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arXiv cs/0702108cs.ITmath.IT
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用于鲁棒低成本通信的正交码

Orthogonal Codes for Robust Low-Cost Communication

Wenyi Zhang, Urbashi Mitra

摘要:

正交编码方案,已知渐近实现单位成本容量(CPUC)的单用户遍历无记忆信道与零成本的输入符号,研究了单用户复合无记忆信道,这表现出不确定性,在其输入输出统计关系。一个极小极大制定,以达到鲁棒性。首先,一类可实现的单位成本(ARPUC)的推导,并通过几个有代表性的案例研究证明其效用。其次,当信道转移统计量的不确定性集满足凸性时,利用极大极小鲁棒性的结果对ARPUC类进行优化。由此得到的CPUC下限指示的正交编码方案的最终性能,并符合一定的限制条件下的CPUC。最后,仍然根据凸性属性,它表明,CPUC通常可以实现,通过利用所谓的混合策略,其中正交码包含不同的非零成本输入符号的适当组合。

英文摘要:

Orthogonal coding schemes, known to asymptotically achieve the capacity per unit cost (CPUC) for single-user ergodic memoryless channels with a zero-cost input symbol, are investigated for single-user compound memoryless channels, which exhibit uncertainties in their input-output statistical relationships. A minimax formulation is adopted to attain robustness. First, a class of achievable rates per unit cost (ARPUC) is derived, and its utility is demonstrated through several representative case studies. Second, when the uncertainty set of channel transition statistics satisfies a convexity property, optimization is performed over the class of ARPUC through utilizing results of minimax robustness. The resulting CPUC lower bound indicates the ultimate performance of the orthogonal coding scheme, and coincides with the CPUC under certain restrictive conditions. Finally, still under the convexity property, it is shown that the CPUC can generally be achieved, through utilizing a so-called mixed strategy in which an orthogonal code contains an appropriate composition of different nonzero-cost input symbols.

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