Low-Complexity Parallel Chien Search Structure Using Two-Dimensional Optimization

To achieve a high-throughput decoder, massive-parallel computations are normally applied to the Chien search, but the parallel realization increases the hardware complexity significantly. To reduce the hardware complexity of the parallel Chien search, this brief proposes a 2-D optimization method. In contrast to the previous 1-D optimizations, the proposed method maximizes the sharing of common subexpressions in both the row and column directions. All the partial products needed in the parallel structure are represented in a single matrix, and the finite-field adders are completely eliminated in effect. Simulation results show that the proposed 2-D optimization leads to a significant reduction of the hardware complexity. For the (8191, 7684, 39) BCH code, the count of xor gates in the parallel Chien search is reduced by 92% and 22%, compared to the straightforward and strength-reduced structures, respectively.