A method for constructing low-density convolutional (LDC) codes with the degree distribution optimized for block low-density parity-check (LDPC) codes is presented. If the degree distribution is irregular, the constructed LDC codes are also irregular. In this letter we give the encoding and decoding method for LDC codes, and study how to avoid the short cycles of LDC codes. Some simulation results are also presented.

Richardson and Urbanke developed a powerful method density evolution which determines, for various channels, the capacity of irregular low-density parity-check code ensembles. We develop generalized density evolution for minutely represented ensembles and show it includes conventional representation as a special case. Furthermore, we present an example of code ensembles used over binary erasure channel and binary input additive white Gaussian noise channel which have better thresholds than highly optimized ensembles with conventional representation.