Reduced-state representations for trellis codes using constellation symmetry

This paper presents a symmetry-based technique for trellis-code state-diagram reduction that has more general applicability than the quasi-regularity technique of Rouanne et al. and Zehavi et al. for trellis codes using standard constellations and labelings. For a 2/sup /spl nu/x/-state trellis code, the new technique reduces the 2/sup 2/spl nu/x/ state diagram to 2/sup /spl nu/x+/spl nu/q/-state diagram where 0/spl les//spl nu//sub q//spl les//spl nu//sub x/. The particular value of /spl nu//sub q/ depends on the constellation labeling and the convolutional encoder. For standard rate-k/(k+1) set-partitioned trellis codes, /spl nu//sub q/=0, and the overall number of states is the same with the new technique as with quasi-regularity. For codes that are not quasi-regular (and thus not amenable to the quasi-regularity technique), the new technique often provides some improvement (when /spl nu//sub q/</spl nu//sub x/). For 8-phase-shift-keying trellis codes, the new technique always yields /spl nu//sub q/=0.

[1]  Richard D. Wesel,et al.  Reduced complexity trellis code transfer function computation , 1999, 1999 IEEE Communications Theory Mini-Conference (Cat. No.99EX352).

[2]  Dariush Divsalar,et al.  Introduction to Trellis-Coded Modulation With Applications , 1991 .

[3]  William E. Ryan,et al.  Reduced-complexity error-State diagrams in TCM and ISI channel performance evaluation , 2004, IEEE Transactions on Communications.

[4]  Michael P. Fitz,et al.  Distance spectrum analysis of space-time trellis-coded Modulations in quasi-static Rayleigh-fading channels , 2003, IEEE Trans. Inf. Theory.

[5]  Richard D. Wesel,et al.  Edge profile optimal constellation labeling , 2000, 2000 IEEE International Conference on Communications. ICC 2000. Global Convergence Through Communications. Conference Record.

[6]  Richard D. Wesel,et al.  Constellation labeling for linear encoders , 2001, IEEE Trans. Inf. Theory.

[7]  G. David Forney,et al.  Convolutional codes I: Algebraic structure , 1970, IEEE Trans. Inf. Theory.

[8]  S. Benedetto,et al.  Performance evaluation of trellis-coded modulation schemes , 1992, [Conference Record] GLOBECOM '92 - Communications for Global Users: IEEE.

[9]  William E. Ryan,et al.  Concatenated codes for class IV partial response channels , 2001, IEEE Trans. Commun..

[10]  Ezio Biglieri,et al.  High-Level Modulation and Coding for Nonlinear Satellite Channels , 1984, IEEE Trans. Commun..

[11]  Ikuo Oka,et al.  Error probability for digital transmission over nonlinear channels with application to TCM , 1990, IEEE Trans. Inf. Theory.

[12]  Daniel J. Costello,et al.  An algorithm for computing the distance spectrum of trellis codes , 1989, IEEE Journal on Selected Areas in Communications.

[13]  Ikuo Oka,et al.  Error probability bounds for trellis coded modulation over sequence dependent channels , 1989 .

[14]  Andrew J. Viterbi,et al.  Convolutional Codes and Their Performance in Communication Systems , 1971 .

[15]  Richard D. Wesel,et al.  Efficient computation of trellis code generating functions , 2004, IEEE Transactions on Communications.

[16]  William E. Ryan,et al.  Concatenated code system design for storage channels , 2001, IEEE J. Sel. Areas Commun..

[17]  Boris D. Kudryashov,et al.  Distance spectra and upper bounds on error probability for trellis codes , 1995, IEEE Trans. Inf. Theory.

[18]  M.P. Fitz,et al.  New views of transfer function based performance analysis of coded modulations , 1999, Conference Record of the Thirty-Third Asilomar Conference on Signals, Systems, and Computers (Cat. No.CH37020).

[19]  K. X. M. Tzeng,et al.  Convolutional Codes and 'Their Performance in Communication Systems , 1971 .

[20]  Richard D. Wesel,et al.  Trellis code design for periodic interleavers , 1999, IEEE Communications Letters.

[21]  Melek Diker Yücel,et al.  Efficient performance computations for trellis-coded modulation , 1999, IEEE Trans. Commun..

[22]  Jack K. Wolf,et al.  On the performance evaluation of trellis codes , 1987, IEEE Trans. Inf. Theory.

[23]  Peter J. McLane,et al.  Uniform distance and error probability properties of TCM schemes , 1991, IEEE Trans. Commun..

[24]  G. David Forney,et al.  Geometrically uniform codes , 1991, IEEE Trans. Inf. Theory.

[25]  Gottfried Ungerboeck,et al.  Channel coding with multilevel/phase signals , 1982, IEEE Trans. Inf. Theory.

[26]  Wei Shi,et al.  Periodic symbol puncturing of trellis codes , 1997, Conference Record of the Thirty-First Asilomar Conference on Signals, Systems and Computers (Cat. No.97CB36136).

[27]  Richard D. Wesel,et al.  Trellis codes for periodic erasures , 2000, IEEE Trans. Commun..