We summarize the results on the soft decision decoding of block codes

discuss certain prelms in the design of decoding algorithms

and propose some problems which remain to be studied. The paper consists of four parts. the first part brtiefly describes the main results on constructing Shannon codes

the basic methods of decoding linear block codes are presented in the second part

and in the third part

we discuss both the trellis structures and the corresponding decoding algorithms of linear block codes

finally

we introduce the current situation and trend for studying bob the turbo codes and their iterative feed back soft decision decoding algorithms.