In this paper, we construct a large family of projective linear codes over${\mathbb F}_{q}$from the general simplicial complexes of${\mathbb F}_{q}^{m}$via the defining-set construction, which generalizes the results of [IEEE Trans. Inf. Theory 66(11):6762-6773, 2020]. The parameters and weight distributions of this class of codes are completely determined. By using the Griesmer bound, we give a necessary and sufficient condition such that the codes are Griesmer codes and a sufficient condition such that the codes are distance-optimal. For a special case, we also present a necessary and sufficient condition for the codes to be near Griesmer codes. Moreover, by discussing the cases of simplicial complexes with one, two and three maximal elements respectively, the parameters and weight distributions of the codes are given more explicitly, which shows that the codes are at most 2-weight, 5-weight and 19-weight respectively. By studying the optimality of the codes for the three cases in detail, many infinite families of optimal linear codes with few weights over${\mathbb F}_{q}$are obtained, including Griesmer codes, near Griesmer codes and distance-optimal codes.

In this work, we present I2-SDF, a new method for intrinsic indoor scene reconstruction and editing using differentiable Monte Carlo raytracing on neural signed distance fields (SDFs). Our holistic neural SDF-based frame-work jointly recovers the underlying shapes, incident radiance and materials from multi-view images. We introduce a novel bubble loss for fine-grained small objects and error-guided adaptive sampling scheme to largely improve the reconstruction quality on large-scale indoor scenes. Further, we propose to decompose the neural radiance field into spatially-varying material of the scene as a neural field through surface-based, differentiable Monte Carlo raytracing and emitter semantic segmentations, which enables physically based and photorealistic scene relighting and editing applications. Through a number of qualitative and quantitative experiments, we demonstrate the superior quality of our method on indoor scene reconstruction, novel view synthesis, and scene editing compared to state-of-the-art baselines. Our project page is at https://jingsenzhu.github.io/i2-sdf.

With increasing popularity of virtual reality and augmented reality, application of point clouds is in critical demand as it enables users to freely navigate in an immersive scene with six degrees of freedom. However, point clouds usually comprise large amounts of data, and are thus difficult to stream in bandwidth-constrained networks. It is therefore important, yet challenging, to efficiently stream the resource-intensive point clouds, such that the user’s quality of experience (QoE) is guaranteed on a high-level but with a low bandwidth consumption. To this end, we propose a QoE-driven adaptive streaming approach for the tile-based point cloud transmission, to maximize the user’s QoE while reducing the transmission redundancy. By exploiting the perspective projection, we specifically model the QoE of a 3D tile as a function of the bitrate of its representation, user’s view frustum and spatial position, occlusion between tiles, and the resolution of rendering device. Based on this QoE model, we then formulate the QoE-optimized rate adaptation problem as a multiple-choice knapsack problem, which allocates bitrates for different tiles under a given transmission capacity. It is equivalently converted to a submodular function maximization problem subject to knapsack constraints, and solved by a practical greedy-based algorithm with a theoretical worst-case performance guarantee. The proposed algorithm is able to achieve a near-optimal performance, but with a very low computational complexity. Experimental results further demonstrate superiority of the proposed rate adaptation algorithm over existing schemes, in terms of both user’s visual quality and transmission efficiency.

In this paper, we construct four families of linear codes over finite fields from the complements of either the union of subfields or the union of cosets of a subfield, which can produce infinite families of optimal linear codes, including infinite families of (near) Griesmer codes. We also characterize the optimality of these four families of linear codes with an explicit computable criterion using the Griesmer bound and obtain many distance-optimal linear codes. In addition, by a more in-depth discussion on some special cases of these four families of linear codes, we obtain several classes of (distance-)optimal linear codes with few weights and completely determine their weight distributions. It is shown that most of our linear codes are self-orthogonal or minimal which are useful in applications.

Application of point clouds is in critical demand, which, however, are composed of large amounts of data and difficult to stream in bandwidth-constrained networks. To address this, we propose a QoE-driven and tile-based adaptive streaming approach for point clouds, to reduce transmission redundancy and maximize user’s QoE. Specifically, by utilizing the perspective projection, we model the QoE of a 3D tile as a function of the bitrate of its representation, user’s view frustum and spatial position, occlusion between tiles, and the resolution of rendering device. We then formulate the QoE-optimized rate adaptation problem as a multiple-choice knapsack problem that allocates bitrates for different tiles under a given transmission capacity. We equivalently convert it as a submodular function maximization problem subject to knapsack constraints, and develop a practical greedy algorithm with a theoretical performance guarantee. Experimental results further demonstrate superiority of the proposed rate adaptation algorithm over existing schemes, in terms of both user’s visual quality and transmission efficiency.