TY - GEN
T1 - The error exponent of the binary symmetric channel for asymmetric random codes
AU - Cohen, Rami
AU - Huleihel, Wasim
N1 - Publisher Copyright:
© Copyright 2015 IEEE All rights reserved.
PY - 2014/1/1
Y1 - 2014/1/1
N2 - In this paper, we consider asymmetric binary codes from Shannon's random code ensemble and also from the random linear code ensemble (LCE), used over the the binary symmetric channel (BSC). The asymmetry is in the sense that the codeword symbols are not necessarily chosen in an equiprobable manner. One possible motivation for such asymmetry is mismatch, where the user uses asymmetric codes over the BSC, leading to a degradation in performance. Accordingly, we derive the distance distribution and the error exponents of a typical random code (TRC) from the RCE, and of a typical linear code (TLC) from the LCE. The derivation is based on a fine large-deviation analysis of some distance enumerators, contrary to the usual bounding technique by Gallager. Later, we propose a "time-varying" BSC model, in which the crossover probability of the BSC is time-dependent, and use our results for providing a lower bound on the error exponent of this channel model.
AB - In this paper, we consider asymmetric binary codes from Shannon's random code ensemble and also from the random linear code ensemble (LCE), used over the the binary symmetric channel (BSC). The asymmetry is in the sense that the codeword symbols are not necessarily chosen in an equiprobable manner. One possible motivation for such asymmetry is mismatch, where the user uses asymmetric codes over the BSC, leading to a degradation in performance. Accordingly, we derive the distance distribution and the error exponents of a typical random code (TRC) from the RCE, and of a typical linear code (TLC) from the LCE. The derivation is based on a fine large-deviation analysis of some distance enumerators, contrary to the usual bounding technique by Gallager. Later, we propose a "time-varying" BSC model, in which the crossover probability of the BSC is time-dependent, and use our results for providing a lower bound on the error exponent of this channel model.
UR - http://www.scopus.com/inward/record.url?scp=84941254866&partnerID=8YFLogxK
U2 - 10.1109/EEEI.2014.7005752
DO - 10.1109/EEEI.2014.7005752
M3 - Conference contribution
AN - SCOPUS:84941254866
T3 - 2014 IEEE 28th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2014
BT - 2014 IEEE 28th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2014
PB - Institute of Electrical and Electronics Engineers
T2 - 2014 28th IEEE Convention of Electrical and Electronics Engineers in Israel, IEEEI 2014
Y2 - 3 December 2014 through 5 December 2014
ER -