Xxxxxx Sources Sample Clauses

Xxxxxx Sources. In this section, a characterization of a binary example for Theorem 3 in the case where Xxx’s channel is noisier than the main channel is provided. ∼ | Consider the source RV X Bern( 1 ), PX˜ X is a bi- nary symmetric channel (BSC) with crossover probability p ∈ [0, 1/2], PY |X is a binary erasure channel with erasure probability q ∈ [0, 1], and PZ|X is a BSC with crossover probability ϵ ∈ [0, 1/2]. Note that if the relation of ϵ and q is such that 2q < ϵ < 4q(1 − q), PY |X is less noisy than PZ|X , but PY |X is not a degraded version of PZ|X . An illustration of this setting is described in Fig. 2. ∈ Let the test channel PU|X˜ be a BSC with crossover prob- R R X − (Y, Z). This fact is utilized in the proof of this theorem. As we mentioned in the previous section, two auxiliary RVs U, V with larger alphabet sizes appear in Theorem 1. In contrast, the regions G and C in Theorems 2 and 3 associate with one auxiliary RV. To calculate these regions, ability β [0, 1/2]. The optimal rate regions of the GS and CS models for this case are given below.
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