相关论文: On the Uniqueness of Group Sparse Coding
In a group trellis, the sequence of branches that split from the identity path and merge to the identity path form two normal chains. The Schreier refinement theorem can be applied to these two normal chains. The refinement of the two…
We solve an open question in code-based cryptography by introducing two provably secure group signature schemes from code-based assumptions. Our basic scheme satisfies the CPA-anonymity and traceability requirements in the random oracle…
We introduce explicit schemes based on the polarization phenomenon for the tasks of one-way secret key agreement from common randomness and private channel coding. For the former task, we show how to use common randomness and insecure…
We prove direct quantum coding theorem for random quantum codes. The problem is separated into two parts: proof of distinguishability of codewords by receiver, and that of indistinguishability of codewords by environment (privacy). For a…
We consider the problem of reliable communication over multiple-access channels (MAC) where the channel is driven by an independent and identically distributed state process and the encoders and the decoder are provided with various degrees…
We present sparse graph codes appropriate for use in quantum error-correction. Quantum error-correcting codes based on sparse graphs are of interest for three reasons. First, the best codes currently known for classical channels are based…
We introduce a new type of sparse CSS quantum error correcting code based on the homology of hypermaps. Sparse quantum error correcting codes are of interest in the building of quantum computers due to their ease of implementation and the…
Secure transmission between two agents, Alice and Bob, over block fading channels can be achieved similarly to conventional hybrid automatic repeat request (HARQ) by letting Alice transmit multiple blocks, each containing an encoded version…
In this paper, we show that the Advanced Encryption Standard (AES) cryptosystem can be used as an error-correcting code to obtain reliability over noisy communication and data systems. Moreover, we characterize a family of computational…
Quasi-cyclic (QC) low-density parity-check (LDPC) codes which are known as QC-LDPC codes, have many applications due to their simple encoding implementation by means of cyclic shift registers. In this paper, we construct QC-LDPC codes from…
CSS codes are a subfamily of stabilizer codes especially appropriate for fault-tolerant quantum computations. A very simple method is proposed to encode a general qudit when a Calderbank-Shor-Steane quantum code, defined over a q-ary…
This paper addresses signal denoising when large-amplitude coefficients form clusters (groups). The L1-norm and other separable sparsity models do not capture the tendency of coefficients to cluster (group sparsity). This work develops an…
Sparse coding has been popularly used as an effective data representation method in various applications, such as computer vision, medical imaging and bioinformatics, etc. However, the conventional sparse coding algorithms and its manifold…
We introduce group crosscoders, an extension of crosscoders that systematically discover and analyse symmetrical features in neural networks. While neural networks often develop equivariant representations without explicit architectural…
It will be shown that Pascal's Theorem is equivalent to the associativity of a natural binary operation on conic sections. A novel proof for Pascal's Theorem will then be given by showing that this binary operation is associative…
Group sparse representation has shown promising results in image debulrring and image inpainting in GSR [3] , the main reason that lead to the success is by exploiting Sparsity and Nonlocal self-similarity (NSS) between patches on natural…
Block codes are considered for improving the reliability of messages stored in a computer memory with both stuck-at defects and random errors. It is assumed that the side information about the state of the defects is available to the…
We present a simplification of Jensen's proof of his Coding Theorem (even in the case where 0# exists). The proof avoids Jensen's split into cases according to whether or not 0# exists. In addition, the paper contains self-contained proofs…
An image super-resolution method from multiple observation of low-resolution images is proposed. The method is based on sub-pixel accuracy block matching for estimating relative displacements of observed images, and sparse signal…
A set $M$ of nonzero integers is said to split a finite abelian group $G$ if there exists a subset $S\subseteq G$ such that $M\cdot S = G\setminus\{0\}$. Such a splitting is called purely singular if every prime divisor of $|G|$ divides…