An Upper Bound on the Minimum Distance of Serially Concatenated Convolutional Codes

This correspondence presents an upper bound on the minimum distance of serially concatenated codes with interleaver where the inner code is a systematic recursive convolutional encoder and the outer code is any convolutional encoder. The resulting expression shows that the minimum distance of the concatenated code cannot grow more than O(K
¹
-1/d
_f

^(O)
), where K is the information word length, and d
_f

^(O)
is the free distance of the outer code. The obtained upper bound is shown to agree with and, in some cases, improve over previously known results