Related papers: Huffman coding as an algorithm to construct chains…
This paper presents new lower and upper bounds for the compression rate of binary prefix codes optimized over memoryless sources according to various nonlinear codeword length objectives. Like the most well-known redundancy bounds for…
Matrix code allows one to discover algorithms and to render them in code that is both compilable and is correct by construction. In this way the difficulty of verifying existing code is avoided. The method is especially important for…
In this work, a coding technique called cost constrained Geometric Huffman coding (ccGhc) is developed. ccGhc minimizes the Kullback-Leibler distance between a dyadic probability mass function (pmf) and a target pmf subject to an affine…
An exact algorithm is presented for solving edge weighted graph partitioning problems. The algorithm is based on a branch and bound method applied to a continuous quadratic programming formulation of the problem. Lower bounds are obtained…
In this paper, we revisit the classical data compression problem for domain specific texts. It is well-known that classical Huffman algorithm is optimal with respect to prefix encoding and the compression is done at character level. Since…
In this paper, we study amplitude shaping schemes for the probabilistic amplitude shaping (PAS) framework as well as algorithms for constant-composition distribution matching (CCDM). Huffman-coded sphere shaping (HCSS) is discussed in…
Partitioning is a well studied research problem in the area of VLSI physical design automation. In this problem, input is an integrated circuit and output is a set of almost equal disjoint blocks. The main objective of partitioning is to…
The number of "nonequivalent" Huffman codes of length r over an alphabet of size t has been studied frequently. Equivalently, the number of "nonequivalent" complete t-ary trees has been examined. We first survey the literature, unifying…
In network coding, a flag code is a collection of flags, that is, sequences of nested subspaces of a vector space over a finite field. Due to its definition as the sum of the corresponding subspace distances, the flag distance parameter…
The problem of computing a linear combination of sources over a multiple access channel is studied. Inner and outer bounds on the optimal tradeoff between the communication rates are established when encoding is restricted to random…
We present an algorithm for building probabilistic rule lists that is two orders of magnitude faster than previous work. Rule list algorithms are competitors for decision tree algorithms. They are associative classifiers, in that they are…
Unrefinable partitions are a subset of partitions into distinct parts which satisfy an additional unrefinability property. More precisely, being an unrefinable partition means that none of the parts can be written as the sum of smaller…
We generalize staircase codes and tiled diagonal zipper codes, preserving their key properties while allowing each coded symbol to be protected by arbitrarily many component codewords rather than only two. This generalization which we term…
A weak order on the set of maximal chains of the non-crossing partition lattice is introduced and studied. A $0$-Hecke algebra action is used to compute the radius of the graph on these chains in which two chains are adjacent if they differ…
An implementation-efficient finite alphabet decoder for polar codes relying on coarsely quantized messages and low-complexity operations is proposed. Typically, finite alphabet decoding performs concatenated compression operations on the…
We consider the hash function $h(x) = ((ax+b) \bmod p) \bmod n$ where $a,b$ are chosen uniformly at random from $\{0,1,\ldots,p-1\}$. We prove that when we use $h(x)$ in hashing with chaining to insert $n$ elements into a table of size $n$…
Recursive partitioning is the core of several statistical methods including CART, random forest, and boosted trees. Despite the popularity of tree based methods, to date, there did not exist methods for combining multiple trees into a…
We consider heuristic algorithm for solving graph isomorphism problem. The algorithm based on a successive splitting of the eigenvalues of the matrices which are modifications (to positive defined) of graphs' adjacency matrices.…
We design a heuristic method, a genetic algorithm, for the computation of an upper bound of the minimum distance of a linear code over a finite field. By the use of the row reduced echelon form, we obtain a permutation encoding of the…
A consensus is emerging that continuous (or metric) measures can be useful in phylogenetic systematics. Many of the methods for coding such characters, how- ever, employ elements that are arbitrary and therefore should be excluded from use…