Efficient LDPC code decoding with new minus operator in a finite precision radix system

An apparatus, comprising:

• a check node operator;
• a bit node calculator that is operable to update plurality of edge messages provided from the check node operator using a plurality of bit metrics, wherein:
• the bit node calculator is operable to perform min†− (min-dagger minus) processing when updating the plurality of edge messages;
• the updating of the updating the plurality of edge messages that is performed by the bit node calculator is mathematically performed in the logarithmic domain using min†− processing;
• the bit node calculator includes a min†− processor that is operable to perform the min†− processing when updating the plurality of edge messages;
• the min†− processor is operable to perform min*− (min-star minus) processing on at least 2 input values;
• when the results of the min*− processing on the at least 2 input values is not substantially greater than zero, then the min†− processor is operable to output a zero valued output;
• and
• when the results of the min*− processing on the at least 2 input values is substantially greater than zero, then the min†− processor is operable to output a result generated by the min*− processing on the at least 2 input values.

An apparatus, comprising:

• a min†− (min-dagger minus) processor that includes a min*− (min-star minus) processor that is operable to perform min*− (min-star minus) processing on at least 2 input values, wherein:
• when the results of the min*− processing on the at least 2 input values is not substantially greater than zero, then the min†− processor is operable to output a zero valued output;
• when the results of the min*− processing on the at least 2 input values is substantially greater than zero, then the min†− processor is operable to output a result generated by the min*− processing on the at least 2 input values;
• the min*− processor is operable to determine a minimum value among the at least 2 input values;
• the min*− processor is operable to calculate a logarithmic correction factor using the at least 2 input values;
• and
• the min*− processor is operable to combine the minimum value and the logarithmic correction factor to generate the result of the min*− processing on the at least 2 input values.

A method for updating a plurality of edge messages using min†− (min-dagger minus) processing when decoding an LDPC (Low Density Parity Check) coded signal, the method comprising

• receiving a plurality of edge messages with respect to a plurality of check nodes within an LDPC bipartite graph that corresponds to an LDPC code;
• initializing a minimal absolute valued edge message of the plurality of the plurality of edge messages;
• initializing a minimal index for the plurality of the plurality of edge messages;
• initializing a sign function of a first edge message of the plurality of edge messages;
• performing decoding processing across all other edge messages, besides the first edge message, of the plurality of edge messages that includes:
• selectively replacing the minimal absolute valued edge message with an absolute value of a current edge message when the absolute value of the current edge message is substantially less than or equal with the minimal absolute valued edge message and updating the minimal index for the plurality of the plurality of edge messages;
• computing min* (min-star) results of the absolute values of all edge messages of the plurality of edge messages except for the minimal absolute valued edge message;
• computing a sign function of a current edge message using a sign function of a previous edge message, as defined according to the decoding processing;
• computing min* results of absolute values of all edge messages of the plurality of edge messages;
• and
• updating the plurality of edge messages with respect to a plurality of bit nodes within the LDPC bipartite graph that corresponds to the LDPC code using min†− processing.

An apparatus, comprising:

• a min†− (min-dagger minus) processor that is operable to perform min*− (min-star minus) processing on at least 2 input values, wherein:
• when the results of the min*− processing on the at least 2 input values is not substantially greater than zero, the min†− processor is operable to output a zero valued output;
• when the results of the min*− processing on the at least 2 input values is substantially greater than zero, the min†− processor is operable to output result generated by the min*− processing on the at least 2 input values;
• the min†− processor include a min*− (min-star minus) processor:
• the min*− processor is operable to determine a minimum value among the at least 2 input values;
• the min*− processor is operable to calculate a logarithmic correction factor using the at least 2 input values;
• and
• the min*− processor is operable to combine the minimum value and the logarithmic correction factor to generate the result of the min*− processing on the at least 2 input values.