It is tempting to say that paradigm-shift coming with turbo and LDPC codes instead of earlier popular approaches: convolutional codes, Reed-Solomon codes, BCH codes et.al. is shift from algebra to probability, from order to chaos. I mean that earlier constructions were much dominated by algebra considerations e.g. non-recursive convolutional codes are just the ideals in the ring $F_2[x]\oplus ... \oplus F_2[x]$. While turbo and LDPC are actually constructed and decoded with methods which much influenced by probabilistic and randomized considerations: roughly speaking good LDPC codes can be constructed by sufficiently sparse and random matrix. The decoding methods used for LDPC - belief propagation naturally belong to probability or machine learning maths. rather than algebra.