Block-error performance of root-LDPC codes

This paper investigates the error rate of root-LDPC (RLDPC) codes. These codes were introduced in [1], as a class of codes achieving full diversity D over a nonergodic blockfading transmission channel, and hence with an error probability decreasing as SNR−D at high signal-to-noise ratios. As for their structure, root-LDPC codes can be viewed as a special case of multiedge-type LDPC codes [2]. However, RLDPC code optimization for nonergodic channels does not follow the same criteria as those applied for standard ergodic erasure or Gaussian channels. While previous analyses of RLDPC codes were based on their asymptotic bit threshold for information variables under iterative decoding, in this work we investigate asymptotic block threshold. A stability condition is first derived for a given fading channel realization. Then, in a similar way as for unstructured LDPC codes [3], with the help of Bhattacharyya parameter, we state a sufficient condition for a vanishing block-error probability with the number of decoding iterations.