Universal Decoding for Gaussian Intersymbol Interference Channels

A universal decoding procedure is proposed for the intersymbol interference (ISI) Gaussian channels. The universality of the proposed decoder is in the sense of being independent of the channel parameters, and at the same time, attaining the same random coding error exponent as the optimal maximum-likelihood decoder, which utilizes full knowledge of these unknown parameters. The proposed decoding rule can be regarded as a frequency domain version of the universal maximum mutual information decoder. Contrary to previously suggested universal decoders for ISI channels, our proposed decoding metric can easily be evaluated.

[1]  Neri Merhav,et al.  Analysis of Mismatched Estimation Errors Using Gradients of Partition Functions , 2013, IEEE Transactions on Information Theory.

[2]  Meir Feder,et al.  Universal Communication—Part I: Modulo Additive Channels , 2013, IEEE Transactions on Information Theory.

[3]  Neri Merhav,et al.  Asymptotic MMSE analysis under sparse representation modeling , 2017, Signal Process..

[4]  Jacob Ziv,et al.  Universal decoding for finite-state channels , 1985, IEEE Trans. Inf. Theory.

[5]  Meir Feder,et al.  Communicating using feedback over a binary channel with arbitrary noise sequence , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

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

[7]  Imre Csiszár.  Linear codes for sources and source networks: Error exponents, universal coding , 1982, IEEE Trans. Inf. Theory.

[8]  Neri Merhav.  Universal Decoding for Arbitrary Channels Relative to a Given Class of Decoding Metrics , 2013, IEEE Transactions on Information Theory.

[9]  Meir Feder,et al.  Universal Communication over Modulo-additive Channels with an Individual Noise Sequence , 2010, ArXiv.

[10]  Neri Merhav,et al.  Asymptotic MMSE analysis under sparse representation modeling , 2013, 2014 IEEE International Symposium on Information Theory.

[11]  Neri Merhav,et al.  Universal decoding for Gaussian intersymbol interference channels , 2015, 2015 IEEE International Symposium on Information Theory (ISIT).

[12]  Neri Merhav,et al.  Universal composite hypothesis testing: A competitive minimax approach , 2002, IEEE Trans. Inf. Theory.

[13]  Meir Feder,et al.  Universal decoding for frequency-selective fading channels , 2005, IEEE Transactions on Information Theory.

[14]  Meir Feder,et al.  Communication over Individual Channels -- a general framework , 2012, ArXiv.

[15]  Meir Feder,et al.  Universal Decoding for Channels with Memory , 1998, IEEE Trans. Inf. Theory.

[16]  Albrecht Böttcher,et al.  Spectral properties of banded Toeplitz matrices , 1987 .

[17]  U. Grenander,et al.  Toeplitz Forms And Their Applications , 1958 .

[18]  Imre Csiszár,et al.  Information Theory - Coding Theorems for Discrete Memoryless Systems, Second Edition , 2011 .

[19]  Tsachy Weissman,et al.  The porosity of additive noise sequences , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.

[20]  Amos Lapidoth,et al.  On the Universality of the LZ-Based Decoding Algorithm , 1998, IEEE Trans. Inf. Theory.

[21]  Neri Merhav.  Universal decoding for memoryless Gaussian channels with a deterministic interference , 1993, IEEE Trans. Inf. Theory.

[22]  Isidore Isaac Hirschman,et al.  Studies in real and complex analysis , 1965 .

[23]  Robert M. Gray,et al.  Toeplitz and Circulant Matrices: A Review , 2005, Found. Trends Commun. Inf. Theory.