TY - GEN

T1 - Capacity and zero-error capacity of the chemical channel with feedback

AU - Permuter, Haim

AU - Cuff, Paul

AU - Van Roy, Benjamin

AU - Weissinan, Tsachy

PY - 2007/12/1

Y1 - 2007/12/1

N2 - We consider a family of channels, collectively referred to as the 'chemical channel', which generalizes the trapdoor channel. We show that the feedback capacity of the chemical channel can be cast as the solution to a dynamic programming (DP) problem. We obtain numerical values for the feedback capacity of the chemical channel by approximating the solution of the DP problem using value iteration. For the special case of the trapdoor channel, by solving the DP problem analytically, we prove that the feedback capacity of the trapdoor channel is the logarithm of the golden ratio. Further, we describe a simple scheme that achieves the capacity of the trapdoor channel. The scheme has zero probability of error, which allows us to conclude that the logarithm of the golden ratio is also the zero error capacity of the chemical channel.

AB - We consider a family of channels, collectively referred to as the 'chemical channel', which generalizes the trapdoor channel. We show that the feedback capacity of the chemical channel can be cast as the solution to a dynamic programming (DP) problem. We obtain numerical values for the feedback capacity of the chemical channel by approximating the solution of the DP problem using value iteration. For the special case of the trapdoor channel, by solving the DP problem analytically, we prove that the feedback capacity of the trapdoor channel is the logarithm of the golden ratio. Further, we describe a simple scheme that achieves the capacity of the trapdoor channel. The scheme has zero probability of error, which allows us to conclude that the logarithm of the golden ratio is also the zero error capacity of the chemical channel.

UR - http://www.scopus.com/inward/record.url?scp=46749116284&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2007.4557493

DO - 10.1109/ISIT.2007.4557493

M3 - Conference contribution

AN - SCOPUS:46749116284

SN - 1424414296

SN - 9781424414291

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1866

EP - 1870

BT - Proceedings - 2007 IEEE International Symposium on Information Theory, ISIT 2007

T2 - 2007 IEEE International Symposium on Information Theory, ISIT 2007

Y2 - 24 June 2007 through 29 June 2007

ER -