Title :
Weight Distribution of Low-Density Parity-Check Codes
Author :
Changyan Di ; Richardson, Thomas J. ; Urbanke, Rudiger L.
Author_Institution :
Swiss Fed. Inst. of Technol., Lausanne
Abstract :
We derive the average weight distribution function and its asymptotic growth rate for low-density parity-check (LDPC) code ensembles. We show that the growth rate of the minimum distance of LDPC codes depends only on the degree distribution pair. It turns out that capacity-achieving sequences of standard (unstructured) LDPC codes under iterative decoding over the binary erasure channel (BEC) known to date have sublinearly growing minimum distance in the block length
Keywords :
block codes; channel capacity; channel coding; iterative decoding; parity check codes; sequences; BEC; LDPC; binary erasure channel; block length; capacity-achieving sequence; iterative decoding; low-density parity-check code; weight distribution function; Aerospace materials; Code standards; Distribution functions; Hamming distance; Iterative algorithms; Iterative decoding; Joining processes; Linear code; Parity check codes; Sparse matrices; Binary erasure channel (BEC); capacity-achieving sequences; growth rate; irregular repeat–accumulate (IRA) codes; low-density parity-check (LDPC) codes; minimum distance; weight distribution;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2006.883541
