I'm preparing for my final year project in school and i plan on working on the implementation of Residue Number System in Image Processing. I found this thesis online by Pallab Maji here:
http://ethesis.nitrkl.ac.in/2831/1/Thesis_Final_App_of_RNS_in_Comm__SP.pdf
and i'm currently stuck on generating a Moduli Set, however i checked page 17 which is about Consecutive Moduli Selection and with this
Theorem:
Let ${N_{1}, N_{2}, N_{3} ... N_{k}}$ be a set of k consecutive co-prime numbers. Let these numbers be expressed as : $N_{i} = N_{1} − m_{i−1}$
for i=1,2,3 . . . k, where $m_{i−1} > m_{i−2} > m_{i−3} > ...m_{i−k} > 0$. Let $N_{k+1}$ be another number that can be added to the set of co-prime numbers, i.e. $N_{k+1} = N_{1} − m_{k}$ then $N_{k+1}$ will be co-prime if $gcd(N_{i},m_{k} − m_{i−1}) = 1$, for i=1,2,3 . . . k.
I've been able to identify $N_{1} = 2^{m} - 1$.
Given an example like:
Choose co-prime numbers with b=32 and k=4, i.e., close to $2^{8} (= 256)$, gives us P = {255, 254, 253, 251} using the consecutive moduli selection.
It's known that $m = b/k$ so $m = 8$ therefore,
$N_{1} = 2^{m} - 1 = 2^{8} - 1 = 255$
$N_{2} = N_{1} - m_{i-1}$
So i've not been able to identify the values of $m_{i - 1},m_{i - 2},....$. and i would like to calculate the remaining values for $N_{2}$ to $N_{4}$
Any help would be greatly appreciated