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# How to implement Traceback in Viterbi Decoder

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#### in8214

##### Newbie level 4
Hello Fellows,

I am implementing Trellis in hardware and have Survior path matrix for decoding length 5K where K is constraint length = 7.

Can someone tell me how to implement Track Back part for the viterbi algorithm.

Appreciated,

Ruk Niz

For K=7 and traceback depth of 5*K you will have 35(5*7) nodes. you will start with node 1, calculate branch metric and pathmetric, and move on till you reach 35th node. Now to traceback you have to start from 35th node. At 35th node select the state whic has the least path metric (If 2 or more states are having the same least metric then move to previous state(34th node) of the present least states (35th node) and compare the metric at the previous states and select the one which has the least metric). For every state there will be 2 previous states and 2 next states.from the state(35th node) move to the previous node (34th node) which has least metric (out of 2 previous state select one which has least metric). repeat this process thill you reach node 1.

for more detail goto The Error Correcting Codes (ECC) Page

Hi eesha,

I wonder if you know the answer of another issue I am facing w.r.t to theoretical Probabilty of Bit error equation in Text books.

I don't have Reference [2] which is
[2] L.H. Charles Lee, Convolutional Coding : Fundamentals and Applications. Boston, Mass.: Arctech House,
1997.

I know from Proakis dfree = 6 for K=4, now looking at the description bj is the total number of non-zero information bits in all weigth j- paths .... How to calculate this , looks like I need to simualte this and this could be different based on the receive sequence and the summation is from j=dfree to infinity , but surely I have to stop at finite length.

Thanks

Hi in8214,

I went through few books, but couldn't find the solution to your problem. Will let you know when i find a solution to this.

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