  In this article we focus on the problem of channel decoding in presence of
a-priori information. In particular, assuming that the a-priori information
reliability is not perfectly estimated at the receiver, we derive a novel
analytical framework for evaluating the decoder's performance. It is derived
the important result that a "good code", i.e., a code which allows to fully
exploit the potential benefit of a-priori information, must associate
information sequences with high Hamming weights to codewords with low Hamming
weights. Basing on the proposed analysis, we analyze the performance of
convolutional codes, random codes, and turbo codes. Moreover, we consider the
transmission of correlated binary sources from independent nodes, a problem
which has several practical applications, e.g. in the case of sensor networks.
In this context, we propose a very simple joint source-channel turbo decoding
scheme where each decoder works by exploiting a-priori information given by the
other decoder. In the case of block fading channels, it is shown that the
inherent correlation between information signals provide a form of
non-cooperative diversity, thus allowing joint source-channel decoding to
outperform separation-based schemes.
