In this paper, we present an efficient strategy to enumerate the number of $k$ -cycles, $g\leq k

This paper presents a soft decoding scheme based on the binary representations transferred from the parity-check matrices (PCMs) for Reed-Solomon (RS) codes. Referring to the modified binary PCM that has a systematic part and a high-density part corresponding to the least reliable variable nodes (LRVNs) and the most reliable variable nodes (MRVNs), respectively, an informed dynamic scheduling method, called Nested-Polling Residual Belief Propagation (NP-RBP), is applied to the corresponding Tanner graph.

Data availability (DA) attack is a well-known problem in certain blockchains where users accept an invalid block with unavailable portions. Previous works have used LDPC and 2-D Reed Solomon (2D-RS) codes with Merkle trees to mitigate DA attacks. These codes perform well across various metrics such as DA detection probability and communication cost.

The minimum Hamming distance of a linear block code is the smallest number of bit changes required to transform one valid codeword into another. The code’s minimum distance determines the code’s error-correcting capabilities. Furthermore, The number of minimum weight codewords, a.k.a. error coefficient, gives a good comparative measure for the block error rate (BLER) of linear block codes with identical minimum distance, in particular at a high SNR regime under maximum likelihood (ML) decoding. A code with a smaller error coefficient would give a lower BLER.

Coded computing is a method for mitigating straggling workers in a centralized computing network, by using erasure-coding techniques. Federated learning is a decentralized model for training data distributed across client devices. In this work we propose approximating the inverse of an aggregated data matrix, where the data is generated by clients; similar to the federated learning paradigm, while also being resilient to stragglers. To do so, we propose a coded computing method based on gradient coding.

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.

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.

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.

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.

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.