Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The problem of channel coding with the erasure option is revisited for discrete memoryless channels. The interplay beten the code rate, the undetected and total error probabilities is characterized. Using the information spectrum method, a sequence of codes of increasing blocklengths    $n$    is designed to illustrate this tradeoff. Furthermore, for additive discrete memoryless channels with uniform input distribution,  establish that our analysis is tight with respect to the ensemble average. This is done by analyzing the ensemble performance in terms of a tradeoff beten the code rate, the undetected and total errors. This tradeoff is parameterized by the threshold in a generalized likelihood ratio test. Two asymptotic regimes are studied. First, the code rate tends to the capacity of the channel at a rate slor than    $n^{-1/2}$    corresponding to the moderate deviations regime. In this case, both error probabilities decay subexponentially and asymmetrically. The precise decay rates are characterized. Second, the code rate tends to capacity at a rate of    $n^{-1/2}$   . In this case, the total error probability is asymptotically a positive constant, while the undetected error probability decays as    $\exp (- bn^{ 1/2})$    for some    $b>0$   . The proof techniques involve the applications of a modified (or shifted) version of the Gartner–Ellis theorem and the type class enumerator method to characterize the asymptotic behavior of a sequence of cumulant generating functions.
['Masahito Hayashi', 'Vincent Y. F. Tan']
I am writing a research paper on a idea Asymmetric Evaluations of Erasure and Undetected Error Probabilities
[{"from": "human", "value": "I am writing a research paper on a idea Asymmetric Evaluations of Erasure and Undetected Error Probabilities"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The problem of channel coding with the erasure option is revisited for discrete memoryless channels. The interplay beten the code rate, the undetected and total error probabilities is characterized. Using the information spectrum method, a sequence of codes of increasing blocklengths    $n$    is designed to illustrate this tradeoff. Furthermore, for additive discrete memoryless channels with uniform input distribution,  establish that our analysis is tight with respect to the ensemble average. This is done by analyzing the ensemble performance in terms of a tradeoff beten the code rate, the undetected and total errors. This tradeoff is parameterized by the threshold in a generalized likelihood ratio test. Two asymptotic regimes are studied. First, the code rate tends to the capacity of the channel at a rate slor than    $n^{-1/2}$    corresponding to the moderate deviations regime. In this case, both error probabilities decay subexponentially and asymmetrically. The precise decay rates are characterized. Second, the code rate tends to capacity at a rate of    $n^{-1/2}$   . In this case, the total error probability is asymptotically a positive constant, while the undetected error probability decays as    $\\exp (- bn^{ 1/2})$    for some    $b>0$   . The proof techniques involve the applications of a modified (or shifted) version of the Gartner\u2013Ellis theorem and the type class enumerator method to characterize the asymptotic behavior of a sequence of cumulant generating functions."}]