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.

After reading the wikipedia page about Hamming, a common version is Hamming(7,4) which has 7 total bits, 4 data bits, and 3 parity bits.  This is a Single Error Correcting scheme.

But we have only 3 data bits.  So I assume what can be configured is a Hamming code with an extra parity bit to produce SECDEC:  Single Error Correcting, Double Error Detecting. 

Posted by Larry on 2018-04-28 07:19:46