Browse Theses

Turbo codes were introduced in 1993 and are now considered among the most important developments in coding theory. A Turbo encoder is formed by two parallel concatenated recursive convolutional encoders connected by an interleaver. The interleaver performs permutation of the input sequence. The decoder consists of two iterative maximum a posterior (MAP) decoders connected by an interleaver and a deinterleaver. Turbo codes have excellent bit error rate (BER) performance at low signal-to-noise ratios (SNRs). Performance near Shannon capacity limit can be obtained with large interleavers, and comparatively good performance is possible for any interleaver size. In this thesis, we deal with four important issues of Turbo codes.

The first issue is the sensitivity of Turbo decoders to noise distribution mismatch. We investigate the sensitivity of Turbo decoders to noise distribution mismatch and propose a simple method for on-line estimation of the noise distribution. The simulation results show that the proposed procedure leads to relatively good performance for the class of memoryless generalized Gaussian noise and the class of multimodal Gaussian noise.

The second issue is the “error floor” of Turbo codes, which is the flattening of the performance curve for moderate to high SNR. Since simulation is impractical in this range, we analyze the performance of Turbo codes through union bounds. To do this, we propose a simple recursive method to generate the input redundancy weight enumerating function (IRWEF) of time-invariant recursive systematic convolutional encoders. This method is used to determine the union bound of Turbo codes with different puncturing patterns and termination conditions. We find that the Turbo code performance at high SNR can be significantly improved by trellis termination. For a given rate, different puncturing patterns result in different code performance.

The third issue is the decoding complexity. Standard Turbo decoding is highly complex. To reduce decoding complexity, we introduce a class of error-correcting codes called zigzag codes. A zigzag code is highly structured and can be viewed as a two-state convolutional code. A concatenated zigzag encoder has several encoders connected by several interleavers. The performance is comparable to (though slightly worse than) standard Turbo codes at low SNR. At high SNR, both analysis and simulation results show that parallel concatenated zigzag codes have lower error floor than standard Turbo codes.

The fourth issue is about the interleaver design for concatenated zigzag codes. Three simple interleavers are proposed and simulations show that the proposed interleavers can significantly lower the error floor of concatenated zigzag codes.