Concatenated coding schemes with interleavers consist of a combination of two simple constituent encoders and an interleaver. The parallel concatenation known as “turbo code” has been shown to yield remarkable coding gains close to theoretical limits, yet admitting a relatively simple iterative decoding technique. The recently proposed serial concatenation of interleaved codes may offer performance superior to that of turbo codes. In both coding schemes, the core of the iterative decoding structure is a soft-input soft-output (SISO) module. In this article, we describe the SISO module in a form that continuously updates the maximum a posteriori (MAP) probabilities of input and output code symbols and show how to embed it into iterative decoders for parallel and serially concatenated codes. Results are focused on codes yielding very high coding gain for space applications.