This article deals with the problem of simulating a discrete memoryless channel and proposes two algorithms for channel simulation by using the interval algorithm. The first algorithm provides exact channel simulation and the number of fair random bits per input sample approaches the conditional resolvability of the channel with probability one. The second algorithm provides approximate channel simulation and the approximation error measured by the variational distance vanishes exponentially as the block length tends to infinity, when the number of fair random bits per input sample is above the conditional resolvability. Further, some asymptotic properties of these algorithms as well as the original interval algorithm for random number generation are clarified.
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