| CPC H04L 1/0061 (2013.01) | 18 Claims |

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1. An apparatus comprising:
a receiver for receiving a sequence of bits via a channel, the sequence of bits having been encoded at a source using a linear error correcting code; and
a decoder for decoding the received sequence of bits and outputting a decoded sequence of bits, wherein the decoder implements a message passing schedule determined using a cluster graph representation of the linear error correcting code for passing of joint distribution-based messages between parity check clusters of the cluster graph representation of the linear error correcting code, including iterating message passing until consensus between all the parity check clusters regarding shared bit values is reached, and outputting the decoded sequence of bits when consensus is reached.
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