On Array-based LDPC Codes in Channels With Varying Sampling Rate

We describe a method for enhancing synchronization error correction properties of an array-based LDPC code. The proposed method is based on code expurgation whereby a linear subcode is retained for message encoding and the remaining input bits are used for protection against synchronization errors. The method is easy to implement and incurs a minimal loss in the rate.

[1]  G. Tenengolts,et al.  Nonbinary codes, correcting single deletion or insertion , 1984, IEEE Trans. Inf. Theory.

[2]  V. Levenshtein.  On perfect codes in deletion and insertion metric , 1992 .

[3]  B. V. K. Vijaya Kumar,et al.  Symbol timing recovery for low-SNR partial response recording channels , 2002, Global Telecommunications Conference, 2002. GLOBECOM '02. IEEE.

[4]  M. Mitzenmacher,et al.  Concatenated codes for deletion channels , 2003, IEEE International Symposium on Information Theory, 2003. Proceedings..

[5]  Khaled A. S. Abdel-Ghaffar,et al.  Insertion/deletion correction with spectral nulls , 1997, IEEE Trans. Inf. Theory.

[6]  Efficient Encoding.  Efficient Encoding and Minimum Distance Bounds of Reed-Solomon-Type Array Codes , 2002 .

[7]  John R. Barry,et al.  Per-survivor timing recovery for uncoded partial response channels , 2004, 2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577).

[8]  Jeffrey D. Ullman,et al.  Near-optimal, single-synchronization-error-correcting code , 1966, IEEE Trans. Inf. Theory.

[9]  Robert G. Gallager,et al.  Low-density parity-check codes , 1962, IRE Trans. Inf. Theory.

[10]  S. Olcer,et al.  Decoder architecture for array-code-based LDPC codes , 2003, GLOBECOM '03. IEEE Global Telecommunications Conference (IEEE Cat. No.03CH37489).

[11]  Vladimir I. Levenshtein,et al.  Binary codes capable of correcting deletions, insertions, and reversals , 1965 .

[12]  Gwan S. Choi,et al.  FPGA based implementation of decoder for array low-density parity-check codes , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[13]  Evangelos Eleftheriou,et al.  Rate-compatible low-density parity-check codes for digital subscriber lines , 2002, 2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577).

[14]  David J. C. MacKay,et al.  Reliable communication over channels with insertions, deletions, and substitutions , 2001, IEEE Trans. Inf. Theory.

[15]  Lorenzo Calabi,et al.  A family of codes for the correction of substitution and synchronization errors , 1969, IEEE Trans. Inf. Theory.

[16]  Robert J. McEliece,et al.  The generalized distributive law , 2000, IEEE Trans. Inf. Theory.

[17]  N.J.A. Sloane,et al.  On Single-Deletion-Correcting Codes , 2002, math/0207197.

[18]  Torleiv Kløve,et al.  Codes correcting a single insertion/deletion of a zero or a single peak-shift , 1995, IEEE Trans. Inf. Theory.

[19]  B. V. Vijaya Kumar,et al.  Low-density parity check codes for partial response channels , 2004, IEEE Signal Processing Magazine.

[20]  S. McLaughlin,et al.  Joint timing recovery and turbo equalization for coded partial response channels , 2002 .

[21]  Patrick A. H. Bours,et al.  Construction of fixed-length insertion/deletion correcting runlength-limited codes , 1994, IEEE Trans. Inf. Theory.

[22]  Bane Vasic,et al.  Coding and Signal Processing for Magnetic Recording Systems , 2004 .