployed to gauge the performance of our intelligent and efficient system. For the purpose of efficient and higher data rates, we have incorporated compression efficient source encoding along with error resiliency and transmission robustness features. The proposed system follows the concept of iterations between the Soft-Bit Source-Decoder (SBSD) and Recursive Systematic Convolutional (RSC) decoder. Simulations of the DSTS-SP-assisted CSM system are presented for the correlated narrowband Rayleigh channel, using different CSM rates but constant overall bit-rate budget. The SP-assisted DSTS systems are mainly useful in decoding algorithms that operate without requiring Channel State Information (CSI). The effects of incorporating redundancy via different CSM schemes on the attainable performance and convergence of the proposed system are investigated using EXtrinsic Information Transfer (EXIT) charts. The effectiveness of the proposed system is demonstrated through IT++ based proof-of-concept simulations. The Peak Signal-to-Noise Ratio (PSNR) analysis shows that using Rate-2/6 CSM with minimum Hamming distance ( d H , min ) of 4 offers about 5 dB gain, compared to an identical overall system code rate but with Rate-2/3 CSM and d H , min of 2. Furthermore, for a consistent value of d H , min and overall rate, the Rate-2/3 CSM scheme beats the Rate-5/6 CSM by about 2 dB at the PSNR degradation point of 2 dB. Moreover, the proposed system with Rate-2/3 CSM scheme furnishes an E b / N 0 gain of 20 dB when compared with the uniform-rate benchmarker. Clearly, we can say that higher d H , min and lower CSM values are favourable for our proposed setup.

Volumetric Representation and Sphere Packing of Indoor Space for Three-Dimensional Room Segmentation

Room segmentation is a basic task for the semantic enrichment of point clouds. Recent studies have mainly projected single-floor point clouds to binary images to realize two-dimensional room segmentation. However, these methods have difficulty solving semantic segmentation problems in complex 3D indoor environments, including cross-floor spaces and rooms inside rooms; this is the bottleneck of indoor 3D modeling for non-Manhattan worlds. To make full use of the abundant geometric and spatial structure information in 3D space, a novel 3D room segmentation method that realizes room segmentation directly in 3D space is proposed in this study. The method utilizes volumetric representation based on a VDB data structure and packs an indoor space with a set of compact spheres to form rooms as separated connected components. Experimental results on different types of indoor point cloud datasets demonstrate the efficiency of the proposed method.

Averting BER Floor with Iterative Source and Channel Decoding for Layered Steered Space-Time Codes

The widespread development in wireless technologies and the advancements in multimedia communication have brought about a positive impact on the performance of wireless transceivers. We investigate the performance of our three-stage turbo detected system using state-of-the-art high efficiency video coding (HEVC), also known as the H.265 video standard. The system makes use of sphere packing (SP) modulation with the combinational gain technique of layered steered space-time code (LSSTC). The proposed three-stage system is simulated for the correlated Rayleigh fading channel and the bit-error rate (BER) curve obtained after simulation is free of any floor formation. The system employs low complexity source-bit coding (SBC) for protecting the H.265 coded stream. An intermediate recursive unity-rate code (URC) with an infinite impulse response is employed as an inner precoder. More specifically, the URC assists in the prevention of the BER floor by distributing the information across the decoders. There is an observable gain in the BER and peak signal-to-noise ratio (PSNR) performances with the increasing value of minimum Hamming distance (dH,min) using the three-stage system. Convergence analysis of the proposed system is investigated through an extrinsic information transfer (EXIT) chart. Our proposed system demonstrates better performance of about 22 dB than the benchmarker utilizing LSSTC-SP for iterative source-channel detection, but without exploiting the optimized SBC schemes.

Fourier uniqueness in even dimensions

In recent work, methods from the theory of modular forms were used to obtain Fourier uniqueness results in several key dimensions (d=1,8,24), in which a function could be uniquely reconstructed from the values of it and its Fourier transform on a discrete set, with the striking application of resolving the sphere packing problem in dimensions d=8 and d=24. In this short note, we present an alternative approach to such results, viable in even dimensions, based instead on the uniqueness theory for the Klein–Gordon equation. Since the existing method for the Klein–Gordon uniqueness theory is based on the study of iterations of Gauss-type maps, this suggests a connection between the latter and methods involving modular forms. The derivation of Fourier uniqueness from the Klein–Gordon theory supplies conditions on the given test function for Fourier interpolation, which are hoped to be optimal or close to optimal.

A jamming plane of sphere packings

The concept of jamming has attracted great research interest due to its broad relevance in soft-matter, such as liquids, glasses, colloids, foams, and granular materials, and its deep connection to sphere packing and optimization problems. Here, we show that the domain of amorphous jammed states of frictionless spheres can be significantly extended, from the well-known jamming-point at a fixed density, to a jamming-plane that spans the density and shear strain axes. We explore the jamming-plane, via athermal and thermal simulations of compression and shear jamming, with initial equilibrium configurations prepared by an efficient swap algorithm. The jamming-plane can be divided into reversible-jamming and irreversible-jamming regimes, based on the reversibility of the route from the initial configuration to jamming. Our results suggest that the irreversible-jamming behavior reflects an escape from the metastable glass basin to which the initial configuration belongs to or the absence of such basins. All jammed states, either compression- or shear-jammed, are isostatic and exhibit jamming criticality of the same universality class. However, the anisotropy of contact networks nontrivially depends on the jamming density and strain. Among all state points on the jamming-plane, the jamming-point is a unique one with the minimum jamming density and the maximum randomness. For crystalline packings, the jamming-plane shrinks into a single shear jamming-line that is independent of initial configurations. Our study paves the way for solving the long-standing random close-packing problem and provides a more complete framework to understand jamming.