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In this paper, we first formulate a novel Chase Guruswami-Sudan algorithm which list corrects not only all errors among the Chase flipping symbols but also the number of errors up to the enhanced Johnson bound among remaining positions, for Reed-Solomon and $q$ -ary BCH codes. The enhanced Johnson bound is induced by shortening the code without those Chase flipping symbols. We next devise a novel Chase Kötter-Vardy algorithm for soft decision decoding of Reed-Solomon codes.

Motivated by applications in distributed storage, the notion of a locally recoverable code (LRC) was introduced a few years back. In an LRC, any coordinate of a codeword is recoverable by accessing only a small number of other coordinates. While different properties of LRCs have been well-studied, their performance on channels with random erasures or errors has been mostly unexplored. In this paper, we analyze the performance of LRCs over such stochastic channels.

We propose a new compression scheme for genomic data given as sequence fragments called reads. The scheme uses a reference genome at the decoder side only, freeing the encoder from the burdens of storing references and performing computationally costly alignment operations. The main ingredient of the scheme is a multi-layer code construction, delivering to the decoder sufficient information to align the reads, correct their differences from the reference, validate their reconstruction, and correct reconstruction errors.

Let $[q\rangle $ denote the integer set $\{0,1, {\ldots },q-1\}$ and let ${{\mathbb {B}}}=\{0,1\}$ . The problem of implementing functions $[q\rangle \rightarrow {{\mathbb {B}}}$ on content-addressable memories (CAMs) is considered. CAMs can be classified by the input alphabet and the state alphabet of their cells; for example, in binary CAMs, those alphabets are both ${{\mathbb {B}}}$ , while in a ternary CAM (TCAM), both alphabets are endowed with a “don’t care” symbol.

Distributed filtering is crucial in many applications such as localization, radar, autonomy, and environmental monitoring. The aim of distributed filtering is to infer time-varying unknown states using data obtained via sensing and communication in a network. This paper analyzes continuous-time distributed filtering with sensing and communication constraints. In particular, the paper considers a building-block system of two nodes, where each node is tasked with inferring a time-varying unknown state.

In literature, PIBMA, a linear-feedback-shift-register (LFSR) decoder, has been shown to be the most efficient high-speed decoder for Reed-Solomon (RS) codes. In this work, we follow the same design principles and present two high-speed LFSR decoder architectures for binary BCH codes, both achieving the critical path of one multiplier and one adder. We identify a key insight of the Berlekamp algorithm that iterative discrepancy computation involves only even-degree terms.

Low-capacity scenarios have become increasingly important in the technology of the Internet of Things (IoT) and the next generation of wireless networks. Such scenarios require efficient and reliable transmission over channels with an extremely small capacity. Within these constraints, the state-of-the-art coding techniques may not be directly applicable. Moreover, the prior work on the finite-length analysis of optimal channel coding provides inaccurate predictions of the limits in the low-capacity regime.

Straggler nodes are well-known bottlenecks of distributed matrix computations which induce reductions in computation/communication speeds. A common strategy for mitigating such stragglers is to incorporate Reed-Solomon based MDS (maximum distance separable) codes into the framework; this can achieve resilience against an optimal number of stragglers. However, these codes assign dense linear combinations of submatrices to the worker nodes.

We present a novel distributed computing framework that is robust to slow compute nodes, and is capable of both approximate and exact computation of linear operations. The proposed mechanism integrates the concepts of randomized sketching and polar codes in the context of coded computation. We propose a sequential decoding algorithm designed to handle real valued data while maintaining low computational complexity for recovery.

In this paper, we investigate the problem of decoder error propagation for spatially coupled low-density parity-check (SC-LDPC) codes with sliding window decoding (SWD). This problem typically manifests itself at signal-to-noise ratios (SNRs) close to capacity under low-latency operating conditions. In this case, infrequent but severe decoder error propagation can sometimes occur.