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The study introduces novel codes called irregular repeat quaternary-accumulate (IRqA) codes whose performance is better than that of the standard irregular repeat accumulate (IRA) codes for the medium-to-short block lengths. The codes are a serial concatenation of an irregular repeat code and a quaternary-accumulate (qA) code. The decoding is performed iteratively by exchanging extrinsic information. The decoding of qA codes is executed using two-dimensional BCJR (Bahl, Cocke, Jelinek and Raviv) decoding. Our codes are found by optimising irregular repetition factors, based on EXIT charts. We also present some simulation results, which show that IRqA codes surpass IRA codes with the comparable encoding and decoding complexities.