State diagram connectivity and its effects on the decoding of shift-register-based codes

Coding performance is limited not only by Shannon's (1950) bounds but also by the complexity of decoders. Decoder complexity is in turn governed by the need for the different pieces of the machine to communicate with one another. This paper calculates lower limits on the intra-system information flow for the Viterbi decoding of shift-register-based codes, e.g., convolutional codes. These limits provide practical guidance for the construction of decoders for the current generation of convolutional and trellis codes. In particular, these bounds prove that a very specialized decoder family, called graph partition decoders, have an asymptotically optimum communications growth rate. The techniques used in this paper can, moreover, be applied to the design of new (non-shift-register-based) codes which may possibly circumvent the limits derived in the paper and to the design of parallel processors