Tight Lower and Upper Bounds on the Minimum Distance of LDPC Codes.

In this letter, we obtain lower and upper bounds on the minimum distance dmin of low-density parity-check (LDPC) codes. The bounds are derived by categorizing the non-zero code words of an LDPC code into two categories of elementary and non-elementary. The first category contains code words whose induced subgraph has only degree-2 check nodes. We propose an efficient search algorithm that can find...