Study On Several Coding And Modulation Problems Based On Hadamard Codes

Hadamard matrices are widely used in communication systems, data compression, error correcting codes, cryptography, linear filtering and spectral analysis, etc. The wide applications of Hadamard matrices lie in their simplification and efficiency in realization. The Hadamard codes generated from Hadamard matrices are also widely employed in the design of error correcting codes because of these properties.After having command of the soft-input and soft-output decoding algorithm of Hadamard codes, the author combines the ideas of concatenated coding and iterative decoding in modern coding theory and studies the coded modulation schemes based on Hadamard codes. The author obtains some results listing as follows:(1) Find and proof that there exit single parity check constrains in Hadamard codes consisting of several information bits and certain parity check bit.(2) Design a new kind of low-rate codes: parallel concatenated twist Hadamard codes based on the single parity check constrains in bi-orthogonal Hadamard codes consisting of several information bits and certain parity check bit. Simulation results show that the designed codes have very good error-floor performance.(3) Union bound analysis is presented for parallel concatenated twist Hadamard codes. It can give the reason why the designed codes have very good error-floor performance from a theoretical perspective.(4) Proof the equivalence between the soft-input and soft-output demodulation algorithm of orthogonal modulation and the soft-input and soft-output decoding algorithm of orthogonal Hadamard codes. Then the deducted APP-FHT and FHT are employed to reduce the complexity of orthogonal demodulation.(5) Learn the basic principles of Low-Density Parity-Check (LDPC) codes and pulse position modulation (PPM). And then based on the equivalence between the orthogonal modulation and Hadamard codes, design a new kind of scheme: LDPC-PPM. (6) Design another new kind of scheme: Zigzag-PPM based on Zigzag codes and PPM. This scheme has a regular structure and can use two-way algorithm to decoding, whose complexity is low.(7) Design and optimize LDPC coded bit interleaved orthogonal modulation systems with non-coherent detection over flat Rayleigh fading channels.