By Savo G Glisic

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3 Systematic recursive convolutional codes Systematic convolutional codes generated by feed-forward encoders yield, in general, lower free distances than non-systematic codes. 2 Achievable coding gains with some convolutional codes of rate Rc and constraint length N at different values of the bit error probability. Eight-level quantization soft decision Viterbi decoding is used. 7 a systematic encoder from every rate 1/n 0 non-systematic encoder, which generates a systematic code with the same weight enumerating function as the non-systematic one which is relevant for the free distance [71–98].

As an example we have: u=( 1 1 0 1 1 . ) path S1 → S3 → S4 → S2 → S3 → S4 . . x=( 111 100 010 110 100 . . 15) The concept of a state diagram can be applied to any (n 0 , k0 , N ) code with memory ν. The number of states is Nσ = 2ν . There are 2k0 edges entering each state and 2k0 edges leaving each state. The labels on each edge are sequences of length n0 . 17 respectively. An appropriate measure of the maximum likelihood decoder complexity for a convolutional code is the number of visited edges per decoded bit.

It will make other choices with much lower probability. As a consequence, the decoded word will contain 2t + 1 errors which can be anywhere in the n-bit word. 5. In general, from the figure, one can see that the longer the code the better the performance. One should be aware that this also means higher complexity. This represents the basis for code adaptability and reconfigurability. 6 summarizes these results for a broader class of codes. 5. (511, 502,1) (127. 6 Performance of different BCH and Hamming codes.

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