TY - JOUR
T1 - Second-order resolvability, intrinsic randomness, and fixed-length source coding for mixed sources
T2 - Information spectrum approach
AU - Nomura, Ryo
AU - Han, Te Sun
PY - 2013
Y1 - 2013
N2 - The second-order achievable asymptotics in typical random number generation problems such as resolvability, intrinsic randomness, and fixed-length source coding are considered. In these problems, several researchers have derived the first-order and the second-order achievability rates for general sources using the information spectrum methods. Although these formulas are general, their computations are quite hard. Hence, an attempt to address explicit computation problems of achievable rates is meaningful. In particular, for i.i.d. sources, the second-order achievable rates have earlier been determined simply by using the asymptotic normality. In this paper, we consider mixed sources of two i.i.d. sources. The mixed source is a typical case of nonergodic sources and whose self-information does not have the asymptotic normality. Nonetheless, we can explicitly compute the second-order achievable rates for these sources on the basis of two-peak asymptotic normality. In addition, extensions of our results to more general mixed sources, such as a mixture of countably infinite i.i.d. sources or Markov sources, and a continuous mixture of i.i.d. sources, are considered.
AB - The second-order achievable asymptotics in typical random number generation problems such as resolvability, intrinsic randomness, and fixed-length source coding are considered. In these problems, several researchers have derived the first-order and the second-order achievability rates for general sources using the information spectrum methods. Although these formulas are general, their computations are quite hard. Hence, an attempt to address explicit computation problems of achievable rates is meaningful. In particular, for i.i.d. sources, the second-order achievable rates have earlier been determined simply by using the asymptotic normality. In this paper, we consider mixed sources of two i.i.d. sources. The mixed source is a typical case of nonergodic sources and whose self-information does not have the asymptotic normality. Nonetheless, we can explicitly compute the second-order achievable rates for these sources on the basis of two-peak asymptotic normality. In addition, extensions of our results to more general mixed sources, such as a mixture of countably infinite i.i.d. sources or Markov sources, and a continuous mixture of i.i.d. sources, are considered.
KW - Asymptotic normality
KW - mixed source
KW - random number generation
KW - second-order achievability
KW - source coding
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U2 - 10.1109/TIT.2012.2215836
DO - 10.1109/TIT.2012.2215836
M3 - Article
AN - SCOPUS:84871796514
VL - 59
SP - 1
EP - 16
JO - IRE Professional Group on Information Theory
JF - IRE Professional Group on Information Theory
SN - 0018-9448
IS - 1
M1 - 6289366
ER -