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 - 2013/1/7

Y1 - 2013/1/7

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

UR - http://www.scopus.com/inward/record.url?scp=84871796514&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84871796514&partnerID=8YFLogxK

U2 - 10.1109/TIT.2012.2215836

DO - 10.1109/TIT.2012.2215836

M3 - Article

AN - SCOPUS:84871796514

VL - 59

SP - 1

EP - 16

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 1

M1 - 6289366

ER -