Serially concatenated systems : an iterative coding approach with application to continuous phase modulation
Abstract
Iterative methods for concatenated coding and modulation in digital communication systems are considered. It is assumed that the code and modulation can be described by finite-state machines (FSM). An iterative decoder for such a system typically consists of a posteriori probability (APP) algorithms for the constituent FSMs. Starting with a detailed examination of these algorithms, it is found that their initialization values can be formally justified. Then, possible iterative methods such as fix-point iteration, Jacobi over-relaxation, damped substitution, and Newton’s method are presented and evaluated. The result is that fix-point iteration seems to be the best choice in most situations. As an application of iterative decoding in serially concatenated systems, coded and interleaved continuous phase modulation (CPM) is investigated. An APP algorithm (or maximum APP (MAP) detector) for CPM is derived, based on the classic APP algorithm for channel codes. It is then shown that a good suboptimal algorithm can be obtained using only a small set of receiver filters, which are optimal with respect to the size of the set. The resulting system is analyzed with the aim to determine the main parameters affecting performance. The weight spectrum for coded and interleaved minimum shift keying (MSK) is computed, resulting in a transfer function bound. This is cumbersome for a general CPM system; instead only the most significant error events contributing to the weight spectrum are…
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