We derive various error exponents in the bee identification problem under two different decoding rules. Under na\"ive decoding, which decodes each bee independently of the others, we analyze a general discrete memoryless channel and a relatively wide family of stochastic decoders. Upper and lower bounds to the random coding error exponent are derived and proved to be equal at relatively high coding rates. Then, we propose a lower bound on the error exponent of the typical random code, which improves upon the random coding exponent at low coding rates. We also derive a third bound, which is related to expurgated codes, which turns out to be strictly higher than the other bounds, also at relatively low rates. We show that the universal maximum mutual information decoder is optimal with respect to the typical random code and the expurgated code. Moving further, we derive error exponents under optimal decoding, the relatively wide family of symmetric channels, and the maximum likelihood decoder. We first propose a random coding lower bound, and then, an improved bound which stems from an expurgation process. We show numerically that our second bound strictly improves upon the random coding bound at an intermediate range of coding rates, where a bound derived in a previous work no longer holds.

中文翻译：

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蜜蜂识别问题中的误差指数

我们在两种不同的解码规则下推导出蜜蜂识别问题中的各种错误指数。在独立解码每只蜜蜂的朴素解码下，我们分析了一般的离散无记忆信道和相对广泛的随机解码器系列。推导出随机编码误差指数的上限和下限，并证明在相对较高的编码率。然后，我们提出了典型随机码的错误指数的下限，它改进了低编码率下的随机编码指数。我们还推导出了第三个界，它与删除码有关，它变成out 严格高​​于其他边界，也以相对较低的速率。我们表明，通用最大互信息解码器对于典型的随机码和删除码是最佳的。更进一步，我们在最佳解码、相对广泛的对称通道系列和最大似然解码器下推导出误差指数。我们首先提出了一个随机编码下限，然后提出了一个源于去除过程的改进边界。我们在数值上表明，我们的第二个界限严格改进了在中间编码率范围内的随机编码界限，在以前的工作中得出的界限不再成立。