BELIEF PROPAGATION DECODING FOR SHORT ALGEBRAIC CODES WITH PERMUTATIONS WITHIN THE CODE SPACE

摘要

A method of processing data received over a channel includes receiving data representing probabilities associated with a plurality of variables and receiving a parity check matrix associated with a factor graph which includes variable nodes and check nodes connected by edges. After each exchange of messages between the variable nodes and check nodes, messages are calculated based on messages received at the variable nodes and permuted messages to be sent from the variable nodes in the next iteration are calculated by applying a permutation to the calculated messages. The permutation is of a set of permutations which map each codeword of the set of codewords onto a different codeword of the set of codewords. Soft values associated to variable nodes can be accumulated over two iterations of the message exchange processing.

主权项

1: A method of processing data received over a channel, the method comprising, at a controller of a decoder:
receiving data representing probabilities associated with a plurality of variables of a candidate codeword; receiving a parity check matrix associated with a factor graph and corresponding to a codebook, the codebook comprising a plurality of valid codewords, the factor graph comprising variable nodes, check nodes and edges connecting variable and check nodes; calculating initial messages to be sent from variable nodes to associated check nodes based on the received data; and iteratively exchanging messages between variable nodes and check nodes by iterating the following steps:
sending messages from the variable nodes to associated check nodes;sending messages from the check nodes to associated variable nodes based on messages received at the check nodes; andafter each exchange of messages between the variable nodes and check nodes:
calculating messages based on messages received at the variable nodes; andcalculating permuted messages to be sent from the variable nodes in the next iteration by applying a permutation to the calculated messages, wherein the permutation is of a set of permutations which map each codeword of the set of codewords onto a different codeword of the set of codewords.