Cyclic coded integer-forcing equalization

A discrete-time intersymbol interference (ISI) channel with additive Gaussian noise is considered, where only the receiver has knowledge of the channel impulse response. An approach for combining decision-feedback equalization with channel coding is proposed, where decoding precedes the removal of ISI. The proposed approach involves equalizing the channel impulse response to a response with integer-valued coefficients in conjunction with utilizing cyclic block codes. Leveraging the property that a cyclic code is closed under cyclic integer-valued convolution allows us to perform decoding prior to applying decision feedback. Explicit bounds on the performance of the proposed scheme are derived.

[1]  Fuyun Ling,et al.  Decision-feedback equalization of time-dispersive channels with coded modulation , 1990, IEEE Trans. Commun..

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

[3]  M. Tomlinson,et al.  Cyclotomic idempotent-based binary cyclic codes , 2005 .

[4]  Ofer Amrani,et al.  Joint equalization and coding for intersymbol interference channels , 1997, IEEE Trans. Inf. Theory.

[5]  M. Vedat Eyuboglu,et al.  Detection of coded modulation signals on linear, severely distorted channels using decision-feedback noise prediction with interleaving , 1988, IEEE Trans. Commun..

[6]  Gregory W. Wornell,et al.  Lattice-reduction-aided detectors for MIMO communication systems , 2002, Global Telecommunications Conference, 2002. GLOBECOM '02. IEEE.

[7]  Andrew C. Singer,et al.  Turbo equalization: principles and new results , 2002, IEEE Trans. Commun..

[8]  Meir Feder,et al.  Signal codes , 2008, Proceedings 2003 IEEE Information Theory Workshop (Cat. No.03EX674).

[9]  G. David Forney,et al.  Modulation and Coding for Linear Gaussian Channels , 1998, IEEE Trans. Inf. Theory.

[10]  Meir Feder,et al.  Signal Codes: Convolutional Lattice Codes , 2011, IEEE Transactions on Information Theory.

[11]  Alexandra Duel-Hallen,et al.  Delayed decision-feedback sequence estimation , 1989, IEEE Trans. Commun..

[12]  Frank R. Kschischang,et al.  An Algebraic Approach to Physical-Layer Network Coding , 2010, IEEE Transactions on Information Theory.

[13]  John G. Proakis,et al.  Digital Communications , 1983 .

[14]  Gregory W. Wornell,et al.  A class of block-iterative equalizers for intersymbol interference channels: fixed channel results , 2001, IEEE Trans. Commun..

[15]  Peter Kabal,et al.  Partial-Response Signaling , 1975, IEEE Trans. Commun..

[16]  László Lovász,et al.  Factoring polynomials with rational coefficients , 1982 .

[17]  Shu Lin,et al.  Low-density parity-check codes based on finite geometries: A rediscovery and new results , 2001, IEEE Trans. Inf. Theory.

[18]  Stephan ten Brink,et al.  A close-to-capacity dirty paper coding scheme , 2004, IEEE Transactions on Information Theory.

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

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

[21]  Michael Gastpar,et al.  Integer-forcing linear receivers , 2010, 2010 IEEE International Symposium on Information Theory.

[22]  Michael Gastpar,et al.  Integer-Forcing Linear Receivers: A New Low-Complexity MIMO Architecture , 2010, 2010 IEEE 72nd Vehicular Technology Conference - Fall.

[23]  Mahesh K. Varanasi,et al.  An information-theoretic framework for deriving canonical decision-feedback receivers in Gaussian channels , 2005, IEEE Transactions on Information Theory.

[24]  C. Siegl,et al.  On the Relation between Lattice-Reduction-Aided Equalization and Partial-Response Signaling , 2006, 2006 International Zurich Seminar on Communications.

[25]  Jack K. Wolf,et al.  On saving decoder states for some trellis codes and partial response channels , 1988, IEEE Trans. Commun..

[26]  Shafi Goldwasser,et al.  Complexity of lattice problems - a cryptographic perspective , 2002, The Kluwer international series in engineering and computer science.

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

[28]  Simon Litsyn.  Peak power control in multicarrier communications , 2007 .

[29]  Robert F. H. Fischer,et al.  Low-complexity near-maximum-likelihood detection and precoding for MIMO systems using lattice reduction , 2003, Proceedings 2003 IEEE Information Theory Workshop (Cat. No.03EX674).

[30]  Uri Erez,et al.  Achieving the gains promised by Integer-Forcing equalization with binary codes , 2010, 2010 IEEE 26-th Convention of Electrical and Electronics Engineers in Israel.

[31]  Sirikiat Lek Ariyavisitakul,et al.  Joint coding and decision feedback equalization for broadband wireless channels , 1998, IEEE J. Sel. Areas Commun..

[32]  H. Miyakawa,et al.  Matched-Transmission Technique for Channels With Intersymbol Interference , 1972, IEEE Trans. Commun..

[33]  M. Tomlinson.  New automatic equaliser employing modulo arithmetic , 1971 .

[34]  Michael Gastpar,et al.  Practical code design for compute-and-forward , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[35]  Seung Hee Han,et al.  An overview of peak-to-average power ratio reduction techniques for multicarrier transmission , 2005, IEEE Wireless Communications.

[36]  Sae-Young Chung,et al.  Sphere-bound-achieving coset codes and multilevel coset codes , 2000, IEEE Trans. Inf. Theory.

[37]  Amos Lapidoth,et al.  Nearest neighbor decoding for additive non-Gaussian noise channels , 1996, IEEE Trans. Inf. Theory.

[38]  W. Fischer,et al.  Sphere Packings, Lattices and Groups , 1990 .

[39]  Jae Hong Lee,et al.  An overview of peak-to-average power ratio reduction techniques for multicarrier transmission , 2005, IEEE Wireless Communications.

[40]  G. David Forney,et al.  Shannon meets Wiener II: On MMSE estimation in successive decoding schemes , 2004, ArXiv.

[41]  Evangelos Eleftheriou,et al.  Decoding of trellis-encoded signals in the presence of intersymbol interference and noise , 1989, IEEE Trans. Commun..