TY - JOUR
T1 - Dispersion of the Gilbert-Elliott channel
AU - Polyanskiy, Yury
AU - Poor, H. Vincent
AU - Verdu, Sergio
N1 - Funding Information:
Manuscript received June 20, 2009; revised March 08, 2010; accepted April 07, 2010. Date of current version March 16, 2011. This work was supported by the National Science Foundation under Grants CCF-06-35154 and CNS-09-05398. The authors are with the Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544 USA (e-mail: [email protected]; [email protected]; [email protected]). Communicated by A. Lapidoth, Associate Editor for Shannon Theory. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIT.2011.2111070 1Capacity and all rates in this paper are measured in information units per channel use. 2All logarithms, , and exponents, exp, in this paper are taken with respect to an arbitrary fixed base, which also determines the information units.
PY - 2011/4
Y1 - 2011/4
N2 - Channel dispersion plays a fundamental role in assessing the backoff from capacity due to finite blocklength. This paper analyzes the channel dispersion for a simple channel with memory: the Gilbert-Elliott communication model in which the crossover probability of a binary symmetric channel evolves as a binary symmetric Markov chain, with and without side information at the receiver about the channel state. With side information, dispersion is equal to the average of the dispersions of the individual binary symmetric channels plus a term that depends on the Markov chain dynamics, which do not affect the channel capacity. Without side information, dispersion is equal to the spectral density at zero of a certain stationary process, whose mean is the capacity. In addition, the finite blocklength behavior is analyzed in the non-ergodic case, in which the chain remains in the initial state forever.
AB - Channel dispersion plays a fundamental role in assessing the backoff from capacity due to finite blocklength. This paper analyzes the channel dispersion for a simple channel with memory: the Gilbert-Elliott communication model in which the crossover probability of a binary symmetric channel evolves as a binary symmetric Markov chain, with and without side information at the receiver about the channel state. With side information, dispersion is equal to the average of the dispersions of the individual binary symmetric channels plus a term that depends on the Markov chain dynamics, which do not affect the channel capacity. Without side information, dispersion is equal to the spectral density at zero of a certain stationary process, whose mean is the capacity. In addition, the finite blocklength behavior is analyzed in the non-ergodic case, in which the chain remains in the initial state forever.
KW - Channel capacity
KW - Gilbert-Elliott channel
KW - Shannon theory
KW - coding for noisy channels
KW - finite blocklength regime
KW - hidden Markov models
KW - non-ergodic channels
UR - http://www.scopus.com/inward/record.url?scp=79952824990&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79952824990&partnerID=8YFLogxK
U2 - 10.1109/TIT.2011.2111070
DO - 10.1109/TIT.2011.2111070
M3 - Article
AN - SCOPUS:79952824990
SN - 0018-9448
VL - 57
SP - 1829
EP - 1848
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 4
M1 - 5730589
ER -