Prucnal P R, Teich M C
Appl Opt. 1978 Nov 15;17(22):3576-83. doi: 10.1364/AO.17.003576.
A single-threshold processor is derived for a wide class of classical binary decision problems involving the likelihood-ratio detection of a signal embedded in noise. The class of problems we consider encompasses the case of multiple independent (but not necessarily identically distributed) observations of a nonnegative (nonpositive) signal, embedded in additive, independent, and noninterfering noise, where the range of the signal and noise is discrete. We show that a comparison of the sum of the observations with a unique threshold comprises optimum processing, if a weak condition on the noise is satisfied, independent of the signal. Examples of noise densities that satisfy and violate our condition are presented. The results are applied to a generalized photocounting optical communication system, and it is shown that most components of the system can be incorporated into our model. The continuous case is treated elsewhere [IEEE Trans. Inf. Theory IT-25, (March, 1979)].
针对一类广泛的经典二元决策问题，推导了一种单阈值处理器，这些问题涉及对嵌入噪声中的信号进行似然比检测。我们考虑的问题类别包括对嵌入加性、独立且不干扰噪声中的非负（非正）信号进行多个独立（但不一定同分布）观测的情况，其中信号和噪声的范围是离散的。我们表明，如果满足关于噪声的一个弱条件（与信号无关），将观测值之和与唯一阈值进行比较就构成了最优处理。给出了满足和违反我们条件的噪声密度示例。结果应用于广义光计数光通信系统，并且表明该系统的大多数组件都可以纳入我们的模型。连续情况在其他地方处理[《IEEE信息论学报》IT - 25，（1979年3月）]。
