Related papers: Pseudo-MDP Convolutional Codes for Burst Erasure C…
We study near optimal error correction codes for real-time communication. In our setup the encoder must operate on an incoming source stream in a sequential manner, and the decoder must reconstruct each source packet within a fixed playback…
Entanglement-assisted quantum error correcting codes (EAQECCs) play a significant role in protecting quantum information from decoherence and quantum noise. Recently, constructing entanglement-assisted quantum maximum distance separable…
In this paper, we employ the linear systems representation of a convolutional code to develop a decoding algorithm for convolutional codes over the erasure channel. We study the decoding problem using the state space description and this…
Erasure codes play an important role in storage systems to prevent data loss. In this work, we study a class of erasure codes called Multi-Erasure Locally Recoverable Codes (ME-LRCs) for flash memory array. Compared to previous related…
Maximum distance profile codes are characterized by the property that two trajectories which start at the same state and proceed to a different state will have the maximum possible distance from each other relative to any other…
Partial MDS (PMDS) and sector-disk (SD) codes are classes of erasure codes that combine locality with strong erasure correction capabilities. We construct PMDS and SD codes where each local code is a bandwidth-optimal regenerating MDS code.…
We present families of quantum error-correcting codes which are optimal in the sense that the minimum distance is maximal. These maximum distance separable (MDS) codes are defined over q-dimensional quantum systems, where q is an arbitrary…
In this paper we investigate the design of a low-delay robust streaming PIR scheme on coded data that is resilient to unresponsive or slow servers and can privately retrieve streaming data in a sequential fashion subject to a fixed decoding…
A Maximum Distance Separable code over an alphabet $F$ is defined via an encoding function $C:F^k \rightarrow F^n$ that allows to retrieve a message $m \in F^k$ from the codeword $C(m)$ even after erasing any $n-k$ of its symbols. The…
In this paper, we study binary constrained codes that are resilient to bit-flip errors and erasures. In our first approach, we compute the sizes of constrained subcodes of linear codes. Since there exist well-known linear codes that achieve…
We consider non-binary product codes with MDS components and their iterative row-column algebraic decoding on the erasure channel. Both independent and block erasures are considered in this paper. A compact graph representation is…
MDS array codes are widely used in storage systems due to their computationally efficient encoding and decoding procedures. An MDS code with $r$ redundancy nodes can correct any $r$ node erasures by accessing all the remaining information…
Convolutional network-error correcting codes (CNECCs) are known to provide error correcting capability in acyclic instantaneous networks within the network coding paradigm under small field size conditions. In this work, we investigate the…
We construct two-dimensional codes for correcting burst errors using the finite field Fourier transform. The encoding procedure is performed in the transformed domain using the conjugacy property of the finite field Fourier transform. The…
This paper focuses on error-correcting codes that can handle a predefined set of specific error patterns. The need for such codes arises in many settings of practical interest, including wireless communication and flash memory systems. In…
The problem of recovering from qubit erasures has recently gained attention as erasures occur in many physical systems such as photonic systems, trapped ions, superconducting qubits and circuit quantum electrodynamics. While several…
This paper studies the theory of linear analog error correction coding. Since classical concepts of minimum Hamming distance and minimum Euclidean distance fail in the analog context, a new metric, termed the "minimum (squared Euclidean)…
Maximum-distance separable (MDS) array codes with high rate and an optimal repair property were introduced recently. These codes could be applied in distributed storage systems, where they minimize the communication and disk access required…
Inner and outer bounds are derived on the optimal performance of fixed length block codes on discrete memoryless channels with feedback and errors-and-erasures decoding. First an inner bound is derived using a two phase encoding scheme with…
Most large-scale storage systems employ erasure coding to provide resilience against disk failures. Recent work has shown that tuning this redundancy to changes in disk failure rates leads to substantial storage savings. This process…