Estimating the information rate of a channel with classical input and output and a quantum state

We consider the problem of transmitting classical information over a time-invariant channel with memory. A popular class of time-invariant channels with memory are finite-state-machine channels, where a classical state evolves over time and governs the relationship between the classical input and the classical output of the channel. For such channels, various techniques have been developed for estimating and bounding the information rate. In this paper we consider a class of time-invariant channels where a quantum state evolves over time and governs the relationship between the classical input and the classical output of the channel. We propose algorithms for estimating and bounding the information rate of such channels. In particular, we discuss suitable graphical models for doing the relevant computations.

[1]  G. Forney,et al.  Codes on graphs: normal realizations , 2000, 2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060).

[2]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[3]  Suguru Arimoto,et al.  An algorithm for computing the capacity of arbitrary discrete memoryless channels , 1972, IEEE Trans. Inf. Theory.

[4]  David G. Cory,et al.  Tensor networks and graphical calculus for open quantum systems , 2011, Quantum Inf. Comput..

[5]  Brendan J. Frey,et al.  Factor graphs and the sum-product algorithm , 2001, IEEE Trans. Inf. Theory.

[6]  H.-A. Loeliger,et al.  An introduction to factor graphs , 2004, IEEE Signal Process. Mag..

[7]  Parastoo Sadeghi,et al.  Optimization of Information Rate Upper and Lower Bounds for Channels With Memory , 2007, IEEE Transactions on Information Theory.

[8]  V. Sharma,et al.  Entropy and channel capacity in the regenerative setup with applications to Markov channels , 2001, Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252).

[9]  Wei Zeng,et al.  Simulation-Based Computation of Information Rates for Channels With Memory , 2006, IEEE Transactions on Information Theory.

[10]  Israel Bar-David,et al.  Capacity and coding for the Gilbert-Elliot channels , 1989, IEEE Trans. Inf. Theory.

[11]  R. Werner,et al.  Quantum channels with memory , 2005, quant-ph/0502106.

[12]  Richard E. Blahut,et al.  Computation of channel capacity and rate-distortion functions , 1972, IEEE Trans. Inf. Theory.

[13]  V. Giovannetti,et al.  Quantum channels and memory effects , 2012, 1207.5435.

[14]  D. A. Bell,et al.  Information Theory and Reliable Communication , 1969 .

[15]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[16]  Hans-Andrea Loeliger,et al.  A Generalization of the Blahut–Arimoto Algorithm to Finite-State Channels , 2008, IEEE Transactions on Information Theory.

[17]  Hans-Andrea Loeliger,et al.  Factor Graphs for Quantum Probabilities , 2015, IEEE Transactions on Information Theory.

[18]  Paul H. Siegel,et al.  On the achievable information rates of finite state ISI channels , 2001, GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270).

[19]  Emre Telatar,et al.  Mismatched decoding revisited: General alphabets, channels with memory, and the wide-band limit , 2000, IEEE Trans. Inf. Theory.

[20]  Hans-Andrea Loeliger,et al.  A factor-graph representation of probabilities in quantum mechanics , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.