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This paper presents a new class of irregular low-density parity-check (LDPC) codes of moderate length (103≤n≤104) and high rate (R≥3/4). Codes in this class admit low-complexity encoding and have lower error-rate floors than other irregular LDPC code-design approaches. It is also shown that this class of LDPC codes is equivalent to a class of systematic serial turbo codes and is an extension of irregular repeat-accumulate codes. A code design algorithm based on the combination of density evolution and differential evolution optimization with a modified cost function is presented. Moderate-length, high-rate codes with no error-rate floors down to a bit-error rate of 10-9 are presented. Although our focus is on moderate-length, high-rate codes, the proposed coding scheme is applicable to irregular LDPC codes with other lengths and rates.