On the complexity of bounded distance decoding for the AWGN channel

Earlier work has derived the storage complexity of the bounded distance decoder (BDD) for binary channel convolutional codes. We extend this work to the Gaussian noise channel and to partial-response codes. We show that the storage requirement ~(2^1-R - 1)^-t paths for rate-R convolutional codes over the binary channel becomes ~2 ^2Rt over the Gaussian channel, where the decoder must correct t errors. Thus, convolutional coding over the Gaussian channel is not only 3 dB more energy efficient, but its decoding is simpler as well. Next, we estimate the path storage for partial-response codes, i.e., real-number convolutional codes, over the Gaussian channel. The growth rate depends primarily on the bandwidth of the code. A new optimization procedure is devised to measure the maximum storage requirement in Gaussian noise for these two code types. An analysis based on difference equations predicts the asymptotic storage growth for partial response codes