We use systematic irregular repeat accumulate (IRA) codes as source-channel codes for the transmission of an equiprobable memoryless binary source with side information at the decoder. A special case of this problem is joint source-channel coding for a nonequiprobable memoryless binary source. The theoretical limits of this problem are given by combining the Slepian-Wolf theorem, the source entropy in the special case, with the channel capacity. The approach is based on viewing the correlation between the binary source output and the side information as a separate channel or an enhancement of the original channel. The joint source-channel encoding, decoding and code design procedures are explained in detail. The simulated performance results are better than the recently published solutions using turbo codes and very close to the theoretical limit.