Before reading this tutorial, make sure you have read the tutorial on Convolutional coding and Modulation. This is essential.
What does a rate 1/2 convolutional code do? It takes one bit and puts out 2 bits. This is something that is done at the digital level. These 2 bits are then modulated (i.e. converted to analog form via a carrier) and transmitted. The coding is an digital function and modulation which is an analog function are done separately and independently in most modulations.
In Trellis Coded Modulation (TCM), we combine coding and modulation in one function.
Concepts to know before TCM can be understoodEuclidean Distance
This is the straight line distance between two points. For a point p1 at (x1,
y1) and another point p2 at (x2, y2), the Euclidean distance is give by
sqrt((x1 - x2) ² + (y1 - y2) ²).
This is an analog concept, the concept of distance as we normally perceive
it in the world of real numbers.
Hamming distance
The concept of distance in the world of binary numbers is different. Here
are the co-ordinates of point p1 in the binary world,
011011
another point, p2
101101
The distance between these is the number of places these two numbers differ.
And that number for this example is 4. This distance is called the Hamming
distance. The distance would be zero, if two numbers were the same.
We distinguish these two types of distances by recognizing that one belongs
to the analog world of real numbers and the other to the binary world.
In modulated signals, both types of distances are presnt. First when the
data is in baseband digital form, we have Hamming
distance
between adjacent words (bit sets), and then when the signal is mapped to
symbols, we have Euclidean
distance between the symbols (the small packets of analog carrier). The
value of both of these distances is a factor in the BER experienced by
the signal.
To reduce BER we want the combination of these two distances to be as large as possible. Think of the receiver as a poor-sighted person, so we want all adjacent symbols to be as far apart as possible so the receiver with its poor eye sight can tell them apart with least probability of error. This concept of farapart includes both Hamming and Euclidean distances in TCM.
In work, to be continued…..
In the meanwhile see these links.
http://www.columbia.edu/~rdg74/ee6713/Trellis_Coded_Modulation.PDF
http://www.google.com/search?sourceid=navclient&ie=UTF-8&oe=UTF-8&q=tcm+trellis+coded+modulation
http://www.comlab.hut.fi/opetus/311/tcm_1.pdf
http://www.sce.carleton.ca/courses/sysc-5504/notes/pdf/tcm.pdf
http://ece-classweb.ucsd.edu/archive/summer02/ece259cn/Main/TCM.pdf
http://www.signal.uu.se/Courses/CourseDirs/ModDemKod/2004/LectureSlides/lecture12.pdf
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