Error statistics for concatenated systems on non-renewal time-varying channels

Abstract

The statistics of the error process generated by a discrete super channel formed by the concatenation of a constrained encoder, a non-renewal finite state channel (FSC), and a constrained decoder is studied in this paper. First, recursions are developed for the error weight distribution. This statistics is relevant to the design of coding schemes and interleaving in concatenated systems. We also study the renewal nature of the residual error process as modified by the constrained decoder. Ferreira et al. conjectured that if the channel model is a renewal FSC, the super channel can be modeled as a similar renewal model. We use a statistics called the multigap distribution to analytically disprove this hypothesis. Furthermore, the effect of interleaving is investigated from a new perspective using the variance of the multigap distribution.

Keywords

• finite state channels
• multigap distribution
• constrained codes
• concatenated systems
• Gilbert-Elliott channels
• combinatorial methods