Analysis of Absorbing Sets for Array-Based LDPC Codes

Low density parity check codes (LDPC) are known to perform very well under iterative decoding. However, these codes also exhibit a change in the slope of the bit error rate (BER) vs. signal to noise ratio (SNR) curve in the very low BER region. In our earlier work using hardware emulation in this deep BER regime we argue that this behavior can be attributed to specific structures within the Tanner graph associated with an LDPC code, called absorbing sets. In this paper we provide a detailed theoretical analysis of absorbing sets for array-based LDPC codes C_p.gamma. Specifically, we identify and enumerate all the smallest absorbing sets for these array-based LDPC codes with gamma = 2,3,4 with standard parity check matrix. Experiments carried out on the emulation platform show excellent agreement with our theoretical results.