论文标题
蜜蜂识别问题中的错误指数
Error Exponents in the Bee Identification Problem
论文作者
论文摘要
在两个不同的解码规则下，我们在BEE识别问题中得出了各种错误指数。在幼稚的解码下，将每个蜜蜂独立于其他蜜蜂解码，我们分析了一般离散的无内存通道和相对较宽的随机解码器家族。随机编码误差指数的上限和下限是在相对较高的编码速率下得出的，并且被证明是相等的。然后，我们提出了典型随机代码的误差指数的下限，该指数以低编码率在随机编码指数上改进。我们还得出了第三个界限，该界限与已消除的代码有关，事实证明，该界限严格高于其他界限，也相对较低。我们表明，对于典型的随机代码和消除的代码，通用最大共同信息解码器是最佳的。进一步移动，我们在最佳解码，相对较宽的对称通道家族和最大似然解码器下得出了误差指数。我们首先提出了一个随机编码的下限，然后提出了一个改进的结合，该结合是源于消耗过程的。我们从数字上表明，第二个界限严格改善了在编码速率中间范围内的随机编码上，其中以先前工作的结合不再存在。
We derive various error exponents in the bee identification problem under two different decoding rules. Under naïve 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.
