Related papers: Decoding of Convolutional Codes over the Erasure C…
When computing systems can tolerate the effects of errors or erasures in their communicated data values, they can trade this tolerance for improved resource efficiency. One method for enabling this tradeoff in the I/O subsystems of…
In this paper, we first introduce the concept of elementary linear subspace, which has similar properties to those of a set of coordinates. We then use elementary linear subspaces to derive properties of maximum rank distance (MRD) codes…
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…
In order to scale economically, data centers are increasingly evolving their data storage methods from the use of simple data replication to the use of more powerful erasure codes, which provide the same level of reliability as replication…
Maximum distance separable (MDS) codes are optimal error-correcting codes in the sense that they provide the maximum failure-tolerance for a given number of parity nodes. Suppose that an MDS code with $k$ information nodes and $r=n-k$…
The column Hamming distance of a convolutional code determines the error correction capability when streaming over a class of packet erasure channels. We introduce a metric known as the column sum rank, that parallels column Hamming…
Linear complementary dual (LCD) maximum distance separable (MDS) codes are constructed to given specifications. For given $n$ and $r<n$, with $n$ or $r$ (or both) odd, MDS LCD $(n,r)$ codes are constructed over finite fields whose…
This paper tackles two problems that fall under the study of coding for insertions and deletions. These problems are motivated by several applications, among them is reconstructing strands in DNA-based storage systems. Under this paradigm,…
We consider error decoding of locally repairable codes (LRC) and partial MDS (PMDS) codes through interleaved decoding. For a specific class of LRCs we investigate the success probability of interleaved decoding. For PMDS codes we show that…
In this paper we present a concrete algebraic construction of a novel class of convolutional codes. These codes are built upon generalized Vandermonde matrices and therefore can be seen as a natural extension of Reed-Solomon block codes to…
We consider the problem of optimally decoding a quantum error correction code -- that is to find the optimal recovery procedure given the outcomes of partial "check" measurements on the system. In general, this problem is NP-hard. However,…
This paper presents a new construction of error correcting codes which achieves optimal recovery of a streaming source over a packet erasure channel. The channel model considered is the sliding window erasure model, with burst and arbitrary…
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 construct error correcting codes for jointly transmitting a finite set of independent messages to an 'informed receiver' which has prior knowledge of the values of some subset of the messages as side information. The transmitter is…
In this paper, we propose a very deep fully convolutional encoding-decoding framework for image restoration such as denoising and super-resolution. The network is composed of multiple layers of convolution and de-convolution operators,…
In this paper, we introduce a novel class of pre-transformed polar codes, termed as deep polar codes. We first present a deep polar encoder that harnesses a series of multi-layered polar transformations with varying sizes. Our approach to…
The noise model of deletions poses significant challenges in coding theory, with basic questions like the capacity of the binary deletion channel still being open. In this paper, we study the harder model of worst-case deletions, with a…
We introduce a new erasure decoder that applies to arbitrary quantum LDPC codes. Dubbed the cluster decoder, it generalizes the decomposition idea of Vertical-Horizontal (VH) decoding introduced by Connelly et al. in 2022. Like the VH…
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…
We consider a communication problem in which an update of the source message needs to be conveyed to one or more distant receivers that are interested in maintaining specific linear functions of the source message. The setting is one in…