The Minimum Distance of Turbo-Like Codes
Bazzi, L.; Mahdian, M.; Spielman, D.A.
Information Theory, IEEE Transactions on
Volume 55, Issue 1, Jan. 2009 Page(s):6 - 15
Digital Object Identifier   10.1109/TIT.2008.2008114
Summary:Worst-case upper bounds are derived on the minimum distance of parallel concatenated turbo codes, serially concatenated convolutional codes, repeat-accumulate codes, repeat-convolute codes, and generalizations of these codes obtained by allowing nonlinear and large-memory constituent codes. It is shown that parallel-concatenated turbo codes and repeat-convolute codes with sub-linear memory are asymptotically bad. It is also shown that depth-two serially concatenated codes with constant-memory outer codes and sublinear-memory inner codes are asymptotically bad. Most of these upper bounds hold even when the convolutional encoders are replaced by general finite-state automata encoders. In contrast, it is proven that depth-three serially concatenated codes obtained by concatenating a repetition code with two accumulator codes through random permutations can be asymptotically good.

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