Exploiting Concatenation in the Design of Low-Density Parity-Check Codes

Abstract—This paper describes a method to exploit the concatenation of very simple component codes in order to obtain good low-density parity-check codes. This allows to design codes having a number of benefits, as high flexibility in length and rate and low encoding complexity. We focus on two kinds of concatenation: the former is classic serial concatenation, in which redundancy is progressively added to the encoded word, whereas the latter is the special case of concatenation coinciding with a bi-dimensional product code. The proposed design technique allows to obtain codes characterized by parity-check matrices with a low density of 1 symbols and free of short cycles in their associated Tanner graph; so efficient algorithms based on the belief propagation principle can be adopted for their decoding. In addition, the systematic form of the component codes can ensure rate compatibility; so the proposed codes can be adopted in type-II hybrid automatic repeat request schemes. We analyze their properties through theoretical arguments and provide some design examples to assess their performance. Keywords-LDPC codes; concatenated codes; product codes. I