1. Recently, the exponential rate of convergence of the error probability was provided. 2. It also allowed the calculation of both types of error probabilities . 3. Articles with small deletion margins and high error probabilities are what matters to me. 4. This permits device-independent, high-fidelity data storage for computationally useful periods with bounded error probability . 5. For that, let us sort the 2 ^ k messages by their decoding error probabilities . 6. The bit error ratio can be considered as an approximate estimate of the bit error probability . 7. Phred was able to calculate highly accurate quality scores that were logarithmically linked to the error probabilities . 8. The decoding error probability is exponentially small. 9. Thus the achieved decoding error probability of C ^ { * } is exponentially small as Theorem 1. 10. The mathematics of this approach were rather simple, since Phred quality scores are logarithmically linked to error probabilities .
