Bounds on Rates of LDPC Codes for BEC with Varying Erasure Rate

A binary erasure channel with erasure probability which can take one of two values is considered. Transmission is done by using a low density parity-check code under the requirement that completely successful decoding is possible when the channel is in its better state, while tolerating some predetermined residual erasure fraction when the channel is in its worse state. Upper bounds on the achievable design rate under iterative decoding are derived for this setting. These bounds are compared to rates obtained by practical code profiles. It is also observed that when exceeding the capacity of the erasure channel, the performance of such codes exhibits graceful degradation as measured by the residual erasure fraction.