A certain telemetry message consists of 960 binary digits, 40% of them being zeros, randomly distributed.
Transmitted thru not-perfectly-reliable media, on the average 35% of "ones" become zeroes and 20% of zeroes become "ones".
1. What is the probability of randomly chosen bit to arrive undistorted?
A self-correcting algorithm is applied adding 4 additional bits to each 3-bit "character"(see Hamming on the web). The new block is transmitted through the same faulty media, decoded to get the message only and the same question is asked:
2.What is the probability of randomly chosen bit to arrive undistorted?
Rem: If solved by simulation, define the achieved accuracy.
Your ideas about improving the "reliability figure" will be welcome.
Let P(0) and P(1) be prob of a zero bit and a 1 bit respectively.
Prob (good random bit) = P(0)*P(good 0) + P(1)*P(good 1)
= 0.4 * 0.8 + 0.6 * 0.65
= 0.32 + 0.39
= 0.71 or 71%
Part 2 is trickier because each 3 bit group now has 4 correcting bits and all of the 7 bits in a group are subject to faulty transmission. However, the correcting codes should correct transmission errors.
Need to cogitate a bit there over a cup of Java.