11266

Probability in a Communication Channel

In a binary communication system, the symbols 0 and 1 are sent through a channel, but noise can switch 1 to 0 or vice versa with certain probabilities. The error can be estimated by Bayes' rule.
Let be the event of sending 0 (represented by ) and be the event of sending 1 (represented by ), with corresponding probabilities and . On the receiving side, and are the events of receiving 0 or 1. Represented by and , is the probability of receiving 1 given that 0 was sent, is the probability of receiving 1 given that 1 was sent, is the conditional probability of given , and so on.

THINGS TO TRY

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]

DETAILS

Reference
[1] P. Z. Peebles, Jr., Probability, Random Variables and Random Signal Principles, 4th ed., New York: McGraw-Hill, 2000.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2017 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+