An integer programming based trapping set search technique

Near codewords of low-density parity-check (LDPC) codes are known to be one of the main reasons of errors that occur in decoding. For high signal-to-noise ratios, these codewords cause error floors in decoding and they are called trapping sets. Especially, trapping sets with small size devastate the performance of communication systems that use LDPC codes. Unfortunately, trapping sets are difficult to find since they satisfy almost all of the parity check equations. In this paper, we develop an integer programming based optimization approach to find the smallest trapping set. Moreover, we develop an algorithm to determine the smallest bit set that belongs to the smallest trapping set and causes an oscillation in the decoder.