Shaping EXIT functions of turbo codes

This paper investigates the shaping of the extrinsic information transfer (EXIT) functions of parallel turbo codes, when the turbo code is used as an outer code in a serially concatenated scheme. As opposed to other work, we consider the overall EXIT function of the turbo decoder and not the EXIT chart for the component codes. Three methods for shaping are investigated: (i) individual puncturing of the systematic part and the two parity parts of the turbo codes, (ii) puncturing of the overall turbo code, and (iii) repetition of the overall turbo code. For each case, the EXIT function of the resulting turbo code is computed from the EXIT function of its component codes. Exact results are obtained for the binary erasure channel.