Related papers: Explicit Rate-Optimal Streaming Codes with Smaller…
This paper provides simple lower bounds on the number of iterations which is required for successful message-passing decoding of some important families of graph-based code ensembles (including low-density parity-check codes and variations…
Random Linear Streaming Codes (RLSCs) can dramatically reduce the queuing delay of block codes in real-time services. In this paper, we aim to explore the fundamental limit of large-field-size RLSCs in stochastic symbol erasure channels…
We give an $\widetilde{O}(\sqrt{n})$-space single-pass $0.483$-approximation streaming algorithm for estimating the maximum directed cut size (Max-DICUT) in a directed graph on $n$ vertices. This improves over an $O(\log n)$-space $4/9 <…
The perfect space-time block codes (STBCs) are based on four design criteria - full-rateness, non-vanishing determinant, cubic shaping and uniform average transmitted energy per antenna per time slot. Cubic shaping and transmission at…
The two-receiver broadcast packet erasure channel with feedback and memory is studied. Memory is modeled using a finite-state Markov chain representing a channel state. Two scenarios are considered: (i) when the transmitter has causal…
This paper addresses the issue of design of low-rate sparse-graph codes with linear minimum distance in the blocklength. First, we define a necessary condition which needs to be satisfied when the linear minimum distance is to be ensured.…
The sub-packetization $\ell$ and the field size $q$ are of paramount importance in the MSR array code constructions. For optimal-access MSR codes, Balaji et al. proved that $\ell\geq s^{\left\lceil n/s \right\rceil}$, where $s = d-k+1$.…
A prescription to calculate the minimum number of bits needed for binary strip detector readout is presented. This permits a systematic analysis of the readout efficiency relative to this theoretical minimum number of bits. Different level…
Erasure codes are an efficient means of storing data across a network in comparison to data replication, as they tend to reduce the amount of data stored in the network and offer increased resilience in the presence of node failures. The…
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. On one end of this spectrum of…
In this paper, a streaming transmission setup is considered where an encoder observes a new message in the beginning of each block and a decoder sequentially decodes each message after a delay of $T$ blocks. In this streaming setup, the…
Erasure codes have emerged as an efficient technology for providing data redundancy in distributed storage systems. However, it is a challenging task to repair the failed storage nodes in erasure-coded storage systems, which requires large…
We construct a new family of explicit codes that are list decodable to capacity and achieve an optimal list size of $O(\frac{1}{\epsilon})$. In contrast to existing explicit constructions of codes achieving list decoding capacity, our…
Erasure codes have been widely considered a promising solution to enhance data reliability at low storage costs. However, in modern geo-distributed storage systems, erasure codes may incur high data access latency as they require data…
Spatially-coupled (SC) codes, known for their threshold saturation phenomenon and low-latency windowed decoding algorithms, are ideal for streaming applications. They also find application in various data storage systems because of their…
A rateless code encodes a finite length information word into an infinitely long codeword such that longer prefixes of the codeword can tolerate a larger fraction of errors. A rateless code achieves capacity for a family of channels if, for…
Exact-repair regenerating codes are considered for the case (n,k,d)=(4,3,3), for which a complete characterization of the rate region is provided. This characterization answers in the affirmative the open question whether there exists a…
Folded Reed-Solomon codes are an explicit family of codes that achieve the optimal trade-off between rate and error-correction capability: specifically, for any $\eps > 0$, the author and Rudra (2006,08) presented an $n^{O(1/\eps)}$ time…
We consider the stationaly memoryless channels with input cost. We prove that for transmission rates above the capacity the correct probability of decoding tends to zero exponentially as the block length $n$ of codes tends to infinity. In…
List-decodability of Reed-Solomon codes has received a lot of attention, but the best-possible dependence between the parameters is still not well-understood. In this work, we focus on the case where the list-decoding radius is of the form…