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This paper deals with discrete input one-bit output quantization. A discrete input signal is subject to additive noise and is then quantized to zero or one by comparison with a threshold q. For finitely many fixed support points and fixed threshold q we first determine the mutual information of this channel. The capacity-achieving input distribution is shown to be concentrated on merely two extreme...
The notion of directed information was recently introduced for stochastic processes in continuous time. The key idea of the definition is to consider all possible time partitions of a given interval. Unlike the definition of mutual information of discrete-time random variables with continuous alphabets where the supremum over all possible partitions of the alphabets plays an important role, here the...
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