A New LDPC Code Decoding Method: Expanding the Scope of Ising Machines

Abstract

Low-density parity-check (LDPC) codes have previously been considered as combinatorial optimization problems (COPs) in respect to its decoding. However, after defining it as such, none have gone so far as to convert the LDPC code into a quadratic unconstrained binary optimization (QUBO) problem. Thus, a new method is created: one that converts the LDPC code to a QUBO problem, inputs the QUBO problem into Ising machines (computers based on the Ising model that are designed to solve the QUBO problem), obtains the QUBO solution and converts it to a LDPC solution. By utilizing an actual Ising machine, LDPC solutions with code length of 256-bits have been obtained with an accuracy of 93.9% by average annealing time 214.0ms. The benefit of this newfound methodology goes beyond its theoretical imprint of obtaining LDPC solutions more accurately. It has only been a few years since the Ising machine has been developed. Therefore, in formulating this method, one expands the currently scope of studies involving Ising machines, helping current and future researchers unlock its full range of capabilities and possibilities.