Classification Based on Euclidean Distance Distribution for Blind Identification of Error Correcting Codes in Noncooperative Contexts

The use of channel code is mandatory in current digital communication systems. It allows us to access the information on the receiver side despite the presence of noise. In this paper, we are interested in the blind identification of the parameters of an error correcting code from a received noisy data stream. The literature provides a large amount of contributions for this problem in the hard-decision case but few in the soft-decision case. It is well known that soft-decision methods allow significant gain in decoding techniques. Thence, we propose an algorithm which is able to identify the length of a code through a classification process from the bits likelihood values. It highlights a difference of behavior between an independent identically distributed sequence and an encoded one. This method does not rely on any <italic>a priori</italic> knowledge about the encoder involved. Indeed, the distribution of <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula>-length code words in an <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula>-dimensional space depends on the encoder characteristics. Some areas of this <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> -dimensional space are left vacant because of the redundancy added by the encoder. Despite the presence of noise, it is still possible to detect this phenomenon. Furthermore, an adaptation of a collisions method based on the birthday paradox gives us access to an estimation of the code dimension. Finally, we investigate the performance of this estimation methods to show their efficiency.