LDPC codes for binary asymmetric channels

In this paper we examine the use of low-density parity-check (LDPC) codes in binary asymmetric channels. The problem is interesting since in some types of binary input fading multiple access channels (MAC) without channel state information (CSI), which use the successive decoding scheme, some of the users may experience asymmetric channels. It is well known that the successive decoder is a set of single user decoders and since there is no CSI at the receiver, the corresponding single user channels may be asymmetric in general. In that case the rate of interest of the user with the asymmetric channel is achieved by an unbalanced input distribution of the binary input. We are interested in constructing LDPC codes for these channels that approach the desired rate tuple in the capacity region. A convenient way of making the output distribution unbalanced is by introducing a mapper at the output of the encoder. Here we explain the method of mapping and its effect on the iterative decoding and derive closed form expressions for the upper bound of the probability of error.