相关论文: Optimal Codes Correcting a Burst of Deletions of V…

The interest in channel models in which the data is sent as an unordered set of binary strings has increased lately, due to emerging applications in DNA storage, among others. In this paper we analyze the minimal redundancy of binary codes…

The explosion of the amount of data stored in cloud systems calls for more efficient paradigms for redundancy. While replication is widely used to ensure data availability, erasure correcting codes provide a much better trade-off between…

The high repair cost of (n,k) Maximum Distance Separable (MDS) erasure codes has recently motivated a new class of codes, called Regenerating Codes, that optimally trade off storage cost for repair bandwidth. In this paper, we address…

We consider a real-time streaming system where messages are created sequentially at the source, and are encoded for transmission to the receiver over a packet erasure link. Each message must subsequently be decoded at the receiver within a…

Erasures are the primary type of errors in physical systems dominated by leakage errors. While quantum error correction (QEC) using stabilizer codes can combat erasure errors, it remains unknown which constructions achieve capacity…

In distributed optimization problems, a technique called gradient coding, which involves replicating data points, has been used to mitigate the effect of straggling machines. Recent work has studied approximate gradient coding, which…

We consider the decoding of linear and array codes from errors when we are only allowed to download a part of the codeword. More specifically, suppose that we have encoded $k$ data symbols using an $(n,k)$ code with code length $n$ and…

As sensing and instrumentation play an increasingly important role in systems controlled over wired and wireless networks, the need to better understand delay-sensitive communication becomes a prime issue. Along these lines, this article…

In this paper we consider the problem of encoding data into \textit{repeat-free} sequences in which sequences are imposed to contain any $k$-tuple at most once (for predefined $k$). First, the capacity of the repeat-free constraint are…

In this work, we derive upper bounds on the cardinality of tandem duplication and palindromic deletion correcting codes by deriving the generalized sphere packing bound for these error types. We first prove that an upper bound for tandem…

This paper studies on the cardinality of perfect multi deletion binary codes. The lower bound for any perfect deletion code with the fixed code length and the number of deletions, and the asymptotic achievable of Levenshtein's upper bound…

This paper explores list decoding of convolutional and polar codes for short messages such as those found in the 5G physical broadcast channel. A cyclic redundancy check (CRC) is used to select a codeword from a list of likely codewords.…

Data storage applications require erasure-correcting codes with prescribed sets of dependencies between data symbols and redundant symbols. The most common arrangement is to have $k$ data symbols and $h$ redundant symbols (that each depends…

A $(k,\delta,\epsilon)$-locally decodable code $C: F_{q}^{n} \to F_{q}^{N}$ is an error-correcting code that encodes each message $\vec{x}=(x_{1},x_{2},...,x_{n}) \in F_{q}^{n}$ to $C(\vec{x}) \in F_{q}^{N}$ and has the following property:…

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 presents flexible storage codes, a class of error-correcting codes that can recover information from a flexible number of storage nodes. As a result, one can make a better use of the available storage nodes in the presence of…

We derive the optimum second-order coding rates, known as second-order capacities, for erasure and list decoding. For erasure decoding for discrete memoryless channels, we show that second-order capacity is $\sqrt{V}\Phi^{-1}(\epsilon_t)$…

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…

Imperfect measurement can degrade a quantum error correction scheme. A solution that restores fault tolerance is to add redundancy to the process of syndrome extraction. In this work, we show how to optimize this process for an arbitrary…

We present a semidefinite program optimization approach to quantum error correction that yields codes and recovery procedures that are robust against significant variations in the noise channel. Our approach allows us to optimize the…