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On the Computational Complexity of Blind Detection of Binary Linear Codes
Alexios Balatsoukas-Stimming, Aris Filos-Ratsikas · 2018-06-04 · via cs.IT updates on arXiv.org

In this work, we study the computational complexity of the Minimum Distance Code Detection problem. In this problem, we are given a set of noisy codeword observations and we wish to find a code in a set of linear codes $\mathcal{C}$ of a given dimension $k$, for which the sum of distances between the observations and the code is minimized. We prove that, for the practically relevant case when the set $\mathcal{C}$ only contains a fixed number of candidate linear codes, the detection problem is NP-hard and we identify a number of interesting open questions related to the code detection problem.

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