Bethe Free Energy Approach to LDPC Decoding on Memory Channels
| dc.creator | Anguita, Jaime A. | |
| dc.creator | Chertkov, Michael | |
| dc.creator | Neifeld, Mark A. | |
| dc.creator | Vasic, Bane | |
| dc.date | 2009-04-05 | |
| dc.date.accessioned | 2026-07-07T13:00:41Z | |
| dc.date.available | 2026-07-07T13:00:41Z | |
| dc.description | We address the problem of the joint sequence detection in partial-response (PR) channels and decoding of low-density parity-check (LDPC) codes. We model the PR channel and the LDPC code as a combined inference problem. We present for the first time the derivation of the belief propagation (BP) equations that allow the simultaneous detection and decoding of a LDPC codeword in a PR channel. To accomplish this we follow an approach from statistical mechanics, in which the Bethe free energy is minimized with respect to the beliefs on the nodes of the PR-LDPC graph. The equations obtained are explicit and are optimal for decoding LDPC codes on PR channels with polynomial $h(D) = 1 - a D^n$ (a real, n positive integer) in the sense that they provide the exact inference of the marginal probabilities on the nodes in a graph free of loops. A simple algorithmic solution to the set of BP equations is proposed and evaluated using numerical simulations, yielding bit-error rate performances that surpass those of turbo equalization. | |
| dc.description | 9 pages, 8 figures, submitted to Transactions on Communications | |
| dc.identifier | https://arxiv.org/abs/0904.0747 | |
| dc.identifier | http://arxiv.org/abs/0904.0747 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/225914 | |
| dc.subject | Information Theory | |
| dc.title | Bethe Free Energy Approach to LDPC Decoding on Memory Channels | |
| dc.type | text |