Dependence of dfree in MPCCC systems

This letter first investigates the distribution of the free distance, parameter d_free for multiple parallel concatenated schemes based on random interleavers. The distribution is obtained by computer search for information weight IW=2 error events, which are the most likely events to produce d_free, at least for turbo codes. The dependence upon interleaver length and code memory is also studied. The design of the S-interleaver for turbo codes is shown to depend upon a combination of IW=2 error events (which are dependent on S) and IW=2+2 "crossed" error events (which are independent of S). The limiting value of S (for which the two effects are equal) is calculated for turbo codes and a novel algorithm to increase this limit (and hence, d_free) is presented. The S-random interleaver design is extended to schemes with two interleavers, for which the use of paired S-random interleavers is proposed.