Related papers: Information Sets of Multiplicity Codes
In a recent paper, Kim and Kopparty (Theory of Computing, 2017) gave a deterministic algorithm for the unique decoding problem for polynomials of bounded total degree over a general grid. We show that their algorithm can be adapted to solve…
Incorporating multiple knowledge sources is proven to be beneficial for answering complex factoid questions. To utilize multiple knowledge bases (KB), previous works merge all KBs into a single graph via entity alignment and reduce the…
In continuation to earlier works where the problem of joint information embedding and lossless compression (of the composite signal) was studied in the absence \cite{MM03} and in the presence \cite{MM04} of attacks, here we consider the…
This paper addresses the problem of merging uncertain information in the framework of possibilistic logic. It presents several syntactic combination rules to merge possibilistic knowledge bases, provided by different sources, into a new…
Polar codes are considered the latest major breakthrough in coding theory. Polar codes were introduced by Ar{\i}kan in 2008. In this letter, we show that the binary polar codes are the same as the optimized codes for bitwise multistage…
We develop a general formalism for representing and understanding structure in complex systems. In our view, structure is the totality of relationships among a system's components, and these relationships can be quantified using information…
An efficient decoding algorithm named `divided decoder' is proposed in this paper. Divided decoding can be combined with any decoder using QR-decomposition and offers different pairs of performance and complexity. Divided decoding provides…
Using new techniques for controlling the categoricity spectrum of a structure, we construct a structure with degree of categoricity but infinite spectral dimension, answering a question of Bazhenov, Kalimulin and Yamaleev. Using the same…
In a series of papers N. Ma and P. Ishwar (2011-13) considered a range of distributed source coding problems that arise in the context of iterative computation of functions, characterizing the region of achievable communication rates. We…
Fast-decodable distributed space-time codes are constructed by adapting the iterative code construction introduced in [1] to the N -relay multiple-input multiple-output channel, leading to the first fast-decodable distributed space-time…
This was also extended from the previous article quant-ph/9705043, especially in a realization of the decoding process.
Existing works in image retrieval often consider retrieving images with one or two query inputs, which do not generalize to multiple queries. In this work, we investigate a more challenging scenario for composing multiple multimodal queries…
Recommender Systems have been widely used to help users in finding what they are looking for thus tackling the information overload problem. After several years of research and industrial findings looking after better algorithms to improve…
The multiplicity Schwartz-Zippel lemma asserts that over a field, a low-degree polynomial cannot vanish with high multiplicity very often on a sufficiently large product set. Since its discovery in a work of Dvir, Kopparty, Saraf and Sudan…
In coding theory, an error-correcting code can be encoded either systematically or non-systematically. In a systematic encode, the input data is embedded in the encoded output. Conversely, in a non-systematic code, the output does not…
It is informally understood that the purpose of modal type constructors in programming calculi is to control the flow of information between types. In order to lend rigorous support to this idea, we study the category of classified sets, a…
Kolmogorov complexity of a finite binary word reflects both algorithmic structure and the empirical distribution of symbols appearing in the word. Words with symbol frequencies far from one half have smaller combinatorial richness and…
The serial concatenation of a repetition code with two or more accumulators has the advantage of a simple encoder structure. Furthermore, the resulting ensemble is asymptotically good and exhibits minimum distance growing linearly with…
Information entropy is applied to the state of knowledge of reaction amplitudes in pseudoscalar meson photoproduction, and a scheme is developed that quantifies the information content of a measured set of polarization observables. It is…
Reed-Muller codes belong to the family of affine-invariant codes. As such codes they have a defining set that determines them uniquely, and they are extensions of cyclic group codes. In this paper we identify those cyclic codes with…