Codes and iterative decoding on general graphs

Until recently, most known decoding procedures for error-correcting codes were based either on algebraically calculating the error pattern or on some sort of tree or trellis search. With the advent of turbo coding, a third decoding principle has finally had its breakthrough: iterative decoding. With respect to Viterbi decoding, a code is most naturally described by means of a trellis diagram. The main thesis of the present paper is that, with respect to iterative decoding, the natural way of describing a code is by means of a Tanner graph, which may be viewed as a generalized trellis. More precisely, it is the "time axis" of a trellis that is generalized to a Tanner graph.