The ﬁrst pictures of Mars were taken at a resolution of 700 × 832 pixels. The images used 64 different shades of grey. The pictures were transmitted back to Earth by sending one pixel at a time, so we can think of a message as a single number between 0 and 63. The channel could send the two binary digits 0 and 1. Encoding each pixel as a string of 6 bits would not have worked well. A survey gave a probability of 0.05 that a bit would be ﬂipped by the channel, implying that about 26% of the image would be wrong.
It was acceptable for each pixel to be encoded by up to 32 bits, so Mariner sent a volume of more than five times of the original data. But by doing so error-detection and correction techniques could be used so that finally a picture had less than 100 incorrect pixels. Mariner transmitted over 7200 pictures of Mars like this.
Coding Theory is a branch of mathematics that uses Galois fields, polynomials, vector spaces and matrices.
|135,000,000 km far, sent with a 20 watt transmitter|