An analysis of the computational complexity of sequential decoding of specific tree codes over Gaussian channels

Seminal work by Chevillat and Costello showed that for specific convolutional codes transmitted over a binary symmetric channel and decoded by sequential decoding, a measure of decoding effort decreases exponentially with the column distance function of the code. This has led to a large body of research in the design of codes with good distance profiles which are also used for transmission over Gaussian channels. In this paper we analyze the computational complexity of a stack decoder working on a specific tree code with real (as opposed to binary) symbols, transmitted over a memoryless Gaussian channel. In contrast to prior work that used random coding arguments, we use the intuition provided by the original proof to prove that decoding effort exhibits similar behavior even for a memoryless Gaussian channel. Our result is applicable to convolutional codes with antipodal signaling, sequence detection over Gaussian ISI channels and some sensor networks.