Related papers: Space-Efficient Huffman Codes Revisited
We construct a new family of explicit codes that are list decodable to capacity and achieve an optimal list size of $O(\frac{1}{\epsilon})$. In contrast to existing explicit constructions of codes achieving list decoding capacity, our…
Two classes of turbo codes over high-order finite fields are introduced. The codes are derived from a particular protograph sub-ensemble of the (dv=2,dc=3) low-density parity-check code ensemble. A first construction is derived as a…
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…
A family of $\omega$-circulant balanced weighing matrices with classical parameters is used for the construction of optimal constant weight codes over an alphabet of size $g+1$ and length $n=(q^m -1)/(q-1)$, where $q$ is an odd prime power,…
Number-conserved subspace encoding reduces resources needed for quantum simulations, but scalable complexity trade-off bounds for $M$ modes and $N$ particles with $\mathcal{O}(N\log M)$ qubits have remained unknown. We study…
We show that the compressed suffix array and the compressed suffix tree for a string of length $n$ over an integer alphabet of size $\sigma\leq n$ can both be built in $O(n)$ (randomized) time using only $O(n\log\sigma)$ bits of working…
We give efficient algorithms for ranking Lyndon words of length $n$ over an alphabet of size $\sigma$. The rank of a Lyndon word is its position in the sequence of lexicographically ordered Lyndon words of the same length. The outputs are…
We present a new variable-length computation-friendly encoding scheme, named SFDC (Succinct Format with Direct aCcesibility), that supports direct and fast accessibility to any element of the compressed sequence and achieves compression…
A family of error-correcting codes is list-decodable from error fraction $p$ if, for every code in the family, the number of codewords in any Hamming ball of fractional radius $p$ is less than some integer $L$ that is independent of the…
We say a subset $C \subseteq \{1,2,\dots,k\}^n$ is a $k$-hash code (also called $k$-separated) if for every subset of $k$ codewords from $C$, there exists a coordinate where all these codewords have distinct values. Understanding the…
We consider coding schemes for computationally bounded channels, which can introduce an arbitrary set of errors as long as (a) the fraction of errors is bounded with high probability by a parameter $p$ and (b) the process which adds the…
We propose an unsupervised hashing method which aims to produce binary codes that preserve the ranking induced by a real-valued representation. Such compact hash codes enable the complete elimination of real-valued feature storage and allow…
Simulating the time evolution of a physical system at quantum mechanical levels of detail -- known as Hamiltonian Simulation (HS) -- is an important and interesting problem across physics and chemistry. For this task, algorithms that run on…
As a crucial approach for compact representation learning, hashing has achieved great success in effectiveness and efficiency. Numerous heuristic Hamming space metric learning objectives are designed to obtain high-quality hash codes.…
According to the circle-packing theorem, the packing efficiency of a hexagonal lattice is higher than an equivalent square tessellation. Consequently, in several contexts, hexagonally sampled images compared to their Cartesian counterparts…
This paper investigates the size in bits of the LZ77 encoding, which is the most popular and efficient variant of the Lempel-Ziv encodings used in data compression. We prove that, for a wide natural class of variable-length encoders for…
This paper presents encoding and decoding algorithms for several families of optimal rank metric codes whose codes are in restricted forms of symmetric, alternating and Hermitian matrices. First, we show the evaluation encoding is the right…
We introduce a new, quadratically convergent algorithm for finding maximum absolute value entries of tensors represented in the canonical format. The computational complexity of the algorithm is linear in the dimension of the tensor. We…
We investigate two source coding problems with secrecy constraints. In the first problem we consider real--time fully secure transmission of a memoryless source. We show that although classical variable--rate coding is not an option since…
Quantum error-correcting codes protect fragile quantum information by encoding it redundantly, but identifying codes that perform well in practice with minimal overhead remains difficult due to the combinatorial search space and the high…