TY - GEN

T1 - Feedback capacity and coding for the (0, k)-RLL input-constrained BEC

AU - Peled, Ori

AU - Sabag, Oron

AU - Permuter, Haim H.

N1 - Publisher Copyright:
© 2017 IEEE.

PY - 2017/8/9

Y1 - 2017/8/9

N2 - The input-constrained binary erasure channel (BEC) with strictly causal feedback is studied. The channel input sequence must satisfy the (0, k)-runlength limited (RLL) constraint, i.e., no more than k consecutive zeros are allowed. The feedback capacity of this channel is derived for all k≥1 Cfn(0, k)(ϵ) = max ϵH2(δ0)+Σk-1i=1(ϵi+1H2)(δi)Πi-1m=0δm)/1+Σk-1i=0(ϵi+1Πim=0δm) where ϵ is the erasure probability, ϵ=1-ϵ, H2(·) is the binary entropy function and the maximization is only over δk-1, while the other parameters δ0,..., δk-2 are simple functions of δk-1. A simple coding scheme is constructed for all k, establishing that the feedback capacity can be achieved using variable length zero-error coding. In addition, it is shown that non-causal knowledge of the erasures at the encoder does not increase the feedback capacity.

AB - The input-constrained binary erasure channel (BEC) with strictly causal feedback is studied. The channel input sequence must satisfy the (0, k)-runlength limited (RLL) constraint, i.e., no more than k consecutive zeros are allowed. The feedback capacity of this channel is derived for all k≥1 Cfn(0, k)(ϵ) = max ϵH2(δ0)+Σk-1i=1(ϵi+1H2)(δi)Πi-1m=0δm)/1+Σk-1i=0(ϵi+1Πim=0δm) where ϵ is the erasure probability, ϵ=1-ϵ, H2(·) is the binary entropy function and the maximization is only over δk-1, while the other parameters δ0,..., δk-2 are simple functions of δk-1. A simple coding scheme is constructed for all k, establishing that the feedback capacity can be achieved using variable length zero-error coding. In addition, it is shown that non-causal knowledge of the erasures at the encoder does not increase the feedback capacity.

UR - http://www.scopus.com/inward/record.url?scp=85034108093&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2017.8006836

DO - 10.1109/ISIT.2017.8006836

M3 - Conference contribution

AN - SCOPUS:85034108093

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1783

EP - 1787

BT - 2017 IEEE International Symposium on Information Theory, ISIT 2017

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2017 IEEE International Symposium on Information Theory, ISIT 2017

Y2 - 25 June 2017 through 30 June 2017

ER -