Parity Check Matrix Estimation of k/n Convolutional Coding in Noisy Environment Based on Walsh-Hadamard Transform

Blind estimation of Physical layer transmission parameters, is one of the challenges for smart radios to adapt itself to network standards. These parameters could be transmission rate, modulation and coding scheme that is used for combating with channel errors. Therefore, Channel Coding Estimation, including code parameters, parity check matrix and generator matrix estimation, is one the interesting research topics in the context of software radios. Algebraic methods like Euclidean methods and Rank-based methods are usually performed on intercepted received sequence to estimate the code. Poor efficiency in a high error probability environment is the main drawback of this methods. Transform-based methods, like Walsh-Hadamard transform is one of the methods that could solve channel coding estimation problem. In this paper, new algorithm based on Walsh-Hadamard Transform is proposed that could reconstruct the parity check matrix of convolutional code with general k/n rate in a high error probability environments (BER>0.07), that has much better performance compared to other methods. This algorithm exploits algebraic properties of convolutional code in order to form k-n equation for estimation of k-n rows of the parity check matrix and then use Walsh-Hadamard transform to solve these equations. Simulation results verified excellent performance of the proposed algorithm in high error probability environments compared to other approaches.