Note: Correction to the 1997 tutorial on Reed–Solomon coding

In 1997, SPE published a tutorial by Plank [19] on implementi ng Reed-Solomon codes for erasure correction in redundant data storage systems. The motivation of this tutori al was to present these codes, which are typically described mathematically by coding theorists, in a way accessible to t he programmers who need to implement them. The tutorial as published presented an information dispersal matrix A, which does not have the properties claimed – that the deletion of anym rows results in an invertable n n matrix. The purpose of this note is to present a correct infor mation dispersal matrix that has the desired properties, and to put the work in current context.

[1]  James S. Plank,et al.  A practical analysis of low-density parity-check erasure codes for wide-area storage applications , 2004, International Conference on Dependable Systems and Networks, 2004.

[2]  Mark Watson,et al.  Forward Error Correction (FEC) Building Block , 2007, RFC.

[3]  Mark Handley,et al.  The Use of Forward Error Correction (FEC) in Reliable Multicast , 2002, RFC.

[4]  Antony I. T. Rowstron,et al.  Storage management and caching in PAST, a large-scale, persistent peer-to-peer storage utility , 2001, SOSP.

[5]  Ben Y. Zhao,et al.  OceanStore: an architecture for global-scale persistent storage , 2000, SIGP.

[6]  Witold Litwin,et al.  LH*RS: a high-availability scalable distributed data structure using Reed Solomon Codes , 2000, SIGMOD '00.

[7]  Michael Mitzenmacher,et al.  Accessing multiple mirror sites in parallel: using Tornado codes to speed up downloads , 1999, IEEE INFOCOM '99. Conference on Computer Communications. Proceedings. Eighteenth Annual Joint Conference of the IEEE Computer and Communications Societies. The Future is Now (Cat. No.99CH36320).

[8]  P.J.M. Hayinga Energy efficiency of error correction on wireless systems , 1999, WCNC. 1999 IEEE Wireless Communications and Networking Conference (Cat. No.99TH8466).

[9]  Paul J. M. Havinga,et al.  Energy efficiency of error correction on wireless systems , 1999, WCNC.

[10]  Michael Luby,et al.  A digital fountain approach to reliable distribution of bulk data , 1998, SIGCOMM '98.

[11]  Luigi Rizzo,et al.  RMDP: an FEC-based reliable multicast protocol for wireless environments , 1998, MOCO.

[12]  Michael Mitzenmacher,et al.  Analysis of random processes via And-Or tree evaluation , 1998, SODA '98.

[13]  James S. Plank,et al.  A tutorial on Reed–Solomon coding for fault‐tolerance in RAID‐like systems , 1997, Softw. Pract. Exp..

[14]  Daniel A. Spielman,et al.  Practical loss-resilient codes , 1997, STOC '97.

[15]  Luigi Rizzo,et al.  Effective erasure codes for reliable computer communication protocols , 1997, CCRV.

[16]  James S. Plank,et al.  Improving the performance of coordinated checkpointers on networks of workstations using RAID techniques , 1996, Proceedings 15th Symposium on Reliable Distributed Systems.

[17]  Marek Karpinski,et al.  An XOR-based erasure-resilient coding scheme , 1995 .

[18]  Garth A. Gibson,et al.  RAID: high-performance, reliable secondary storage , 1994, CSUR.

[19]  Garth A. Gibson Redundant disk arrays: Reliable, parallel secondary storage. Ph.D. Thesis , 1990 .

[20]  Randy H. Katz,et al.  Failure correction techniques for large disk arrays , 1989, ASPLOS III.

[21]  Michael O. Rabin,et al.  Efficient dispersal of information for security, load balancing, and fault tolerance , 1989, JACM.

[22]  J.L. Massey The theory of error-correcting codes , 1980, Proceedings of the IEEE.

[23]  F. MacWilliams,et al.  The Theory of Error-Correcting Codes , 1977 .

[24]  Franklin Lowenthal Linear algebra with linear differential equations , 1974 .