LP decoding of regular LDPC codes in memoryless channels

Nissim Halabi*, Guy Even

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We study error bounds for linear programming decoding of regular low-density parity-check (LDPC) codes. For memoryless binary-input output-symmetric channels, we prove bounds on the word error probability that are inverse doubly exponential in the girth of the factor graph. For memoryless binary-input AWGN channel, we prove lower bounds on the threshold for regular LDPC codes whose factor graphs have logarithmic girth under LP-decoding. Specifically, we prove a lower bound of σ=0.735 (upper bound of Eb/N0=2.67 dB) on the threshold of (3, 6)-regular LDPC codes whose factor graphs have logarithmic girth. Our proof is an extension of a recent paper of Arora, Daskalakis, and Steurer [STOC 2009] who presented a novel probabilistic analysis of LP decoding over a binary symmetric channel. Their analysis is based on the primal LP representation and has an explicit connection to message passing algorithms. We extend this analysis to any MBIOS channel.

Original languageEnglish
Article number5695116
Pages (from-to)887-897
Number of pages11
JournalIEEE Transactions on Information Theory
Issue number2
StatePublished - Feb 2011


  • Additive white Gaussian noise (AWGN) channel
  • channel coding
  • error bounds
  • factor graphs
  • linear programming decoding
  • low-density parity-check (LDPC) codes
  • memoryless binary-input output-symmetric (MBIOS) channel
  • thresholds


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