Concatenation of a discrete memoryless channel and a quantizer

The concatenation of an arbitrary discrete memoryless channel with binary input followed by a quantizer is considered. For a restricted quantizer alphabet size, it is shown that the maximum of the mutual information between the channel input and the quantizer output can be found by dynamic programming. Numerical examples are given to illustrate the results. This problem is shown to be an example of concave programming.

[1]  I. M. Jacobs,et al.  Principles of Communication Engineering , 1965 .

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

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

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

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

[6]  P. Pardalos,et al.  Handbook of global optimization , 1995 .

[7]  Gibong Jeong,et al.  Optimal quantization for soft-decision turbo decoder , 1999, Gateway to 21st Century Communications Village. VTC 1999-Fall. IEEE VTS 50th Vehicular Technology Conference (Cat. No.99CH36324).

[8]  Naftali Tishby,et al.  The information bottleneck method , 2000, ArXiv.

[9]  Rüdiger L. Urbanke,et al.  The capacity of low-density parity-check codes under message-passing decoding , 2001, IEEE Trans. Inf. Theory.

[10]  Costas N. Georghiades,et al.  On quantization of low-density parity-check coded channel measurements , 2003, GLOBECOM '03. IEEE Global Telecommunications Conference (IEEE Cat. No.03CH37489).

[11]  Jeremy Thorpe,et al.  Memory-efficient decoding of LDPC codes , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[12]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[13]  Leo Liberti,et al.  Introduction to Global Optimization , 2006 .

[14]  Brian M. Kurkoski,et al.  Noise Thresholds for Discrete LDPC Decoding Mappings , 2008, IEEE GLOBECOM 2008 - 2008 IEEE Global Telecommunications Conference.