An information-theoretic framework for deriving canonical decision-feedback receivers in Gaussian channels

A framework is presented that allows a number of known results relating feedback equalization, linear prediction, and mutual information to be easily understood. A lossless, additive decomposition of mutual information in a general class of Gaussian channels is introduced and shown to produce an information-preserving canonical decision-feedback receiver. The approach is applied to intersymbol interference (ISI) channels to derive the well-known minimum mean-square error (MMSE) decision-feedback equalizer (DFE). When applied to the synchronous code-division multiple-access (CDMA) channel, the result is the MMSE (or signal-to-interference ratio (SIR) maximizing) decision-feedback detector, which is shown to achieve the channel sum-capacity at the vertices of the capacity region. Finally, in the case of the asynchronous CDMA channel we are able to give new connections between information theory, decision-feedback receivers, and structured factorizations of multivariate spectra.

[1]  N. Wiener,et al.  The prediction theory of multivariate stochastic processes , 1957 .

[2]  Amiel Feinstein,et al.  Information and information stability of random variables and processes , 1964 .

[3]  D. Luenberger.  Optimization by Vector Space Methods , 1968 .

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

[5]  G. Wilson.  The Factorization of Matricial Spectral Densities , 1972 .

[6]  G. David Forney,et al.  Maximum-likelihood sequence estimation of digital sequences in the presence of intersymbol interference , 1972, IEEE Trans. Inf. Theory.

[7]  L. H. Brandenburg,et al.  Capacity of the Gaussian channel with memory: The multivariate case , 1974 .

[8]  Dante C. Youla,et al.  Bauer-type factorization of positive matrices and the theory of matrix polynomials orthogonal on the unit circle , 1978 .

[9]  Bruno O. Shubert,et al.  Random variables and stochastic processes , 1979 .

[10]  Gerald B. Folland,et al.  Real Analysis: Modern Techniques and Their Applications , 1984 .

[11]  J.E. Mazo,et al.  Digital communications , 1985, Proceedings of the IEEE.

[12]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[13]  John G. Proakis,et al.  Probability, random variables and stochastic processes , 1985, IEEE Trans. Acoust. Speech Signal Process..

[14]  J. Jeek,et al.  Paper: Efficient algorithm for matrix spectral factorization , 1985 .

[15]  Vladimír Kucera,et al.  Efficient algorithm for matrix spectral factorization , 1985, Autom..

[16]  Sidney C. Port,et al.  Probability, Random Variables, and Stochastic Processes—Second Edition (Athanasios Papoulis) , 1986 .

[17]  Sergio Verdú,et al.  The capacity region of the symbol-asynchronous Gaussian multiple-access channel , 1989, IEEE Trans. Inf. Theory.

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

[19]  Alexandra Duel-Hallen,et al.  Decorrelating decision-feedback multiuser detector for synchronous code-division multiple-access channel , 1993, IEEE Trans. Commun..

[20]  James L. Massey,et al.  Proper complex random processes with applications to information theory , 1993, IEEE Trans. Inf. Theory.

[21]  J. Yang,et al.  Joint transmitter-receiver optimization for multi-input multi-output systems with decision feedback , 1994, IEEE Trans. Inf. Theory.

[22]  John M. Cioffi,et al.  MMSE decision-feedback equalizers and coding. II. Coding results , 1995, IEEE Trans. Commun..

[23]  Alexandra Duel-Hallen,et al.  A family of multiuser decision-feedback detectors for asynchronous code-division multiple-access channels , 1995, IEEE Trans. Commun..

[24]  G. P. Dudevoir,et al.  MMSE Decision-Feedback Equalizers and Coding-Part 11: Coding Results , 1995 .

[25]  John M. Cioffi,et al.  MMSE decision-feedback equalizers and coding. I. Equalization results , 1995, IEEE Trans. Commun..

[26]  Shlomo Shamai,et al.  The intersymbol interference channel: lower bounds on capacity and channel precoding loss , 1996, IEEE Trans. Inf. Theory.

[27]  Edward A. Lee,et al.  Capacity penalty due to ideal zero-forcing decision-feedback equalization , 1996, IEEE Trans. Inf. Theory.

[28]  M. Varanasi,et al.  Multiuser Decision-Feedback Receivers for the General Gaussian Multiple-Access Channel , 1996 .

[29]  Gerard J. Foschini,et al.  Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas , 1996, Bell Labs Technical Journal.

[30]  M. Varanasi,et al.  Achieving vertices of the capacity region of the synchronous Gaussian correlated-waveform multiple-access channel with decision-feedback receivers , 1997, Proceedings of IEEE International Symposium on Information Theory.

[31]  G. Forney,et al.  Generalized Decision-Feedback Equalization for Packet Transmission with ISI and Gaussian Noise , 1997 .

[32]  T. Guess,et al.  Optimum decision feedback multiuser equalization with successive decoding achieves the total capacity of the Gaussian multiple-access channel , 1997, Conference Record of the Thirty-First Asilomar Conference on Signals, Systems and Computers (Cat. No.97CB36136).

[33]  Sergio Verdu,et al.  Multiuser Detection , 1998 .

[34]  Reinaldo A. Valenzuela,et al.  Detection algorithm and initial laboratory results using V-BLAST space-time communication architecture , 1999 .

[35]  M. Varanasi,et al.  Deriving Optimal Successive Decoders for the Asynchronous CDMA Channel Using Information Theory , 2000 .

[36]  Lizhong Zheng,et al.  Diversity and multiplexing: a fundamental tradeoff in multiple-antenna channels , 2003, IEEE Trans. Inf. Theory.

[37]  Hao Zhang,et al.  Asymptotical analysis of the outage capacity of rate-tailored BLAST , 2003, GLOBECOM '03. IEEE Global Telecommunications Conference (IEEE Cat. No.03CH37489).

[38]  Constantinos B. Papadias,et al.  Analysis and performance of some basic space-time architectures , 2003, IEEE J. Sel. Areas Commun..

[39]  Hao Zhang,et al.  The outage capacity of BLAST for MIMO channels , 2003, IEEE International Conference on Communications, 2003. ICC '03..

[40]  Narayan Prasad,et al.  Outage capacities of space-time architectures , 2004, Information Theory Workshop.