Bootstrap hybrid decoding using the multiple stack algorithm

When in 1948 Claude Shannon published his landmark paper on the mathematical theory of communication, he showed that the error probability in transmitting a message over a noisy channel could be made as small as desired if the information rate was below a certain value, called the capacity, characteristic of the channel. Since his arguments were based on random codes with undefined encoding/decoding complexity, it soon became clear that the task of finding codes with rates close to the capacity and enough structure to allow for practical implementation, yet enough randomness to yield low error probabilities, was not going to be easy. The most common solution adopted was to devise codes with rates sufficiently low to have moderate decoding complexities. We analyze the gains in performance of a sequential decoder when used as part of a coding/decoding scheme, called bootstrap hybrid decoding, that uses algebraic constraints across a set of convolutionally encoded streams to generate extra redundant streams. These are used by the decoder in an iterative way to provide a more reliable metric for sequential decoding. This has the net effect of reducing the gap between the cut-off rate and capacity, thus allowing sequential decoding to work closer to the capacity.