Error correction codes, such as low-density parity check (LDPC) codes, are required to be larger scale to meet the increasing demands for reliable and massive data transmission. However, the construction of such a large-scale decoder will result in high complexity and hinder its silicon implementation. Thanks to the advantages of natural computing in high parallelism and low power, we propose a method to synthesize a uniform molecular LDPC decoder by implementing the belief-propagation algorithm with chemical reaction networks (CRNs). This method enables us to flexibly design the LDPC decoder with arbitrary code length, code rate, and node degrees. Compared with existing methods, our proposal reduces the number of reactions to update the variable nodes by 42.86% and the check nodes by 47.37%. Numerical results are presented to show the feasibility and validity of our proposal.
Keywords: belief-propagation algorithm; chemical kinetics; chemical reaction networks (CRNs); low-density parity check (LDPC) codes; molecular computing.