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The traditional chip-synchronous assumption used in the analyses of optical codes in optical code-division multiple access gives a pessimistic performance upper bound, while a more realistic chip-asynchronous assumption gives a more accurate performance. It is also known that a hard-limiter can be placed at the front end of an optical decoder to reduce the effects of multiple-access interference and the near-far problem. In this paper, the "hard-limiting" performance of two-dimensional (2-D) optical codes is analyzed under the chip-asynchronous assumption. We apply a Markov-chain method for a more accurate analysis, which can be generalized to 2-D optical codes with arbitrary maximum cross-correlation values. The performance of 2-D optical codes with the hard-limiting and chip-asynchronous assumptions is also compared with the soft-limiting and chip- synchronous assumptions.