Non-Binary LDPC Codes Over Non-Associative Finite Division Near Rings

摘要

The present disclosure is directed to an apparatus and method for decoding non-binary LDPC codes over non-associative finite division near rings. A non-associative finite division near ring is a type of algebraic structure that includes a finite set of elements on which the operations of addition and multiplication are defined. The operation of addition is commutative, associative, and closed, and may have an additive identity for all elements in the finite set. The operation of multiplication is closed but not commutative or associative, and has a multiplicative inverse but not a multiplicative identity for all elements in the finite set. The two operations of addition and multiplication may be related by the distributive property.