Exact Free Distance and Trapping Set Growth Rates for LDPC Convolutional Codes

Abstract

Ensembles of (J,K)-regular low-density parity-check convolutional (LDPCC) codes are known to be asymptotically good, in the sense that the minimum free distance grows linearly with the constraint length. In this paper, we use a protograph-based analysis of terminated LDPCC codes to obtain an upper bound on the free distance growth rate of ensembles of periodically time-varying LDPCC codes. This bound is compared to a lower bound and evaluated numerically. It is found that, for a sufficiently large period, the bounds coincide. This approach is then extended to obtain bounds on the trapping set numbers, which define the size of the smallest, non-empty trapping sets, for these asymptotically good, periodically time-varying LDPCC code ensembles.

To be presented at the 2011 IEEE International Symposium on Information Theory

References in corpus (2)

• Asymptotically Good LDPC Convolutional Codes Based on Protographs
• Free Distance Bounds for Protograph-Based Regular LDPC Convolutional Codes

Cited by in corpus (5)

• A Scaling Law to Predict the Finite-Length Performance of Spatially-Coupled LDPC Codes
• Probabilistic MIMO Symbol Detection with Expectation Consistency Approximate Inference
• Spatially-Coupled Codes and Threshold Saturation on Intersymbol-Interference Channels
• Improving the Finite-Length Performance of Spatially Coupled LDPC Codes by Connecting Multiple Code Chains
• Free Pseudodistance Growth Rates for Spatially Coupled LDPC Codes over the BEC