Decoding with a-priori information: analysis and codes' design criteria

An analytical framework for evaluating the performance of decoding in presence of a-priori is provided. It is shown that a "good code", i.e., a code which allows to fully exploit the potential benefit of a-priori information, must be characterized by both a high minimum Hamming weight and a high minimum information weight. This is a completely novel result which may help the design of good channel codes in presence of apriori information. Basing on the proposed analysis, we derive a measure of the performance gain due to a-priori information that can be obtained by random codes with infinite length. It is then shown that turbo codes with very long interleavers approach the behavior of random codes. Finally, an effective joint source-channel decoding scheme is proposed in a wireless sensors network scenario where two nodes detect correlated sources and deliver them to a central collector.