To harness the ever growing capacity and decreasing cost of storage, providing an abstraction of dependable storage in the presence of crash-stop and Byzantine failures is compulsory. We propose a decentralized Reed Solomon coding mechanism with minimum communication overhead. Using a progressive data retrieval scheme, a data collector contacts only the necessary number of storage nodes needed to guarantee data integrity. The scheme gracefully adapts the cost of successful data retrieval to the number of storage node failures. Moreover, by leveraging the Welch-Berlekamp algorithm, it avoids unnecessary computations. Compared to the state-of-the-art decoding scheme, the implementation and evaluation results show that our progressive data retrieval scheme has up to 35 times better computation performance for low Byzantine node rates. Additionally, the communication cost in data retrieval is derived analytically and corroborated by Monte-Carlo simulation results. Our implementation is flexible in that the level of redundancy it provides is independent of the number of data generating nodes, a requirement for distributed storage systems
Preface. List of Program Files. List of Laboratory Exercises. List of Algorithms. List of Figures. List of Tables. List of Boxes. PART I: INTRODUCTION AND FOUNDATIONS. 1. A Context for Error Correcting Coding. PART II: BLOCK CODES. 2. Groups and Vector Spaces. 3. Linear Block Codes. 4. Cyclic Codes, Rings, and Polynomials. 5. Rudiments of Number Theory and Algebra. 6. BCH and Reed-Solomon Codes: Designer Cyclic Codes. 7. Alternate Decoding Algorithms for Reed-Solomon Codes. 8. Other Important Block Codes. 9. Bounds on Codes. 10. Bursty Channels, Interleavers, and Concatenation. 11. Soft-Decision Decoding Algorithms. PART III: CODES ON GRAPHS. 12. Convolution Codes. 13. Trefils Coded Modulation. PART IV: INTERATIVELY DECODED CODES. 14. Turbo Codes. 15. Low-Density Parity-Check Codes. 16. Decoding Algorithms on Graphs. PART V: SPACE-TIME CODING. 17. Fading Channels and Space-Time Coding. References. Index.