In the era of artificial intelligence and big data, the demand for data processing has surged, leading to larger datasets and computation capability. Distributed machine learning (DML) has been introduced to address this challenge by distributing tasks among multiple workers, reducing the resources required for each worker. However, in distributed systems, the presence of slow machines, commonly known as stragglers, or failed links can lead to prolonged runtimes and diminished performance. This survey explores the application of coding techniques in DML and coded edge computing in the distributed system to enhance system speed, robustness, privacy, and more. Notably, the study delves into coding in Federated Learning (FL), a specialized distributed learning system. Coding involves introducing redundancy into the system and identifying multicast opportunities. There exists a tradeoff between computation and communication costs. The survey establishes that coding is a promising approach for building robust and secure distributed systems with low latency.

Vehicle-to-vehicle (V2V) communication has gained significant attention in the field of intelligent transportation systems. In this paper, we focus on communication scenarios involving vehicles moving in the same and opposite directions. Specifically, we model a V2V network as a dynamic multi-source single-sink network with two-way lanes. To address rapid changes in network topology, we employ random linear network coding (RLNC), which eliminates the need for knowledge of the network topology. We begin by deriving the lower bound for the generation probability. Through simulations, we analyzed the probability distribution and cumulative probability distribution of latency under varying packet loss rates and batch sizes. Our results demonstrated that our RLNC scheme significantly reduced the communication latency, even under challenging channel conditions, when compared to the non-coding case.

In large-scale parallel computing systems, machines and the network suffer from non-negligible faults, often leading to system crashes. The traditional method to increase reliability is to restart the failed jobs. To avoid unnecessary time wasted on reboots, we propose an optimal scheduling strategy to enable fault-tolerant reliable computation to protect the integrity of computation. Specifically, we determine the optimal redundancy-failure rate tradeoff to incorporate redundancy into parallel computing units running multiple-precision arithmetics, like the Chinese Remainder Theorem, that are useful for applications such as asymmetric cryptography and fast integer multiplication. Inspired by network coding in distributed storage for disk failures, we propose coding matrices to strategically map partial computation to available computing units, so that the central unit can reliably reconstruct the results of any failed machine without recalculations to yield the final correct computation output. We propose optimization-based algorithms to efficiently construct the optimal coding matrices subject to fault tolerance specifications. Performance evaluation demonstrates that the optimal scheduling effectively reduces the overall running time of parallel computing while resisting wide-ranging failure rates.

In a conventional Symmetric Multilevel Diversity Coding System (SMDCS), sources of varying importance are encoded by multiple encoders and a level- k decoder, if given access to any k encoders, can decode the first k most important sources. In practical large-scale applications like Non-terrestrial Networks, sinks (e.g., land earth stations) may be only interested in some functions of the sources (e.g., orbiting satellites) rather than the sources themselves. This paper introduces linear network function computations into the SMDCS, where a level- k decoder requests a linear function of the first k sources. The coding rate region of the 3-encoder (i.e., 3-level) SMDCS with linear computations (SMDCS-LC) was obtained. It is shown that when the coefficient vectors are dependent, coding between sources may help in reducing the information under transmission by encoders. However, when they are independent, superposition (i.e., sources-separated) coding is optimal. Furthermore, the minimum sum rate of the generic L -level SMDCS-LC is obtained. This can find applications like federated learning aggregation in Non-Terrestrial Networks.

This paper proposes a novel polar coding scheme tailored for indoor visible light communication (VLC) systems. Simulation results demonstrate a significant reduction in bit error rate (BER) compared to uncoded transmission, with a coding gain of at least 5 dB. Furthermore, the reliable communication area of the VLC system is substantially extended. Building on this foundation, this study explores the joint design of polar codes and physical-layer network coding (PNC) for VLC systems. Simulation results illustrate that the BER of our scheme closely approaches that of the conventional VLC relay scheme. Moreover, our approach doubles the throughput, cuts equipment expenses in half, and boosts effective bit rates per unit time-slot twofold. This proposed design noticeably advances the performance of VLC systems and is particularly well-suited for scenarios with low-latency demands.