论文标题
源编码合成相关的随机性
Source Coding for Synthesizing Correlated Randomness
论文作者
论文摘要
我们考虑了一个方案，其中提供了两个派对爱丽丝和鲍勃$ x_ {1}^{n} $和$ x_ {2}^{n} $ - 来自pmf $ p_ {x_1 x_2} $的样本。爱丽丝（Alice）和鲍勃（Bob）可以分别与查尔斯（Charles）交流（无噪声）$ r_1 $和$ r_2 $的通信链接。他们的目标是启用Charles生成样本$ y^{n} $，以使三$（x_ {1}^{n}，x_ {2}^{n}，y^{n}）$具有接近的PMF，总变化为$ \ prod P_ p_ p_ p_ p_ p_ {x_1 x_1 x_2 y} $。此外，这三方可能会以$ C_1 $和$ C_2 $的价格成对共享共同的随机性。我们解决了表征汇率四倍体集合$（R_1，R_2，C_1，C_2）$的问题，可以完成上述目标。我们提供了一组足够的条件，即与可实现的速率区域的内部结合，以及必要的条件，即这三方设置的外部与费率区域的绑定。我们提供了基于联合典型的随机编码参数，涉及编码和解码操作以执行软覆盖和对编码器的PMF要求的相关放松。
We consider a scenario wherein two parties Alice and Bob are provided $X_{1}^{n}$ and $X_{2}^{n}$ -- samples that are IID from a PMF $P_{X_1 X_2}$. Alice and Bob can communicate to Charles over (noiseless) communication links of rate $R_1$ and $R_2$ respectively. Their goal is to enable Charles generate samples $Y^{n}$ such that the triple $(X_{1}^{n},X_{2}^{n},Y^{n})$ has a PMF that is close, in total variation, to $\prod P_{X_1 X_2 Y}$. In addition, the three parties may posses pairwise shared common randomness at rates $C_1$ and $C_2$. We address the problem of characterizing the set of rate quadruples $(R_1,R_2,C_1,C_2)$ for which the above goal can be accomplished. We provide a set of sufficient conditions, i.e. an inner bound to the achievable rate region, and necessary conditions, i.e. an outer bound to the rate region for this three party setup. We provide a joint-typicality based random coding argument involving encoding and decoding operations to perform soft covering and a pertinent relaxation of the PMF requirement for the encoders.
