CISS05 Regular Paper Submission: On the Typicality of the Linear Code among the LDPC Coset Code Ensemble

Density evolution (DE) is one of the most powerful analytical tools for low-density parity-check (LDPC) codes on memoryless binary-input/symmetric-output channels. The case of non-symmetric chan-nels is tackled either by the LDPC coset code ensemble (a channel symmetrizing argument) or by the gen-eralized DE for linear codes on non-symmetric channels. Existing simulations show that the performance discrepancy of these two different approaches is nearly identical. This paper explains this phenomenon by proving that as the minimum check node degree dc becomes sufficiently large, the performance discrep-ancy of the linear and the coset LDPC codes is theoretically indistinguishable. This typicality of linear codes among the LDPC coset code ensemble provides insight into the concentration theorem of LDPC coset codes.