Lower Bounds for Quantized LDPC Min-Sum Decoders Based on Absorbing Sets

Previously published lower bounds on the error-floor performance of low-density parity-check (LDPC) codes with quantized sum-product algorithm (SPA) decoders need modification to apply to min-sum algorithm (MSA) decoders. In this paper we show that, due to the sub-optimality of MSA decoders, certain assumptions that apply to SPA decoders are not valid for MSA decoders. Based on appropriately modified assumptions, an improved technique is then proposed to evaluate lower bounds on the error floor performance of LDPC codes for an additive white Gaussian noise channel and a quantized MSA decoder. This new technique not only results in error floor bounds for MSA decoders, but also for SPA decoders. The obtained bound is based on an absorbing set, and a good error floor approximation can be obtained when the multiplicity of the absorbing set is known.