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arXiv 1007.1986cs.ITmath.IT
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高斯信道中带速率限制反馈的可压缩误差指数

Achievable Error Exponents in the Gaussian Channel with Rate-Limited Feedback

Reza Mirghaderi, Andrea Goldsmith, Tsachy Weissman

摘要:

本文研究了在AWGN离散时间无记忆信道中,采用无噪声无时延速率限制反馈的通信系统的可达错误概率。对于反馈速率R_FB低于在前向信道上传输的数据率R的情况,我们证明了错误概率的衰减在块长度上至多是指数的,并且由于反馈而获得错误指数增加的上界。此外,我们表明,在这种情况下使用的反馈结果在一个错误指数,至少RF B高于在没有反馈的错误指数。对于反馈速率超过前向速率(R_FB \geq R)的情况,我们提出了一种简单的迭代方案,该方案实现了随着码字块长度n双指数衰减的错误概率。更一般地,对于某个正整数L,如果R_FB \geq(L-1)R,我们证明了L阶指数误差衰减是可实现的。我们证明,上述结果持有的反馈约束是否表示在平均反馈率或每信道使用反馈率。我们的结果表明,作为R_FB的函数的误差指数在R处具有很强的不连续性,在那里它从有限值跳到无穷大。

英文摘要:

We investigate the achievable error probability in communication over an AWGN discrete time memoryless channel with noiseless delay-less rate-limited feedback. For the case where the feedback rate R_FB is lower than the data rate R transmitted over the forward channel, we show that the decay of the probability of error is at most exponential in blocklength, and obtain an upper bound for increase in the error exponent due to feedback. Furthermore, we show that the use of feedback in this case results in an error exponent that is at least RF B higher than the error exponent in the absence of feedback. For the case where the feedback rate exceeds the forward rate (R_FB \geq R), we propose a simple iterative scheme that achieves a probability of error that decays doubly exponentially with the codeword blocklength n. More generally, for some positive integer L, we show that a L-th order exponential error decay is achievable if R_FB \geq (L-1)R. We prove that the above results hold whether the feedback constraint is expressed in terms of the average feedback rate or per channel use feedback rate. Our results show that the error exponent as a function of R_FB has a strong discontinuity at R, where it jumps from a finite value to infinity.

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。

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