Related papers: Coding for Locality in Reconstructing Permutations
We prove a lower and an upper bound on the number of block moves necessary to sort a permutation. We put our results in contrast with existing results on sorting by block transpositions, and raise some open questions.
Permutation is the different arrangements that can be made with a given number of things taking some or all of them at a time. The notation P(n,r) is used to denote the number of permutations of n things taken r at a time. Permutation is…
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…
Node failures are inevitable in distributed storage systems (DSS). To enable efficient repair when faced with such failures, two main techniques are known: Regenerating codes, i.e., codes that minimize the total repair bandwidth; and codes…
We approach index coding as a special case of rate-distortion with multiple receivers, each with some side information about the source. Specifically, using techniques developed for the rate-distortion problem, we provide two upper bounds…
Distributed storage systems must handle both data heterogeneity, arising from non-uniform access demands, and device heterogeneity, caused by time-varying node reliability. In this paper, we study convertible codes, which enable the…
We consider stamps with different values (denominations) and same dimensions, and an envelope with a fixed maximum number of stamp positions. The local postage stamp problem is to find the smallest value that cannot be realized by the sum…
Network codes designed specifically for distributed storage systems have the potential to provide dramatically higher storage efficiency for the same availability. One main challenge in the design of such codes is the exact repair problem:…
Digital contents in large scale distributed storage systems may have different reliability and access delay requirements, and for this reason, erasure codes with different strengths need to be utilized to achieve the best storage…
Error-correcting codes resilient to synchronization errors such as insertions and deletions are known as insdel codes. Due to their important applications in DNA storage and computational biology, insdel codes have recently become a focal…
To reduce computational complexity and delay in randomized network coded content distribution, and for some other practical reasons, coding is not performed simultaneously over all content blocks, but over much smaller, possibly overlapping…
We give new lower bounds for $M(n,d)$, for various positive integers $n$ and $d$ with $n>d$, where $M(n,d)$ is the largest number of permutations on $n$ symbols with pairwise Hamming distance at least $d$. Large sets of permutations on $n$…
Existing decentralized coded caching solutions cannot guarantee small loads in the general scenario with arbitrary file sizes and cache sizes. In this paper, we propose an optimization framework for decentralized coded caching in the…
Coded distributed computing introduced by Li et al. in 2015 is an efficient approach to trade computing power to reduce the communication load in general distributed computing frameworks such as MapReduce. In particular, Li et al. show that…
We consider a distributed source coding system in which several observations are communicated to the decoder using limited transmission rate. The observations must be separately coded. We introduce a robust distributed coding scheme which…
The goal of this paper is to set a constraint programming framework to solve lot-sizing problems. More specifically, we consider a single-item lot-sizing problem with time-varying lower and upper bounds for production and inventory. The…
We consider the design of regenerating codes for distributed storage systems that enjoy the property of local, exact and uncoded repair, i.e., (a) upon failure, a node can be regenerated by simply downloading packets from the surviving…
We describe the limit (for two topologies) of large uniform random square permutations, i.e., permutations where every point is a record. The starting point for all our results is a sampling procedure for asymptotically uniform square…
In this paper we describe a variation of the classical permutation decoding algorithm that can be applied to any affine-invariant code with respect to certain type of information sets. In particular, we can apply it to the family of…
List-decoding of Reed-Solomon (RS) codes beyond the so called Johnson radius has been one of the main open questions since the work of Guruswami and Sudan. It is now known by the work of Rudra and Wootters, using techniques from high…