Message-passing decoding beyond the girth with local-optimality guarantees

Nissim Halabi*, Guy Even

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We present a new message-passing iterative decoding algorithm, called normalized weighted min-sum (NWMS). NWMS-decoding is a BP-type algorithm that applies to any irregular Tanner code with single parity-check local codes (e. g. , LDPC codes and HDPC codes). The decoding guarantee of NWMS applies whenever there exists a locally optimal codeword. We prove that if a locally-optimal codeword with respect to height parameter h exists, then NWMS-decoding finds it in h iterations. This decoding guarantee holds for every finite value of h and is not limited by the girth. Because local optimality of a codeword implies that it is the unique ML-codeword, the decoding guarantee also has an ML-certificate.

Original languageEnglish
Title of host publication2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012
DOIs
StatePublished - 2012
Event2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012 - Eilat, Israel
Duration: 14 Nov 201217 Nov 2012

Publication series

Name2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012

Conference

Conference2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012
Country/TerritoryIsrael
CityEilat
Period14/11/1217/11/12

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