Error Detecting Code Optimization for Feedback Systems
Let us consider the following formulation of the main problem considered in this chapter. We assume given some discrete channel (in the general case non-symmetric and with memory), a required reliability (e.g. bound on Peq or P av , and some ARQ protocol. We define the optimal error detecting code for the feedback system as the code which provides the highest throughput efficiency (TE) under the given conditions. As has been explained in Chapter 3, not all codes are proper for the BSC. A similar situation may occur for other channels, with a “less noisy” channel giving a higher P1e. This is an undesirable situation. Therefore we introduce another condition: the code should provide the given reliability for any better states of the channel (for example for the BSCp, the provided reliability should be provided for any BSCp’ where p’ ≤ p.
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