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The outage probability limit is a fundamental and achievable lower bound on the word error rate of coded communication systems affected by fading. This limit is mainly determined by two parameters: the diversity order and the coding gain. With linear precoding, the maximum achievable coding rate yielding full diversity on a block fading channel can exceed the upper limit given by the standard Singleton bound. However, the effect of precoding on the coding gain is not well known, mainly due to the complicated expression of the outage probability. This paper establishes simple upper bounds on the outage probability, from which the optimal precoding matrices minimizing these upper bounds can be determined.
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