The Research Of The Logic Algebra Decoding Method Of (2, 1, 4) Convolutional Code

With the rapid development of digital communication, data processing and computer communication networks, the more reliability and efficiency of information transmission is demanded. As an important channel error-correcting code, convolutional code has excellent performance, and plays an important role in many fields , such as mobile communication , satellite communication and space communication. The traditional decoding methods of convolutional code can be classified into two types: threshold decoding and probability decoding. The latter can be divided into sequential decoding and Viterbi algorithm. Searching a new decoding method with simple algorithm and good performance for convolutional code has important practicality.In this paper, a new decoding method of convolutional codes named Logic Algebra Decoding is constructed using the reversibility of Mode 2 operation in Logic Algebra, and the decoding method of (2, 1, 4) convolutional code is deep researched and discussed. The fundamental of Logic Algebra Decoding is analyzed at first. Then the bit error types of (2, 1, 4) convolutional code are discussed, and 19 bit error types in a constraint length including 10 bits are found, if one or two bit errors are considered. Furthermore, the bit error decision rules are researched, and it is proved that the syndrome is a function only of the error pattern and is independent of the information sequence from encoder. The corresponding syndrome for each of the 19 bit error types is obtained through the error patterns analysis. Among the 19 syndromes, 8 syndromes and their bit error types exist ambiguity which can be solved by increasing the observational time. Thus, the one-to-one relationship between the 19 syndromes and the bit error types is established, and the Logic Algebra Decoding algorithm of (2, 1,4) convolutional...