Related papers: Variable-Length Constrained Coding and Kraft Condi…
We consider a variable-length source coding problem subject to local decodability constraints. In particular, we investigate the blocklength scaling behavior attainable by encodings of $r$-sparse binary sequences, under the constraint that…
In this paper, the stability condition for low-density parity-check (LDPC) codes on the binary erasure channel (BEC) is extended to generalized LDPC (GLDPC) codes and doublygeneralized LDPC (D-GLDPC) codes. It is proved that, in both cases,…
It is well noted that coordinate based MLPs benefit -- in terms of preserving high-frequency information -- through the encoding of coordinate positions as an array of Fourier features. Hitherto, the rationale for the effectiveness of these…
A challenging problem related to the design of polar codes is "robustness against channel parameter variations" as stated in Ar{\i}kan's original work. In this paper, we describe how the problem of robust polar code design can be viewed as…
We investigate weakly constrained codes, in which specific patterns occur with prescribed frequencies rather than being strictly forbidden as in conventional constrained coding. We propose a capacity-achieving construction of a weakly…
Encoding data structures store enough information to answer the queries they are meant to support but not enough to recover their underlying datasets. In this paper we give the first encoding data structure for the challenging problem of…
Spatially-coupled low-density parity-check codes attract much attention due to their capacity-achieving performance and a memory-efficient sliding-window decoding algorithm. On the other hand, the encoder needs to solve large linear…
If a sender and a receiver lack precise knowledge about the communication line that connects them, designing a scheme to reliably transmit information becomes more challenging. This has been studied in classical and quantum information…
Parity constraints, common in application domains such as circuit verification, bounded model checking, and logical cryptanalysis, are not necessarily most efficiently solved if translated into conjunctive normal form. Thus, specialized…
We consider a problem in which a source is encoded into N packets, an unknown number of which are subject to adversarial errors en route to the decoder. We seek code designs for which the decoder is guaranteed to be able to reproduce the…
In this paper, within a unified framework of the condition number theory we present the explicit expression of the projected condition number of the equality constrained indefinite least squares problem. By setting specific norms and…
This paper introduces a new inequality in algorithmic information theory that can be seen as an extended coding theorem. This inequality has applications in new bounds between quantum complexity measures.
Recently it has been proposed to construct quantum error-correcting codes that embed a finite-dimensional Hilbert space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables [D. Gottesman et al.,…
In this work, we provide a detailed analysis of the issue of encoding of quantum information which is invariant with respect to arbitrary Lorentz transformations. We significantly extend already known results and provide compliments where…
This paper considers mathematical programs, whose constraints are expressed by a parameterized vector equilibrium problem. The latter is a well recognized framework, which is able to cover multicriteria optimization, vector variational…
We propose a conditional positional encoding (CPE) scheme for vision Transformers. Unlike previous fixed or learnable positional encodings, which are pre-defined and independent of input tokens, CPE is dynamically generated and conditioned…
A necessary condition is given for a sequence of identically distributed and pairwise positively quadrant dependent random variables obeying the strong laws of large numbers with respect to the normalising constants $n^{1/p}$ $(1 \leqslant…
Relative positional encoding is widely used in vanilla and linear transformers to represent positional information. However, existing encoding methods of a vanilla transformer are not always directly applicable to a linear transformer,…
Encodings or the proof of their absence are the main way to compare process calculi. To analyse the quality of encodings and to rule out trivial or meaningless encodings, they are augmented with encodability criteria. There exists a bunch…
Entanglement, one of the most intriguing aspects of quantum mechanics, marks itself into different features of quantum states. For this reason different criteria can be used for verifying entanglement. In this paper we review some of the…