Generalized Unit-Memory Convolutional Concatenated Codes

We develop and analyze a concatenated coding system with inner unit-memory convolutional codes and outer Reed–Solomon codes. We prove the existence of embedded inner code systems in which the main code and all the subcodes have optimal error-correcting properties. We investigate an inner-code decoding algorithm which allows erasures, and tradeoff relations are obtained for error and erasure probabilities. These results lead to the development of a concatenated decoding algorithm for generalized unit-memory convolutional concatenated codes and produce bounds on the decoding error exponent of this algorithm. A bound on decoding complexity of these codes is given.