In this part, we consider a practical problem from coding theory and communications. What is the error probability when a digital message is transmitted over a communications channel? The answer builds on two pieces of fundamental theory. From probability theory we need binomial distributions, and from statistics, we need estimation techniques.
All the classroom sessions revolve around one concrete example, with a specific code and a specific channel. We illuminate this problem using both statistical analysis, probability theory, and simulation. After you have seen the theory in practice, we hope you will find it relatively easy to learn further details from textbooks and video.
The classroom sessions will focus on the exercises as posted under each session in the table below.
At the end of the two-week period, you will need to submit the mandatory coursework. You will be able to reuse much of the material from the session exercises.
You will have to manage your own time and progress, using the available material, including video lectures, exercise sheets, textbook, google, classroom help etc. as best you can, to suit your preferred learning style.
Mandatory coursework is due Monday 2 February 8:15 am 2015.
|Session 1 (Wednesday 21 January 2015)||Videos||Time||Slides||Reading|
|Exercises||The Binary Symmetric Channel (A Bernouilli Trial)||MPEG4 / OGG||5:53|
|Words on the Channel||MPEG4 / OGG||4:40|
|Random Binary Vectors (Matlab Demo)||MPEG4 / OGG||5:45||summary||help rand in Matlab|
|Session 2 (Thursday 22 January 2015)||Videos||Time||Slides||Reading|
|Exercises||The Binomial Distribution (Error Words on the BSC)||MPEG4 / OGG||7:59||clean
|Frisvold and Moe pp. 100-104.|
|Expected Value for the Binomial Distribution||MPEG4 / OGG||4:16|
|Variance for the Binomial Distribution||MPEG4 / OGG||5:04|
|The Binomial Distribution in Matlab (Probability Distribution Function)||MPEG4 / OGG||5:52||summary||Matlab help: pdf, plot, bar, figure, hold|
|Comparing Probability Distributions (The Binomial Distribution in Matlab II)||MPEG4 / OGG||6:34||summary|
|Cummulative Distribution Function (The Binomial Distribution in Matlab III)||MPEG4 / OGG||7:51||summary||Frisvold and Moe pp. (55), 56-59, «vanlige forkortelser» p. 61; help cdf in Matlab|
|Session 3 (Friday 23 January 2015)||Videos||Time||Slides||Reading|
This session builds on Session 1, but can be done before Session 2 with little difficulty.
|The Hamming Code (A little coding theory)||MPEG4 / OGG||8:55||clean
|Finding Error Probabilities (Monte Carlo Simulation)||MPEG4 / OGG||8:35||clean
|Shiflet and Shiflet pp. 358-360(+)|
|Decoding Error Probabilities (A Case for Estimation)||MPEG4 / OGG||9:03||clean
|Session 4 (Wednesday 28 January 2015)||Videos||Time||Slides||Reading|
|Estimating Error Probabilities (Point Estimation)||MPEG4 / OGG||6:31||Frisvold and Moe pp. 145-147.|
|Binomial Probabilities (solving the exercise from the previous video)||MPEG4 / OGG||6:08|
|The Distribution of the Error Rate (The Normal Distribution)||MPEG4 / OGG||7:51||clean
|Frisvold and Moe pp. 120+, 132.|
|Session 5 (Thursday 29 January 2015)||Videos||Time||Slides||Reading|
|Confidence Intervals (Interval Estimation)||MPEG4 / OGG||7:35||Frisvold and Moe pp. 147-148, 163-165.|
|Estimating Binomial Proportions
(The Confidence Interval)
This video and the next have a certain overlap and can be viewed in arbitrary order.
|MPEG4 / OGG||9:59||Frisvold and Moe pp. 167-169.|
|For further depth, see separate page on estimation. The videos on that page will be appear at different stages of the module. For some students it may be useful to jump ahead.|
|Session 6 (Friday 30 January 2015)||Videos||Time||Slides||Reading|
|Review of previous material. Questions and answers.||Channels with Memory (Statistical Dependence)||MPEG4 / OGG||5:25||Frisvold and Moe pp. 36-38(+).|
|Session 7 (Wednesday 4 February 2015)||Videos||Time||Slides||Reading|
This session will review the first project, and we will generalise some of the ideas to estimation of the mean.
|Point Estimation (Introduction to Estimation and Statistical Inference)||MPEG4 / OGG||4:43|
|The Sample Mean (Point Estimation by Example)||MPEG4 / OGG||7:36|
|The Standard Error (The Random Nature of Estimators)||MPEG4 / OGG||5:10||clean
|Frisvold and Moe page 147|
|Interval Estimation (What is the Confidence Interval?)||MPEG4 / OGG||6:17||Frisvold and Moe pp. 147-148, 163-165.|
|Error Margin (Estimating the Mean with Known Variance)||MPEG4 / OGG||11:17||clean
|Frisvold and Moe pp. 149-150.|