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A construction of big convolutional codes from short codes called blockMarkov superposition transmission (BMST) is proposed. The BMST is very similarto superposition blockMarkov encoding (SBME), which has been widely used toprove multiuser coding theorems. The encoding process of BMST can be as fast asthat of the involved short code, while the decoding process can be implementedas an iterative sliding-window decoding algorithm with a tunable delay. Moreimportantly, the performance of BMST can be simply lower-bounded in terms ofthe transmission memory given that the performance of the short code isavailable. Numerical results show that, 1) the lower bounds can be matched witha moderate decoding delay in the low bit-error-rate (BER) region, implying thatthe iterative slidingwindow decoding algorithm is near optimal; 2) BMST withrepetition codes and single parity-check codes can approach the Shannon limitwithin 0.5 dB at BER of 10^{-5} for a wide range of code rates; and 3) BMST canalso be applied to nonlinear codes.

Block Markov Superposition Transmission: Construction of Big Convolutional Codes from Short Codes