Linear distances as branch metrics for Viterbi decoding of trellis codes

In the Viterbi algorithm for decoding convolutional and trellis codes, squared Euclidean distance is the optimum branch metric for decoding sequences transmitted in Additive White Gaussian Noise channels and in Rayleigh fading channels when the Channel State Information is appropriately included. For high bit-rate applications, multiple parallel branch metric computation units may be required. Duplication of the multipliers or large look-up tables to obtain the squared distances can increase the decoder complexity significantly. Furthermore, the multipliers and the delay occurred in accessing large look-up tables can become the bottleneck for a fully pipelined Viterbi decoder. In this paper, we show that linear distances can be used to represent the branch metrics, without compromising the Viterbi decoder performance. Thus, adders rather than multipliers can be used to compute the branch metrics and this breaks the potential bottleneck in the Viterbi decoder.