Error correction in data communication system using iterative belief propagation with syndrome sent over a separate channel

摘要

To enable error correction of subject data (m) sent over a noisy first channel (40) between transmitting and receiving apparatus (20, 30), a target syndrome (s) determined as an ordered plurality of modulo-2 summations of the bit values of respective predetermined selections of bits of the subject data (m) is also sent but over an error-free or error-corrected second channel (45). At receiving apparatus (30) the errored received subject data (r) is error corrected by applying iterative belief propagation to adjust bit-value probabilities of the received subject data (r) such that an ordered plurality of modulo-2 summations of the probable bit values of the respective predetermined selections of bits matches the received target syndrome (s). Preferably, the bit selections for the modulo-2 summations are determined in accordance with a logical network independently generated in a pseudo-random manner in the transmitting and receiving apparatus (20, 30). LDPC codes are used. Applications include quantum key distribution (QKD).