相关论文: On the Existence of Universally Decodable Matrices

Unambiguous unitary maps and unambiguous unitary quantum channels are introduced and some of their properties are derived. These properties ensure certain simple form for the measurements involved in realizing an unambiguous unitary quantum…

Precoding for multiple-input, multiple-output (MIMO) antenna systems is considered with perfect channel knowledge available at both the transmitter and the receiver. For 2 transmit antennas and QAM constellations, an approximately optimal…

Motivated by applications of biometric identification and content identification systems, we consider the problem of random coding for channels, where each codeword undergoes lossy compression (vector quantization), and where the decoder…

A lonesum matrix is a $(0,1)$-matrix that is uniquely determined by its row and column sum vectors. In this paper, we introduce lonesum decomposable matrices and study their properties. We provide a necessary and sufficient condition for a…

We construct a new family of quantum MDS codes from classical generalized Reed-Solomon codes and derive the necessary and sufficient condition under which these quantum codes exist. We also give code bounds and show how to construct them…

This paper deals with a universal coding problem for a certain kind of multiterminal source coding network called a generalized complementary delivery network. In this network, messages from multiple correlated sources are jointly encoded,…

An efficient decoder for the generalized first-order Reed-Muller code RM_q(1,m) is essential for the decoding of various block-coding schemes for orthogonal frequency-division multiplexing with reduced peak-to-mean power ratio. We present…

We propose a coding scheme that achieves the capacity of the compound MIMO channel with algebraic lattices. Our lattice construction exploits the multiplicative structure of number fields and their group of units to absorb ill-conditioned…

Over binary input channels, uniform distribution is a universal prior, in the sense that it allows to maximize the worst case mutual information over all binary input channels, ensuring at least 94.2% of the capacity. In this paper, we…

Deep learning architectures are highly diverse. To prove their universal approximation properties, existing works typically rely on model-specific proofs. Generally, they construct a dedicated mathematical formulation for each architecture…

A present challenge in wireless communications is the assurance of ultra-reliable and low-latency communication (URLLC). While the reliability aspect is well known to be improved by channel coding with long codewords, this usually implies…

Unitary matrices are the basis of a large number of signal processing applications. In many of these applications, finding ways to efficiently store, and even transmit these matrices, can significantly reduce memory and throughput…

The union-find decoder is a leading algorithmic approach to the correction of quantum errors on the surface code, achieving code thresholds comparable to minimum-weight perfect matching (MWPM) with amortised computational time scaling…

Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…

Explicit codes are constructed that achieve the diversity-multiplexing gain tradeoff of the cooperative-relay channel under the dynamic decode-and-forward protocol for any network size and for all numbers of transmit and receive antennas at…

Fast decoders that achieve strong error suppression are essential for fault-tolerant quantum computation (FTQC) from both practical and theoretical perspectives. The union-find (UF) decoder for the surface code is widely regarded as a…

The decomposition of large unitary matrices into smaller ones is important, because it provides ways to realization of classical and quantum information processing schemes. Today, most of the methods use planar meshes of tunable two-channel…

Linear codes with complementary duals (abbreviated LCD) are linear codes whose intersection with their dual is trivial. When they are binary, they play an important role in armoring implementations against side-channel attacks and fault…

Diagonalization, or eigenvalue decomposition, is very useful in many areas of applied mathematics, including signal processing and quantum physics. Matrix decomposition is also a useful tool for approximating matrices as the product of a…

Parity check matrices (PCMs) are used to define linear error correcting codes and ensure reliable information transmission over noisy channels. The set of codewords of such a code is the null space of this binary matrix. We consider the…