Graph-Matched LDPC Codes for Partial-Response Channels

In this paper, we propose an LDPC coding scheme based on repeat-accumulate (RA) codes for partial-response (PR) channels. We modify the original RA encoder in such a way that there exists a one-to-one relationship between a sequence called the D-codeword (which is not the transmitted codeword but contains the information bits) and the noiseless received sequence at the output of the PR channel. A consequence of this is that the graph used for decoding the D-codeword, which is different from the encoder graph, is of low complexity. Moreover, with the appropriate modification of the RA encoder, the graph used for decoding is the same of any PR channel, which makes sense calling these codes graph-matched. The simplicity of the decoder, resulting from the "binary" interference removal (precoding) and the linear, as opposed to quadratic, complexity of the encoder make the proposed scheme attractive. For a code rate R = 3641/4096 = 0.89 and for the PR4 channel, an LDPC code has been designed and a simulated coding gain of about 5 dB for a bit error rate less than 10-5 was obtained.

[1]  Trellis matched codes for partial response channels , 1997, Proceedings of IEEE International Symposium on Information Theory.

[2]  Kjell Jørgen Hole,et al.  Improved coding techniques for preceded partial-response channels , 1994, IEEE Trans. Inf. Theory.

[3]  Jing Li,et al.  On the performance of high-rate TPC/SPC codes and LDPC codes over partial response channels , 2002, IEEE Trans. Commun..

[4]  H. Thapar,et al.  A class of partial response systems for increasing storage density in magnetic recording , 1987 .

[5]  Daniel J. Costello,et al.  A multilevel approach to constructing trellis-matched codes for binary-input partial-response channels , 1999, IEEE Trans. Inf. Theory.

[6]  Ajay Dholakia,et al.  Reduced-complexity decoding of low density parity check codes for generalized partial response channels , 2001 .

[7]  Christian Schlegel,et al.  Trellis and turbo coding , 2004 .

[8]  Bartolomeu F. Uchôa Filho,et al.  Good convolutional codes for the precoded (1-D)(1+D)n partial-response channels , 1997, IEEE Trans. Inf. Theory.

[9]  Bartolomeu F. Uchôa Filho,et al.  Distance spectra of convolutional codes over partial-response channels , 2001, IEEE Trans. Commun..

[10]  Evangelos Eleftheriou,et al.  Performance analysis of magnetic recording systems , 2001, ICC 2001. IEEE International Conference on Communications. Conference Record (Cat. No.01CH37240).

[11]  X. Jin.  Factor graphs and the Sum-Product Algorithm , 2002 .

[12]  Krishna R. Narayanan.  Effect of precoding on the convergence of turbo equalization for partial response channels , 2001, IEEE J. Sel. Areas Commun..

[13]  Dariush Divsalar,et al.  Coding theorems for 'turbo-like' codes , 1998 .

[14]  L. R. Carley,et al.  Generalized partial response signalling and efficient MLSD using linear Viterbi branch metrics , 1999, Seamless Interconnection for Universal Services. Global Telecommunications Conference. GLOBECOM'99. (Cat. No.99CH37042).