Implementation of Reed Solomon Code Over GF(9) and 9-Ary Symmetric Channel

Reed-Solomon and related codes have recently become very important for erasure correction in large disk arrays used in data centers. In this paper, we will implement a 3-error correcting Reed-Solomon encoder and decoder over the field GF(9) generated by the primitive polynomial D^2 + D + 2 over GF(3) and the decoding is carried out by the Berlekamp. We simulate the encoder and decoder using Monte-Carlo simulations over the 9-ary symmetric channel that outputs the correct symbol with probability (1-p), and outputs one of the other 8 possible incorrect symbols with probability p/8. Then, we compare the simulated probability of symbol error P(E) of out code with the union upper bound.

LoRa Channel Characterization for Flexible and High Reliability Adaptive Data Rate in Multiple Gateways Networks

We characterize the LoRa channel in terms of multi-path fading, loss burstiness, and assess the benefits of Forward Error Correction as well as the influence of frame length. We make these observations by synthesizing extensive experimental measurements realized with The Things Network in a medium size city. We then propose to optimize the LoRaWAN Adaptive Data Rate algorithm based on this refined LoRa channel characterization and taking into account the LoRaWAN inherent macro-diversity from multi-gateway reception. Firstly, we propose ADRopt, which adjusts Spreading Factor and frame repetition number to maintain the communication below a target Packet Error Rate ceiling with optimized Time-On-Air. Secondly, we propose ADRIFECC, an extension of ADRopt in case an Inter-Frame Erasure Correction Code is available. The resulting protocol provides very high reliability even over low quality channels, with comparable Time on Air and similar downlink usage as the currently deployed mechanism. Simulations corroborate the analysis, both over a synthetic random wireless link and over replayed real-world packet transmission traces.

Minimum-storage regenerating codes resistant to special adversary

Introduction: In order to deal with temporarily unavailable nodes in a distributed storage system, engineers apply special classes of erasure correction codes. These codes allow you to repair a temporarily unavailable node by downloading small amounts of data from the remaining ones. However, this creates safety threats in the presence of an eavesdropper. Purpose: Introducing a new mathematical model in which the eavesdropper has a limited access to all nodes in the system, and developing codes resistant to it. Methods: Information-theoretic arguments, and mixing information symbols with random ones by systematic Reed — Solomon code. Results: We introduced a new mathematical model of an eavesdropper with limited access to all nodes in a distributed storage system. Note that the proposed eavesdropper is passive, being unable to change the accessed data. We found parameters for optimal regenerating codes resistant to such adversary, and provided a technique to ensure necessary resistance. As a result, we obtained the construction of optimal minimum storage regenerating codes resistant to such adversary. Practical relevance: The proposed constructions can provide resistance to adversary while ensuring effective data repair.