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A lowcomplexity subspace based decoding algorithm for real BCH DFT codes

Decoding of real BCH DFT (RBDFT) codes is considered in this paper. RBDFT codes find applications in several areas. Though the generator matrix of RBDFT codes is real, the parity check matrix is still complex, because of which complex arithmetic operations are necessary at the decoder. But for a real message vector, the syndromes of RBDFT code preserve Hermitian symmetry. This Hermitian symmetric structure is exploited and a new alternative subspace based formulation is proposed in this paper. The performance of the proposed formulation is identical to the current state-of-art RBDFT decoding algorithm, while it requires only real arithmetic operations. Simulation results are provided which demonstrates the reduction in the decoding complexity with no degradation in the performance.