Overview of LDPC Codes

In light of the history of LDPC codes and relevant research advances in recent years, this paper probes into the encoding and decoding techniques related to this capacity-approaching error-correction technology. Besides the general expression as an equation, LDPC codes can also be examined with a Tanner graph. The encoding of LDPC codes comprises two tasks: construct a sparse parity-check matrix, and generate codewords with the matrix. The decoding of LDPC codes can be divided into three phases: initialization, message update, and validation. With a conventional model of communication systems, common decoding algorithms of LDPC codes are scrutinized. In particular, the sum-product algorithm is analyzed in an elaborate fashion. The logarithmic sum- product algorithm and the min-sum algorithm are two important variations of the sum-product algorithm. The logarithmic sum-product algorithm reduces multiplication to addition by introducing logarithmic likelihood ratio while the latter simplifies computation at the cost of precision.