If ‘r’ is the code rate and ‘d free ’ is the free distance of the

| If ‘r’ is the code rate and ‘d_free’ is the free distance of the convolutional code, then the Asymptotic codic gain of a binary symmetric channel is:

A. \(10{\log _{10}}\left( {\frac{{{d_{free}}.r}}{2}} \right)\left( {dB} \right)\)

B. 10 log10(dfree.r) (dB)

C. \(10\;{\log _{10}}\left( {\frac{{{d_{free}}}}{{2.r}}} \right)\left( {dB} \right)\)

D. \(10\log \left( {\frac{{{d_{free}}}}{r}} \right)\left( {dB} \right)\)

Please scroll down to see the correct answer and solution guide.

Right Answer is: A

SOLUTION

Asymptotic coding gain is a quantity that is used as a figure of merit for a particular code.

It depends on the code rate ‘r’ and the minimum distance and can be defined for both the unquantized channel and the binary quantized channel.

The asymptotic coding gain for a Binary symmetric AWGN channel is given by

\(r = 10{\log _{10}}\left( {\frac{{r \cdot {d_{free}}}}{2}} \right)\)

If ‘r’ is the code rate and ‘d free ’ is the free distance of the

Right Answer is: A

SOLUTION

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