arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1010.1303cs.ITmath.IT
收藏

多址信道的误差指数:下限

Error Exponent for Multiple-Access Channels:Lower Bounds

Ali Nazari, Achilleas Anastasopoulos, S. Sandeep Pradhan

摘要:

给出了一个统一的框架,以获得所有已知的下界(随机编码,典型的随机编码和删除界)的点到点离散无记忆信道(DMC)的可靠性函数。通过对两用户离散无记忆(DM)多址接入信道(MAC)使用类似的思想,推导出可靠性函数的三个下界。第一个(随机编码)与DM-MAC的可靠性函数的最佳已知下限相同。结果表明,随机编码界是恒定组成码系综中平均码的性能。第二个界限(典型随机编码)是恒定组成码集合的典型性能。为了得到第三边界(删除),我们从码本中以较大的速率消除一些码字。这是该类型中第一个明确使用MAC删除方法的绑定。结果表明,对于所有速率对,典型随机编码的指数和删除的界都大于或等于已知随机编码界的指数。此外,给出了一个例子,其中删除界的指数严格较大。所有这些界限可以普遍获得的所有离散无记忆MAC与给定的输入和输出字母。

英文摘要:

A unified framework to obtain all known lower bounds (random coding, typical random coding and expurgated bound) on the reliability function of a point-to-point discrete memoryless channel (DMC) is presented. By using a similar idea for a two-user discrete memoryless (DM) multiple-access channel (MAC), three lower bounds on the reliability function are derived. The first one (random coding) is identical to the best known lower bound on the reliability function of DM-MAC. It is shown that the random coding bound is the performance of the average code in the constant composition code ensemble. The second bound (Typical random coding) is the typical performance of the constant composition code ensemble. To derive the third bound (expurgated), we eliminate some of the codewords from the codebook with larger rate. This is the first bound of this type that explicitly uses the method of expurgation for MACs. It is shown that the exponent of the typical random coding and the expurgated bounds are greater than or equal to the exponent of the known random coding bounds for all rate pairs. Moreover, an example is given where the exponent of the expurgated bound is strictly larger. All these bounds can be universally obtained for all discrete memoryless MACs with given input and output alphabets.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑