Related papers: Multipermutation Codes in the Ulam Metric for Nonv…
In this paper, we introduce a new way of constructing and decoding multipermutation codes. Multipermutations are permutations of a multiset that generally consist of duplicate entries. We first introduce a class of binary matrices called…
Polar codes are a class of capacity-achieving error correcting codes that have been selected for use in enhanced mobile broadband in the 3GPP 5th generation (5G) wireless standard. Most polar code research examines the original Arikan polar…
The current flash memory technology focuses on the cost minimization of its static storage capacity. However, the resulting approach supports a relatively small number of program-erase cycles. This technology is effective for consumer…
Motivated by communication channels in which the transmitted sequences are subject to random permutations, as well as by certain DNA storage systems, we study the error control problem in settings where the information is stored/transmitted…
The exponential growth in data generation and large-scale data analysis creates an unprecedented need for inexpensive, low-latency, and high-density information storage. This need has motivated significant research into multi-level memory…
Low-density parity-check (LDPC) codes are an important feature of several communication and storage applications, offering a flexible and effective method for error correction. These codes are computationally complex and require the…
The sum-rank metric naturally extends both the Hamming and rank metrics in coding theory over fields. It measures the error-correcting capability of codes in multishot matrix-multiplicative channels (e.g. linear network coding or the…
The current mobile applications have rapidly growing memory footprints, posing a great challenge for memory system design. Insufficient DRAM main memory will incur frequent data swaps between memory and storage, a process that hurts…
Motivated by recent interest in permutation arrays, we introduce and investigate the more general concept of frequency permutation arrays (FPAs). An FPA of length n=m lambda and distance d is a set T of multipermutations on a multiset of m…
A frequency permutation array (FPA) of length $n=m\lambda$ and distance $d$ is a set of permutations on a multiset over $m$ symbols, where each symbol appears exactly $\lambda$ times and the distance between any two elements in the array is…
The huge amount of data produced in the fifth-generation (5G) networks not only brings new challenges to the reliability and efficiency of mobile devices but also drives rapid development of new storage techniques. With the benefits of fast…
For discrete memoryless multiple-access channels, we propose a general definition of variable length codes with a measure of the transmission rates at the receiver side. This gives a receiver perspective on the multiple-access channel…
Molecular communication suffers from severe inter-symbol interference, which makes constrained coding essential for reliable transmission. Run-length-limited ISI-mitigation codes are attractive because they select low-weight constrained…
Many performance critical systems today must rely on performance enhancements, such as multi-port memories, to keep up with the increasing demand of memory-access capacity. However, the large area footprints and complexity of existing…
We propose a list-decoding scheme for reconstruction codes in the context of uniform-tandem-duplication noise, which can be viewed as an application of the associative memory model to this setting. We find the uncertainty associated with…
Permutation decoding is a technique which involves finding a subset $S$, called PD-set, of the permutation automorphism group of a code $C$ in order to assist in decoding. An explicit construction of $\left \lfloor{\frac{2^m-m-1}{1+m}}…
The capacity of next generation of cellular networks using femtocaches is studied when multihop communications and decentralized cache placement are considered. We show that the storage capability of future network User Terminals (UT) can…
Unary coding is useful but it is redundant in its standard form. Unary coding can also be seen as spatial coding where the value of the number is determined by its place in an array. Motivated by biological finding that several neurons in…
The Ulam distance of two permutations on $[n]$ is $n$ minus the length of their longest common subsequence. In this paper, we show that for every $\varepsilon>0$, there exists some $\alpha>0$, and an infinite set $\Gamma\subseteq…
We construct new families of multi-error-correcting quantum codes for the amplitude damping channel. Our key observation is that, with proper encoding, two uses of the amplitude damping channel simulate a quantum erasure channel. This…