Related papers: The Narayana Universal Code
A general lossless joint source-channel coding scheme based on linear codes is proposed and then analyzed in this paper. It is shown that a linear code with good joint spectrum can be used to establish limit-approaching joint source-channel…
In the present paper we find a new interpretation of Narayana polynomials N_n(x) which are the generating polynomials for the Narayana numbers N_{n,k} counting Dyck paths of length n and with exactly k peaks. Strangely enough Narayana…
We discuss various universality aspects of numerical computations using standard algorithms. These aspects include empirical observations and rigorous results. We also make various speculations about computation in a broader sense.
Narayana's sequence is a ternary recurrent sequence defined by the recurrence relation $\mathcal{N}_n=\mathcal{N}_{n-1}+\mathcal{N}_{n-3}$ with initial terms $\mathcal{N}_0=0$ and $\mathcal{N}_1=\mathcal{N}_2=\mathcal{N}_3=1$. Let…
Several upper bounds on the size of quantum codes are derived using the linear programming approach. These bounds are strengthened for the linear quantum codes.
We propose two types of universal codes that are suited to two asymptotic regimes when the output alphabet is possibly continuous. The first class has the property that the error probability decays exponentially fast and we identify an…
Series of maximum distance quantum error-correcting codes are developed and analysed. For a given rate and given error-correction capability, quantum error-correcting codes with these specifications are constructed. The codes are explicit…
This paper describes a universal model for paraphrasing that transforms according to defined criteria. We showed that by using different criteria we could construct different kinds of paraphrasing systems including one for answering…
We construct a universal code for stationary and memoryless classical-quantum channel as a quantum version of the universal coding by Csisz\'{a}r and K\"{o}rner. Our code is constructed by the combination of irreducible representation, the…
This paper deals with the problem of increasing the minimum distance of a linear code by adding one or more columns to the generator matrix. Several methods to compute extensions of linear codes are presented. Many codes improving the…
Unary coding has found applications in data compression, neural network training, and in explaining the production mechanism of birdsong. Unary coding is redundant; therefore it should have inherent error correction capacity. An expression…
We show how good quantum error-correcting codes can be constructed using generalized concatenation. The inner codes are quantum codes, the outer codes can be linear or nonlinear classical codes. Many new good codes are found, including both…
To advance Polar code design for 6G applications, we develop a reinforcement learning-based universal sequence design framework that is extensible and adaptable to diverse channel conditions and decoding strategies. Crucially, our method…
In this article we propose a general method of obtaining infinite sums of products with functions that count patterns in numbers.
Random Linear Network Coding (RLNC) provides a theoretically efficient method for coding. Some of its practical drawbacks are the complexity of decoding and the overhead due to the coding vectors. For computationally weak and battery-driven…
The science of versification and analysis of verse in Sanskrit is governed by rules of metre or chandas. Such metre-wise classification of verses has numerous uses for scholars and researchers alike, such as in the study of poets and their…
In this note, by counting some colored plane trees we obtain several binomial identities. These identities can be viewed as specific evaluations of certain generalizations of the Narayana polynomials. As consequences, it provides…
A list decoding scheme for universal polar codes is presented. Our scheme applies to the universal polar codes first introduced by Sasoglu and Wang, and generalized to processes with memory by the authors. These codes are based on the…
One of the main weakness of the family of centralizer codes is that its length is always $n^2$. Thus we have taken a new matrix equation code called intertwining code. Specialty of this code is the length of it, which is of the form $nk$.…
Linear codes can be employed to construct authentication codes, which is an interesting area of cryptography. The parameters of the authentication codes depend on the complete weight enumerator of the underlying linear codes. In order to…