19,540 research outputs found
Jar Decoding: Non-Asymptotic Converse Coding Theorems, Taylor-Type Expansion, and Optimality
Recently, a new decoding rule called jar decoding was proposed; under jar
decoding, a non-asymptotic achievable tradeoff between the coding rate and word
error probability was also established for any discrete input memoryless
channel with discrete or continuous output (DIMC). Along the path of
non-asymptotic analysis, in this paper, it is further shown that jar decoding
is actually optimal up to the second order coding performance by establishing
new non-asymptotic converse coding theorems, and determining the Taylor
expansion of the (best) coding rate of finite block length for
any block length and word error probability up to the second
order. Finally, based on the Taylor-type expansion and the new converses, two
approximation formulas for (dubbed "SO" and "NEP") are
provided; they are further evaluated and compared against some of the best
bounds known so far, as well as the normal approximation of
revisited recently in the literature. It turns out that while the normal
approximation is all over the map, i.e. sometime below achievable bounds and
sometime above converse bounds, the SO approximation is much more reliable as
it is always below converses; in the meantime, the NEP approximation is the
best among the three and always provides an accurate estimation for . An important implication arising from the Taylor-type expansion of
is that in the practical non-asymptotic regime, the optimal
marginal codeword symbol distribution is not necessarily a capacity achieving
distribution.Comment: submitted to IEEE Transaction on Information Theory in April, 201
The Spirituality of Watchman Nee from a Neo-Confucian Perspective
Watchman Nee (Ni Tuosheng, 1903-1972) is one of the most influential Chinese theologians. His theology formed in the early twentieth century and still attracts Chinese people today. This thesis undertakes an innovative twofold-perspective investigation into Nee’s idea of sanctification. By clarifying Nee’s synthesizing of the Holiness Movement theologies and examining his view of sanctification through the lens of the neo-Confucian idea of moral cultivation, this work argues that the practical pursuit of living in holiness and the synthesis of rational thinking and mystical intuition of Nee’s spirituality both deeply resonated within the Chinese spiritual neo-Confucian mindset. Viewing Nee’s theology as a bridge connecting profound Western theological traditions and potential Chinese cultural elements, this thesis deepens the understanding of Nee’s theology, suggests possible spiritual interactions between Christianity and Chinese culture, and explores the future viability of Charismatic Chinese Christianity in relation to Nee’s vision of Chinese Christianity
Investigations on the application of complex cell models in the simulation of bioprocesses
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