A proof of the hadamard transform decoding of the belief propagation algorithm for LDPCC over GF(q)

Xiangming Li; M. R. Soleymani

doi:10.1109/VETECF.2004.1400507

A proof of the hadamard transform decoding of the belief propagation algorithm for LDPCC over GF(q)

Xiangming Li^*
, M. R. Soleymani

^*Corresponding author for this work

Chongqing University of Posts and Telecommunications
Concordia University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

16 Citations (Scopus)

Abstract

LDPCC belief-propagation decoding algorithm uses a bipartite graph and sends belief messages between the variable symbols and the checks in an iterative process. The message that a check sends to a variable symbol can be calculated using Hadamard transform, as introduced in. However, the explicit proof of the correctness of the FHT implementation of the decoding algorithm has not been seen in the literature so far. In this paper, we give a proof for the FHT implementation of the decoding algorithm for LDPC codes over GF(q).

Original language	English
Title of host publication	2004 IEEE 60th Vehicular Technology Conference, VTC2004-Fall
Subtitle of host publication	Wireless Technologies for Global Security
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2518-2519
Number of pages	2
Edition	4
ISBN (Print)	0780385217
DOIs	https://doi.org/10.1109/VETECF.2004.1400507
Publication status	Published - 2004
Externally published	Yes
Event	60th IEEE Vehicular Technology Conference, VTC 2004-Fall - Los Angeles, CA, United States Duration: 26 Sept 2004 → 29 Sept 2004

Publication series

Name	IEEE Vehicular Technology Conference
Number	4
Volume	60
ISSN (Print)	1550-2252

Conference

Conference	60th IEEE Vehicular Technology Conference, VTC 2004-Fall
Country/Territory	United States
City	Los Angeles, CA
Period	26/09/04 → 29/09/04

Keywords

Belief-propagation algorithm
Fast hadamard transform (FHT)
Low-density parity-check codes (LDPCC)

Access to Document

10.1109/VETECF.2004.1400507

Cite this

Li, X., & Soleymani, M. R. (2004). A proof of the hadamard transform decoding of the belief propagation algorithm for LDPCC over GF(q). In 2004 IEEE 60th Vehicular Technology Conference, VTC2004-Fall: Wireless Technologies for Global Security (4 ed., pp. 2518-2519). (IEEE Vehicular Technology Conference; Vol. 60, No. 4). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/VETECF.2004.1400507

@inproceedings{2c10e2f2be894293931932f42aea118c,

title = "A proof of the hadamard transform decoding of the belief propagation algorithm for LDPCC over GF(q)",

abstract = "LDPCC belief-propagation decoding algorithm uses a bipartite graph and sends belief messages between the variable symbols and the checks in an iterative process. The message that a check sends to a variable symbol can be calculated using Hadamard transform, as introduced in. However, the explicit proof of the correctness of the FHT implementation of the decoding algorithm has not been seen in the literature so far. In this paper, we give a proof for the FHT implementation of the decoding algorithm for LDPC codes over GF(q).",

keywords = "Belief-propagation algorithm, Fast hadamard transform (FHT), Low-density parity-check codes (LDPCC)",

author = "Xiangming Li and Soleymani, \{M. R.\}",

year = "2004",

doi = "10.1109/VETECF.2004.1400507",

language = "English",

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series = "IEEE Vehicular Technology Conference",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "4",

pages = "2518--2519",

booktitle = "2004 IEEE 60th Vehicular Technology Conference, VTC2004-Fall",

address = "United States",

edition = "4",

note = "60th IEEE Vehicular Technology Conference, VTC 2004-Fall ; Conference date: 26-09-2004 Through 29-09-2004",

}

Li, X & Soleymani, MR 2004, A proof of the hadamard transform decoding of the belief propagation algorithm for LDPCC over GF(q). in 2004 IEEE 60th Vehicular Technology Conference, VTC2004-Fall: Wireless Technologies for Global Security. 4 edn, IEEE Vehicular Technology Conference, no. 4, vol. 60, Institute of Electrical and Electronics Engineers Inc., pp. 2518-2519, 60th IEEE Vehicular Technology Conference, VTC 2004-Fall, Los Angeles, CA, United States, 26/09/04. https://doi.org/10.1109/VETECF.2004.1400507

A proof of the hadamard transform decoding of the belief propagation algorithm for LDPCC over GF(q). / Li, Xiangming; Soleymani, M. R.
2004 IEEE 60th Vehicular Technology Conference, VTC2004-Fall: Wireless Technologies for Global Security. 4. ed. Institute of Electrical and Electronics Engineers Inc., 2004. p. 2518-2519 (IEEE Vehicular Technology Conference; Vol. 60, No. 4).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Soleymani, M. R.

PY - 2004

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N2 - LDPCC belief-propagation decoding algorithm uses a bipartite graph and sends belief messages between the variable symbols and the checks in an iterative process. The message that a check sends to a variable symbol can be calculated using Hadamard transform, as introduced in. However, the explicit proof of the correctness of the FHT implementation of the decoding algorithm has not been seen in the literature so far. In this paper, we give a proof for the FHT implementation of the decoding algorithm for LDPC codes over GF(q).

AB - LDPCC belief-propagation decoding algorithm uses a bipartite graph and sends belief messages between the variable symbols and the checks in an iterative process. The message that a check sends to a variable symbol can be calculated using Hadamard transform, as introduced in. However, the explicit proof of the correctness of the FHT implementation of the decoding algorithm has not been seen in the literature so far. In this paper, we give a proof for the FHT implementation of the decoding algorithm for LDPC codes over GF(q).

KW - Belief-propagation algorithm

KW - Fast hadamard transform (FHT)

KW - Low-density parity-check codes (LDPCC)

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DO - 10.1109/VETECF.2004.1400507

M3 - Conference contribution

AN - SCOPUS:17144421183

SN - 0780385217

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Li X, Soleymani MR. A proof of the hadamard transform decoding of the belief propagation algorithm for LDPCC over GF(q). In 2004 IEEE 60th Vehicular Technology Conference, VTC2004-Fall: Wireless Technologies for Global Security. 4 ed. Institute of Electrical and Electronics Engineers Inc. 2004. p. 2518-2519. (IEEE Vehicular Technology Conference; 4). doi: 10.1109/VETECF.2004.1400507

A proof of the hadamard transform decoding of the belief propagation algorithm for LDPCC over GF(q)

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