Channel Coding Techniques with Emphasis on Convolutional and Turbo Codes

In this thesis, a family of low complexity convolutional codes is constructed, by modifying appropriately the trellis diagram of punctured convolutional codes. The goal is to improve performance at the expense of a reasonable low increase of the trellis complexity. Many new convolutional codes of various code rates and values of complexity are provided. In many cases, a small increase in complexity can lead to a great improvement of performance, compared to punctured convolutional codes. Furthermore, a method is presented for designing new flexible convolutional codes, by combining the techniques of path pruning and puncturing. The new codes can vary their rate, as well as the complexity of their trellis diagram, and hence the computational complexity of the decoding algorithm, leading to coding schemes that manage more efficiently the system resources, compared to classical variable rate convolutional codes. The complexity of the trellis diagram affects the computational complexity of every trellis based decoding algorithm, like BCJR and its variations. Thus, the possibility of applying the aforementioned results using recursive convolutional encoders, which are used as constituent encoders in turbo codes, is investigated. The goal is to construct efficient flexible turbo coding schemes. Simulation results indicate that in specific ranges of the signal to noise ratio, a great decrease in the computational complexity of the decoding procedure can even result to a decrease in the bit error rate.