  Interactive encoding and decoding based on binary low-density parity-check
codes with syndrome accumulation (SA-LDPC-IED) is proposed and investigated.
Assume that the source alphabet is $\mathbf{GF}(2)$, and the side information
alphabet is finite. It is first demonstrated how to convert any classical
universal lossless code $\mathcal{C}_n$ (with block length $n$ and side
information available to both the encoder and decoder) into a universal
SA-LDPC-IED scheme. It is then shown that with the word error probability
approaching 0 sub-exponentially with $n$, the compression rate (including both
the forward and backward rates) of the resulting SA-LDPC-IED scheme is upper
bounded by a functional of that of $\mathcal{C}_n$, which in turn approaches
the compression rate of $\mathcal{C}_n$ for each and every individual sequence
pair $(x^n,y^n)$ and the conditional entropy rate $\mathrm{H}(X |Y)$ for any
stationary, ergodic source and side information $(X, Y)$ as the average
variable node degree $\bar{l}$ of the underlying LDPC code increases without
bound. When applied to the class of binary source and side information $(X, Y)$
correlated through a binary symmetrical channel with cross-over probability
unknown to both the encoder and decoder, the resulting SA-LDPC-IED scheme can
be further simplified, yielding even improved rate performance versus the bit
error probability when $\bar{l}$ is not large. Simulation results (coupled with
linear time belief propagation decoding) on binary source-side information
pairs confirm the theoretic analysis, and further show that the SA-LDPC-IED
scheme consistently outperforms the Slepian-Wolf coding scheme based on the
same underlying LDPC code. As a by-product, probability bounds involving LDPC
established in the course are also interesting on their own and expected to
have implications on the performance of LDPC for channel coding as well.
