In Quantum Key Distribution (QKD), identical data is shared between 2 nodes. Further, for example, a random number sharing system and a quantum cryptography system also need such data sharing.
A transmitter generally sends a signal including data through a noisy channel. The noisy channel may introduce errors into the signal. Therefore, the data sent by the transmitter may be different from the data received by the receiver. In order to share identical data between the transmitter and the receiver, it is necessary for the signal to be error corrected. Error correction can remove the noise introduced by the noisy channel from the data received by the receiver.
One method of error correction is using forward error correcting codes. According to forward error correction, the transmitter transforms (i.e. encodes) an original signal into a longer signal before sending. The longer signal can be called encoded signal. The encoded signal includes redundant information (which may be called parity bits). The transmitter sends the encoded signal to the receiver. As described above, the noisy channel may introduce errors into the encoded signal. However, the receiver can then inversely transforms (i.e. decodes) the noisy encoded signal back into the original signal by using the redundant information to correct any errors introduced by the noisy channel.
Low Density Parity Check (LDPC) codes are a certain type of forward error correcting codes. LDPC codes can be used for correcting errors introduced through communication. LDPC codes can correct errors with close to the theoretical minimum amount of redundant information added. Further LDPC codes can also be decoded computationally efficiently using iterative decoding.
Slepian-Wolf coding is one of known schemes of the forward error correction described above. According to Slepian-Wolf coding, the transmitter does not encode the original signal. However, the transmitter uses the error correction code to calculate an additional “syndrome” message based on the original signal. The syndrome message includes redundant information. The transmitter sends the original signal through a noisy channel and sends the syndrome message through a clear channel. The receiver receives both the noisy original signal and the syndrome message. The receiver can then use the redundant information in the syndrome message to decode the received noisy original signal back to the original signal. In particular, the receiver can perform the same decoding process as in standard forward error correction.
In error correction the rate at which the received signal can be processed to remove errors (expressed as the throughput rate, in bits per second) is important for many applications. The throughput rate is typically limited by the computational effort of encoding the original signal into the encoded signal and subsequently decoding the noisy encoded signal back into the original signal.
However, according to Slepian-Wolf coding, the encoding process can be replaced by the syndrome calculation process. Here, the syndrome calculation process is computationally much simpler than the encoding process. Therefore, in Slepian-Wolf coding, the main limitation on the throughput rate is only the decoding process performed by the receiver.