Semi-Random Interleaver Design Criteria

Christine Fragouli and Ri hard D. Wesel Ele tri al Engineering Department University of California, Los Angeles hristin ee.u la.edu, wesel ee.u la.edu Abstra t A spread interleaver [1℄ of length N is a semi-random interleaver based on the random sele tion without repla ement of N integers from 1 to N under a design onstraint. This paper extends the spread-interleaver design method to multiple error events, based on the interleaver's role in overall error event distan es. The extension helps to explain why the spread interleaver is spe i ally designed to be semi-random. Simulation results show the performan e a hieved for a symbolinterleaved parallel on atenated trellis oded modulation (PCTCM) s heme [2℄. 1 Introdu tion Interleaver design for turbo odes is mainly targeted towards lowering the error oor, whi h is the attening of the error-rate urve that turbo odes exhibit for moderate and high values of SNR. A good interleaver design may also lead to earlier de oder onvergen e. In this s ope, Perez et al. [3℄ have shown that the turbo ode asymptoti performan e approa hes the free-distan e asymptote. The error oor observed with turbo odes is due to their relatively small free distan e and onsequently relatively at free-distan e asymptote. Thus to lower the error oor the free-distan e of the turbo ode must be maximized for a xed interleaver length. Based on this observation various methods (for example [4, 5℄ ) have been proposed to maximize the turbo ode output distan e by designing the interleaver tailored to spe i onstituent odes, and trying to break turbo ode error events of low output weight. Some methods (for example [6, 7℄) also propose interleaver design through ost fun tion minimization. This paper starts with the spread-interleaver introdu ed by Divsalar and Pollara and extends the design This work was supported by NSF CAREER award #9733089, Conexant Systems In ., and the Xetron Corporation. riteria to multiple error events based on the interleaver's role in the overall error event distan es. This extension provides an understanding for the reason the spread interleaver is spe i ally designed to be semirandom as is explained in detail in following se tions. The paper is organized as follows: Se tion 2 des ribes the interleaver's role in the overall turbo ode error events. Se tion 3 reviews the spread-interleaver, and extends the design riteria to multiple error-events. Se tion 4 provides motivation for the extended design riteria. Se tion 5 presents simulation results and nally Se tion 6 on ludes the paper. 2 Review of Interleaver Role Consider a parallel on atenated turbo ode as in Fig. 1. The interleaver takes the input blo k of the upper en oder and produ es the input blo k for the lower enoder. During de oding, an error event at the output