A simple construction of low rate convolutional codes with application to low rate turbo-like code design

We introduce a simple method to construct very low rate systematic recursive convolutional codes from a standard rate 1/2 code. These codes in turn are used in parallel concatenation to obtain very low rate turbo codes. This construction always leads to a class or convolutional codes for which the signals on trellis transition are a subset or complete bi-orthogonal signal set for any given code rate. The resulting codes are rate compatible and require low complexity decoders. By applying this construction methodology to the rate 1/2 turbo code used in 3G standard, we show that an additional coding gain of approximately 1.2 dB is achievable at a bit error rate of 10^-5.