Researches On Decoding Of Concatenated Codes

Channel coding is a fundamental method to improve the communication reliability. Since Shannon proposed his famous channel encoding theorem, peoples have do their best to reach the channel capacity. Concatenated code is one of the most prospective method to solve this difficult problem. Therefore, the fast and efficient decoding algorithms are the key to the practice of these codes. This thesis puts its emphasis on the new concatenated constructions, their fast decoding algorithm and performance. The main results include: 1. Propose a stage BD decoding method of the multilevel code based on the Euclidean distance, and prove that its a BD algorithm, too. 2. Propose a multi-level concatenated construction of Hexacode. On the basis of this result, present a BD algorithm of the Hexacode, which has better performance and comparable complexity to that of the fastest known algorithm. Some modification can further improve the performance of the new algorithm. 3. On the basis of different multi-level structure, propose several BD algorithms for the Golay code. Their performance near to that of MLD with increment of the decoding complexity, but the computation amounts is only half of the fastest MLD algorithm. 4. Propose a new multi-level concatenated construction of the (32,16,8) Reed- Muller code based on the quaternazy (8,4,4)4 code for the first time, and then obtain a fastest algorithm for the (32,1 6,8)Reed-Muller code. Three another BD algorithms are also presented. 5. Propose a BD algorithm for the Leech lattice using the decoder of the Hexacode, which is a good trade-off between the performance and the complexity. 6. Derive a formula to calculate the error probability of the concatenated code of the Reed-Solomon codes and block codes. Give some numeral results for several codes. Implement a cascaded error correcting module using DSP. 7. For (N,K) block parallel concatenated codes, derive a fast and efficient soft- output decode algorithm. The Complexity is the amount of (N+K)IN VA. 8. Study the selection of permutations of block parallel product codes. Using the condition weight distribution enumerator function, we propose three criteria and permutation design method for the Hamming parallel product codes for the first time. 9. Implement a voice band 4.8Kbps modem using multicarrier modulation technique.