Layered LDGM codes: a capacity-approaching structure for arbitrary rates

Abstract

Layered LDGM (low-density generator matrix) codes are a novel LDPC coding structure that consists of the serial concatenation of several systematic LDGM codes. In this work we show how properly optimized layered LDGM codes are able to approach the theoretical capacity limits over a wide range of rates (varying from values close to one down to rates as low as 1/50). The primary advantage of layered LDGM codes with respect to previous work is that they keep the simplicity and flexibility of LDPC codes because they only use single parity check (SPC) constraints, instead of the more sophisticated Hadamard check constraints, to approach capacity in the low rate regime.