Low-density parity-check codes for multilevel modulation

The application of low-density parity-check (LDPC) codes to multilevel modulation systems is studied. A family of binary LDPC codes that offer good performance and do not suffer from error-floor effects at low bit-error rates is introduced. A number of properties render these codes attractive for practical applications: they are specified via a small number of parameters, are encodable in linear time, and the generation of their parity-check matrix is deterministic, involving a small number of preprocessing operations. In addition, the symbol-mapping technique based on "double Gray-code labeling" for obtaining coded multilevel transmit symbols is described. Finally, it is shown that the proposed LDPC coding technique is well suited for multicarrier digital-subscriber-line transmission applications as it permits a wide range of trade-offs between latency, complexity, and system performance.