TY - GEN
T1 - Erasure coding with the finite radon transform
AU - Normand, Nicolas
AU - Svalbe, Imants
AU - Parrein, Benoît
AU - Kingston, Andrew
PY - 2010
Y1 - 2010
N2 - The Mojette transform and the finite Radon transform (FRT) are discrete data projection methods that are exactly invertible and are computed using simple addition operations. Incorporation of a known level of redundancy into data and projection spaces enables the use of the FRT to recover the exact, original data when network packets are lost during data transmission. The FRT can also be shown to be Maximum Distance Separable (MDS). By writing the FRT transform in Vandermonde form, explicit expressions for discrete projection and inversion as matrix operations have been obtained. A cyclic, prime-sized Vandermonde form for the FRT approach is shown here to yield explicit polynomial expressions for the recovery of image rows from projected data and vice-versa. These polynomial solutions are consistent with the heuristic algorithms for "row-solving" that have been published previously. This formalism also opens the way to link "ghost" projections in FRT space and "anti-images" in data space that may provide a key to an efficient method of encoding and decoding general data sets in a systematic form.
AB - The Mojette transform and the finite Radon transform (FRT) are discrete data projection methods that are exactly invertible and are computed using simple addition operations. Incorporation of a known level of redundancy into data and projection spaces enables the use of the FRT to recover the exact, original data when network packets are lost during data transmission. The FRT can also be shown to be Maximum Distance Separable (MDS). By writing the FRT transform in Vandermonde form, explicit expressions for discrete projection and inversion as matrix operations have been obtained. A cyclic, prime-sized Vandermonde form for the FRT approach is shown here to yield explicit polynomial expressions for the recovery of image rows from projected data and vice-versa. These polynomial solutions are consistent with the heuristic algorithms for "row-solving" that have been published previously. This formalism also opens the way to link "ghost" projections in FRT space and "anti-images" in data space that may provide a key to an efficient method of encoding and decoding general data sets in a systematic form.
UR - http://www.scopus.com/inward/record.url?scp=77955043013&partnerID=8YFLogxK
U2 - 10.1109/WCNC.2010.5506385
DO - 10.1109/WCNC.2010.5506385
M3 - Conference contribution
SN - 9781424463985
T3 - IEEE Wireless Communications and Networking Conference, WCNC
BT - 2010 IEEE Wireless Communications and Networking Conference, WCNC 2010 - Proceedings
T2 - IEEE Wireless Communications and Networking Conference 2010, WCNC 2010
Y2 - 18 April 2010 through 21 April 2010
ER -