Trellis Complexity of Short Linear Codes

An extended table of Shuurman's bounds on the state complexity of short binary linear codes is presented. Some new lower and upper bounds are obtained. Most of the newly found codes are based on the so-called double zero-tail termination (DZT) construction

[1]  Rolf Johannesson,et al.  BEAST decoding of block codes obtained via convolutional codes , 2005, IEEE Transactions on Information Theory.

[2]  John Cocke,et al.  Optimal decoding of linear codes for minimizing symbol error rate (Corresp.) , 1974, IEEE Trans. Inf. Theory.

[3]  Jack K. Wolf,et al.  Efficient maximum likelihood decoding of linear block codes using a trellis , 1978, IEEE Trans. Inf. Theory.

[4]  Douglas J. Muder.  Minimal trellises for block codes , 1988, IEEE Trans. Inf. Theory.

[5]  Jr. G. Forney,et al.  Coset Codes-Part 11: Binary Lattices and Related Codes , 1988 .

[6]  M. A. Arcones,et al.  Limit Theorems for Nonlinear Functionals of a Stationary Gaussian Sequence of Vectors , 1994 .

[7]  Frank R. Kschischang,et al.  On the trellis structure of block codes , 1994, IEEE Trans. Inf. Theory.

[8]  A. Robert Calderbank,et al.  Minimal tail-biting trellises: The Golay code and more , 1999, IEEE Trans. Inf. Theory.

[9]  Tom Verhoeff,et al.  An updated table of minimum-distance bounds for binary linear codes , 1987, IEEE Trans. Inf. Theory.

[10]  M. Naranjo.  A central limit theorem for non-linear functionals of stationary Gaussian vector processes , 1995 .

[11]  G. David Forney,et al.  Coset codes-II: Binary lattices and related codes , 1988, IEEE Trans. Inf. Theory.

[12]  P. Schuurman.  A table of state complexity bounds for binary linear codes , 1996, IEEE Trans. Inf. Theory.

[13]  O. Antoine,et al.  Theory of Error-correcting Codes , 2022 .

[14]  Hervé Jégou,et al.  Synchronization Recovery and State Model Reduction for Soft Decoding of Variable Length Codes , 2007, IEEE Transactions on Information Theory.

[15]  Alexander Vardy,et al.  Lower bounds on trellis complexity of block codes , 1995, IEEE Trans. Inf. Theory.

[16]  Rolf Johannesson,et al.  BEAST decoding for block codes , 2004, Eur. Trans. Telecommun..

[17]  Rolf Johannesson,et al.  A BEAST for prowling in trees , 2004, IEEE Transactions on Information Theory.

[18]  Rolf Johannesson,et al.  Low state complexity block codes via convolutional codes , 2004, IEEE Transactions on Information Theory.

[19]  Desmond P. Taylor,et al.  Soft-input soft-output list-based decoding algorithm , 2004, IEEE Transactions on Communications.