Efficient Decoder-Free Minimum Distance Estimation for Concatenated Convolutional Codes

This work presents a novel approach for estimating the minimum distance of concatenated convolutional codes. Unlike most prior methods, the proposed approach relies solely on encoder-side properties, eliminating the need for a decoder in the estimation process. To this end, we introduce an alternative method for identifying return-to-zero sequences, enabling a lowcomplexity, reliable minimum distance estimation. The proposed method is flexible and applicable to both serial and parallel concatenated structures. The results confirm that this approach produces exact minimum distance values for several sizes of the LTE turbo code family while significantly reducing processing time and computational complexity compared to existing methods. For example, in a challenging case study, applying the method to an LTE turbo code with tailbiting termination of length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K=6144$</tex> bits yields an estimated minimum distance of 50 and a multiplicity of 12288 in 100 minutes on a standard personal computer - a reduction by several orders of magnitude in comparison to state of the art methods.