On the effective free distance of turbo codes

An expression for the Hamming weight of the (L+1)th order output of a constituent encoder is derived. This expression enables the determination of the inputs that produce outputs of finite weight. It also facilitates the calculation of the (L+1)th order effective free distance (i.e., minimum output weight) d/sub L+1/ of the encoder. Expressions and bounds for d/sub L+1/ and in particular for d/sub 2/ and d/sub 3/ are presented.