Doctoral Degrees (Electrical and Electronic Engineering)

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Browsing Doctoral Degrees (Electrical and Electronic Engineering) by Author "Babalola, Oluwaseyi Paul"

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    Soft-decision decoding of moderate length binary cycle codes based on parity-check transformation
    (Stellenbosch : Stellenbosch University, 2020-03) Babalola, Oluwaseyi Paul; Versfeld, Daniel Jaco J.; Ogundile, Olayinka O.; Stellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering.
    ENGLISH ABSTRACT: This thesis focuses on obtaining low complexity soft-decision (SD) decoding of binary cyclic codes with coding performance close to the optimal decoding algorithm. The belief propagation (BP) algorithm is commonly used to obtain near-optimal decoding but inappropriate for high-density parity-check (HDPC) codes. Therefore, alternative solutions such as the adaptive belief propagation (ABP) algorithm and the paritycheck transformation algorithm (PTA) have been proposed in the literature, based on matrix transformation, to effectively apply the BP decoding for HDPC codes. The extended parity-check transformation algorithm (EPTA) is introduced in this thesis to obtain a transformed parity-check matrix for the class of binary cyclic (BC) codes. The EPTA reduces the computational complexity of the known adaptive belief propagation (ABP) algorithm. However, it requires more iterative processes to attain comparable results to the ABP. Hence, a generalized parity-check transformation (GPT) algorithm for iterative SD decoding of the class of BC codes is developed. The proposed GPT algorithm is motivated by the EPTA and the belief propagation. The algorithm utilizes a new approach of matrix transformation to overcome the limitation with the BP algorithm for HDPC codes. The transformed matrix is obtained by permuting the columns of the initial parity-check matrix based on the reliability information received from the channel. Results show that the GPT offers a significant performance gain when compared with the hard decision Berlekamp-Massey (B-M) and belief propagation (BP) algorithms. It also produces a reasonable performance gain as compared with other iterative SD decoders. An important feature of the decoder is that it functions within a practical decoding time complexity and can be generally implemented for the class of linear block codes. Furthermore, a perfect knowledge model is developed to verify the optimality of all BP based algorithms for HDPC codes. The PKM computes a list of candidate matrices based on the prior knowledge of the transmitted codeword and it selects the best parity-check matrix according to a distance metric. The selected matrix is optimal since it minimizes the probability of error over various choices in the list. As a result, we show that for a given channel condition, the conventional transformed matrix, obtained by Gaussian reduction, is sub-optimal and will not necessarily contain unitary weighted columns at corresponding columns of the unreliable bits. Here, there exist specific scenarios where this matrix is not the same as the selected matrix from the PKM, giving room for improvement in the matrices of the BP in general. More so, the model can be used to verify performances of newly developed iterative SD decoders based on parity-check equations. In conclusion, the discovery of this thesis is important as it proposes a reduced computational time complexity soft-decision decoder for algebraic block codes. In view of some studies where the potentials of these coding techniques have been successfully demonstrated for cellular telephony, remote radio, spread spectrum communications, and satellite transmissions, the generalized parity-check matrix transformation algorithm can be implemented as a real-time decoder in order to reduce the number of transmission errors in digital communications.