| Because of their complexity, practical coding and modulation systems are usually evaluated using error probability curves derived through simulations. This approach provides much useful information; however, it also has two major drawbacks. First, performance degradation can not be attributed to a single component in the system. Second, the simulations are typically complicated and very time consuming. This thesis provides two alternatives to simulation. The first approach analyzes the performance of concatenated coding systems and modulation schemes by examining the loss of capacity resulting from each of the processing steps. This information-theoretic approach allows the separate evaluation of codes and decoders and thus the identification of where loss of capacity occurs. Knowledge of this capacity loss is useful, for example, in evaluating the benefits of inner decoders that provide information beyond the maximum likelihood estimate to an outer generalized minimum distance decoder and inner decoders that output, on a bit-by-bit basis, the probability a bit is one (e.g., the inner decoders used in turbo codes). The second approach provides new bounds on the size of the performance gap between a random code and the best possible code assuming that each has the same length and rate. It is shown that the gap is small under a surprisingly large range of channel conditions. An upper bound on the random code error probability and a lower bound on the error probability for the best possible code is presented and used to assess several common codes, including turbo codes. |
