Column-layered message-passing LDPC decoder

1. A decoder comprising:

a variable node unit (VNU) comprising:

a variable-to-check lookup table circuit configured to output a variable-to-check message corresponding to a check node based on message value counts,

a hard-decision lookup table circuit configured to output a hard-decision value corresponding to a variable node,

inputs configured to receive check-to-variable messages corresponding to the variable node, and

a plurality of variable-to-check lookup table circuits that includes the variable-to-check lookup table circuit; and

a check node unit (CNU) responsive to the variable-to-check message and configured to generate an updated check-to-variable message.

2. The decoder of claim 1 , wherein:

the VNU is included in a VNU stage that comprises a first number of VNUs corresponding to a column layer of a parity check matrix,

the CNU is included in a CNU stage that comprises a second number of CNUs corresponding to a multiple of a column weight of the parity check matrix, and

the VNU stage and the CNU stage are configured to operate according to a column-layered decoding schedule.

3. The decoder of claim 1 , wherein the variable-to-check lookup table circuit is configured to receive the check-to-variable messages from at least two of the inputs.

4. The decoder of claim 3 , wherein each of the check-to-variable messages includes a two-bit message.

5. The decoder of claim 1 , wherein the VNU comprises a one-hot decoder circuit configured to generate one-hot outputs corresponding to the check-to-variable messages.

6. The decoder of claim 5 , further comprising a summer coupled to the variable-to-check lookup table circuit and configured to output counts of the one-hot outputs.

7. The decoder of claim 1 , wherein the variable-to-check message includes a two-bit message.

8. The decoder of claim 1 , wherein the VNU is configured to receive multiple messages and to generate a count of the multiple messages that have a particular message value.

9. The decoder of claim 1 , wherein the VNU is configured to receive a plurality of distinct message values and to generate a count corresponding to each of the plurality of distinct message values.

10. The decoder of claim 1 , wherein the CNU is configured to generate the updated check-to-variable message based at least in part on the message value counts.

11. The decoder of claim 1 , wherein the CNU is configured to generate a count of variable-to-check messages output from the VNU that indicate a particular magnitude.

12. The decoder of claim 1 , wherein the CNU is configured to generate the updated check-to-variable message based on a determination of whether a syndrome weight associated with the updated check-to-variable message is less than a syndrome weight threshold.

13. The decoder of claim 1 , wherein the CNU is configured to reconstruct the check-to-variable messages based on a count corresponding to variable-to-check messages having a particular magnitude value and based on stored variable-to-check messages.

14. An apparatus comprising:

means for producing a variable-to-check message corresponding to a check node, the means for producing configured to

output the variable-to-check message based on a variable-to-check lookup operation;

means for outputting a hard-decision value corresponding to a variable node, the means for outputting configured to output the hard-decision value based on a hard-decision lookup operation;

means for receiving check-to-variable messages corresponding to the variable node;

means for generating an updated check-to-variable message, the means for generating configured to generate the updated check-to-variable message responsive to the variable-to-check message; and

a one-hot decoder circuit configured to generate one-hot outputs corresponding to the check-to-variable messages.

15. The apparatus of claim 14 , wherein:

the means for producing and the means for outputting are included in a variable node unit (VNU) stage that comprises a first number of VNUs corresponding to a column layer of a parity check matrix,

the means for generating is included in a check node unit (CNU) stage that comprises a second number of CNUs corresponding to a multiple of a column weight of the parity check matrix, and

the VNU stage and the CNU stage are configured to operate according to a column-layered decoding schedule.

16. A method comprising:

outputting a variable-to-check message at a variable-to-check lookup table circuit of a variable node unit (VNU), the variable-to-check message corresponding to a check node of a decoder and generated based on message value counts;

outputting a hard-decision value at a hard-decision lookup table circuit, the hard-decision value corresponding to a variable node of the decoder;

receiving check-to-variable messages corresponding to the variable node;

generating one-hot outputs corresponding to the check-to-variable messages;

outputting counts of the one-hot outputs; and

generating an updated check-to-variable message, the updated check-to-variable message generated at a check node unit (CNU) responsive to the variable-to-check message.

17. The method of claim 16 , wherein:

the VNU is included in a VNU stage that comprises a first number of VNUs corresponding to a column layer of a parity check matrix,

the CNU is included in a CNU stage that comprises a second number of CNUs corresponding to a multiple of a column weight of the parity check matrix, and

the VNU stage and the CNU stage operate according to a column-layered decoding schedule.

18. The method of claim 16 , wherein the VNU receives two-bit check-to-variable messages from the CNU, and wherein the CNU receives two-bit variable-to-check messages from the VNU.

19. The method of claim 16 , further comprising outputting, at the variable-to-check lookup table circuit, a count of check-to-variable messages that are indicative of a particular message value.