A method for decoding Low Density Parity Check (LDPC) codes comprises executing a sum product algorithm to recover a set of information bits from an LDPC code represented as a bipartite graph of symbol nodes and check nodes, the sum product algorithm being responsive to input log likelihood ratios associated with the symbol nodes. The check nodes are updated by generating a set of forward difference metrics and a set of backward difference metrics in dependence on the ratios of logarithmic probabilities each associated with a corresponding symbol node of the LDPC code, updating each metric in the set of forward difference metrics in dependence on the absolute value of the log likelihood ratio associated with the symbol node and the absolute value of the previous metric in the set, updating each metric in the set of backward difference metrics in dependence on the absolute value of the log likelihood ratio associated with the symbol node and the absolute value of the previous metric in the set, and generating log likelihood ratios to be propagated back to each symbol node in dependence on the updated sets of forward and backward difference metrics.
A forward error correction method for decoding coded bits generated by low density parity check matrixes. The method comprises converting each of the coded bits into a log likelihood ratio (LLR) value, and applying the converted values to variable nodes; delivering messages applied to the variable nodes to check nodes; checking a message having a minimum value among the messages, and determining a sign of the message having the minimum value; receiving messages updated in the check nodes, adding up signs of the received messages and a sign of an initial message, applying a weighting factor of 1 when all signs are identical, and when all signs are not identical, updating a message of a variable node by applying a weighting factor; determining LLR of an initial input value; and hard-deciding values of the variable nodes, performing parity check on the hard decision values, and stopping the decoding when no error occurs.
A decoding method for decoding Low-Density Parity Check codes in transmission and recording systems includes a running minimum loop with the following iterative acts: reading a reliability value from the input sequence of input reliability values; comparing the reliability value with a stored value; and overwriting the stored value with the reliability value if the reliability value is smaller than the stored value.
LDPC (Low Density Parity Check) coded modulation hybrid decoding using non-Gray code maps for improved performance. Check node updating and symbol node updating are successively and alternatively performed on bit edge messages for a predetermined number of decoding iterations or until sufficient degree of precision is achieved. The symbol node updating of the bit edge messages uses symbol metrics corresponding to the symbol being decoded and the bit edge messages most recently updated by check node updating. The check node updating of the bit edge messages uses the bit edge messages most recently updated by symbol node updating. The symbol node updating computes possible soft symbol estimates. LDPC coded modulation hybrid decoding can decode an LDPC-BICM (Low Density Parity Check-Bit Interleaved Coded Modulation) signal having a symbol mapped using non-Gray code mapping. By using the non-Gray code mapping, a performance improvement is achieved over an only Gray code mapping system.
A low-density parity-check (LDPC) decoder (304) has a memory (308), and a processor (306). The processor is programmed to initialize (202) the LDPC decoder, calculate (204) a probability for each check node, calculate (206) a probability for each bit node, calculate soft decisions, update the bit nodes according to the calculated soft decisions, calculate (208) values from the calculated soft decisions, perform (210) a parity check on the calculated values, update (218) log-likelihood ratios (LLRs) if a bit error is detected in the calculated values, update the bit nodes according to the updated LLRs, and repeat the foregoing post initialization steps.
LDPC (Low Density Parity Check) coded modulation hybrid decoding. A novel approach is presented wherein a combination of bit decoding and symbol level decoding (e.g., hybrid decoding) is performed for LDPC coded signals. Check node updating and symbol node updating are successively and alternatively performed on bit edge messages for a predetermined number of decoding iterations or until a sufficient degree of precision is achieved. The symbol node updating of the bit edge messages involves using symbol metrics corresponding to the symbol being decoded as well as the bit edge messages most recently updated by check node updating. The check node updating of the bit edge messages involves using the bit edge messages most recently updated by symbol node updating. The symbol node updating also involves computing possible soft symbol estimates for the symbol during each decoding iteration.
