In the new world of CubeSat's and the growing market of satellite photography, data transmission of images continues to be lossy and two-way communication consumes hardware space. Islamic geometric pattern magic squares can be reconstructed with large portions of data missing.
What it does
This program is a PoC for a future package class. The MMU program implements the use of Pan-Magic Squares as a coding mechanism for 8-bit data. The traditional single-error correcting coding schema for 8-bit data is 17-bits long and allows for 1 error at a maximum sustainable error rate of 1 in 17. Using magic squares with error-detecting coding schemas, an 80-bit translation can be made. A pan-magic square can be seen below:
| 2 5 11 12|
|15 8 6 1|
| 4 3 13 10|
| 9 14 0 7|
Using rules for pan-magic square construction, this square could be reconstructed with the following worst-case input:
| 2 * * 12|
| * 8 * *|
| * * 13 *|
| * * * 7|
There are 192 pan-magic squares, which is 64 short of 256, but we attempt a best match for our reconstruction method, with priority given to values 0-192. Our values 193-256 are not pan-magic squares, so they require at least 9 matches.
To attain a magic square with possible accept and deny values, we encode the required 4-bit 0-16 value as a 5-bit error detecting even parity value.
The resulting coding schema translates 8-bits to 80-bits rather than 17-bits, but allots for a floor of 11 bits lost of 80 for 3/4 of data, and a floor off 6 bits lost of 80 for 1/4 of data, or an average floor of 12.1% data loss.
As shown in the documentation for reconstruct, the floor for error loss if worst case bits are lost is 7.5%, and if best case bits are lost, is 68.75%
In future iterations beyond PoC we plan to implement data validation, user error detection, and an efficient coding mapping of non-pan-magic squares to infrequent mapped data (in other words, applying the codes with a floor of 7.5% data loss to the most infrequently occurring data, and a floor of 12.5% data loss to the rest).
How we built it
We first generated and numbered 256 magic squares into a text document, then built a program to load an encoding and decoding dictionary scheme. The program MMU.py was written to apply these schemes to messages, which are strings in this PoC.
Challenges we ran into
Proving that magic squares can tolerate losses and generating those squares. Finding a way to transmit bits over bytes in python UDP.
What's next for MNU
Establishing encoding of images rather than strings. Data validation. Exception handling. Implementation beyond PoC (python library creation).