Rate-compatible low-density parity-check codes for digital subscriber lines

Rate-compatible low-density parity-check (LDPC) codes obtained from the class of array LDPC codes are presented. The design methodology described herein retains practical advantages of array LDPC codes such as excellent performance and efficient encodability across all the codes in a rate-compatible family. Different codes in the rate-compatible family can be specified by a small number of parameters and constructed algebraically with a small amount of preprocessing. The rate-compatible codes can be decoded using a generic decoder architecture, leading to efficient implementations. These properties make the codes attractive for use in DSL systems that need to support a large number of code parameters to cope with channel variability.