In quasi-static fading channels, error probability upper bounds for coded communication systems, such as Hu-Miller Bound, using the Gallager bounding technique trump over the renowned Union bound in terms of tightness. However due to the lack of dominating error events in quasi-static fading channels, knowledge of the exact Bit Weight Enumerating Function (Bit WEF), obtained from manipulating the input-output weight enumerating function (IOWEF) that are traditionally computationally intensive to compute for codes of practical constraint lengths, is required to give a vigorous bound. Divergence and underestimation of the upper bound are resulted otherwise with an insufficient number of truncated Bit WEF terms....[ Read more ]

In quasi-static fading channels, error probability upper bounds for coded communication systems, such as Hu-Miller Bound, using the Gallager bounding technique trump over the renowned Union bound in terms of tightness. However due to the lack of dominating error events in quasi-static fading channels, knowledge of the exact Bit Weight Enumerating Function (Bit WEF), obtained from manipulating the input-output weight enumerating function (IOWEF) that are traditionally computationally intensive to compute for codes of practical constraint lengths, is required to give a vigorous bound. Divergence and underestimation of the upper bound are resulted otherwise with an insufficient number of truncated Bit WEF terms.

We addressed in this thesis the challenge to compute exact IOWEFs and exact Bit WEFs, which can be extremely complex for practical constraint lengths, by combing some advanced algorithms in recent literature such as iterative FSM minimization and accelerated state reduction algorithm for trellis codes which can be represented in state diagrams. The effectiveness of such a scheme is demonstrated by computing Bit WEFs for practical codes such as codes used in IS-95 standard and CDMA2000 standard in manageable time, which are seemingly impossible to be done in the past.

We also deduced an easily computable code search criterion that minimizes the BER upper bounded by the Hu-Miller Bound, and performed a code search for convolutional codes of rate 1/2, 1/3 and 1/4. Simulation results show that the new codes found give noticeable gain as much as 1dB when compared to some known good codes.

When the constraint length is too large, truncation becomes unavoidable but its undesirable effect should be kept at minimal. We proposed an approximation of the Bit WEF and an algorithm, which are not covered in the literature to our best knowledge, to determine the sufficient number of terms to be included in a truncated Bit WEF based on some observation on the nature of truncated Bit WEF terms.