Information processing in ideal coding schemes with code-symbol decoding

Ideal coding schemes are defined as coding schemes that have the minimal symbol-error probability for a given code rate and a given communication channel. Ideal coding schemes with code-symbol decoding are analyzed with respect to their properties of processing mutual information. The wordwise mutual information, the symbol-wise mutual information and the extrinsic mutual information between code symbols and the corresponding decoder outputs are investigated. To analyze the extrinsic mutual information, the concept of information decomposition is introduced