Summary: We present a class of convolutional codes defined by a low-density parity-check matrix and an iterative algorithm of the decoding of these codes. The performance of this decoding is close to the performance of turbo decoding. Our simulation shows that for the rate \(R= 1/2\) binary codes, the performance is substantially better than for ordinary convolutional codes with the same decoding complexity per information bit. As an example, we constructed convolutional codes with memory \(M= 1025,2049\), and 4097 showing that we are about 1 dB from the capacity limit at a bit-error rate of \(10^{-5}\) and a decoding complexity of the same magnitude as a Viterbi decoder for codes having memory \(M= 10\).