High-Efficiency Error Correction for Photon Counting

Today's data-driven society demands high data rates and high-rate communication links. Addressing these needs in everything from gigabit Ethernet network connections and telephone or cable television signals to communication between spacecraft can require high bandwidth, high power, large transmit or receive apertures or both, and high receiver sensitivity. Optical communication is attractive for these applications. High bandwidths are more readily available at optical wavelengths than at radio frequencies, and optical transmitters and receivers can be made compactly, as aperture size requirements scale with the signal wavelength. Highly sensitive photon-detecting receivers can be constructed to achieve high-rate data links capable of transmitting multiple bits per received photon. This exceptional receiver sensitivity requires an expanded bandwidth and powerful codes for correcting errors in the detected data. The bandwidth expansion is mitigated easily, but powerful error correction can be difficult to implement at gigabit-per-second data rates. MIT Lincoln Laboratory is designing efficient forward error correction codes that combine several essential qualities, such as near-capacity rates, very low error floors, and efficient algorithms for coding and decoding. Such properties are desirable in nearly every communications system, but the efficient coding and decoding is particularly important for a high-data-rate, low-power system used in applications such as photon counting. The photon-counting channel shares many characteristics with erasure channels. An erasure is a particular kind of error in which the receiver is unable to detect the transmitted symbol or somehow knows that the received symbol is wrong. In photon counting that uses pulse-Pulse-position modulation (PPM) using a photon-counting receiver produces an extremely sensitive optical communications system, capable of transmitting multiple bits of information for each received photon. Such impressive sensitivity requires powerful error-correction codes that must be computationally efficient to enable high data throughput. Fountain codes combine performance and efficiency for a narrow class of channels, known as erasure channels. A potential application for fountain codes is the photon-counting PPM receiver, which is an approximate erasure channel and includes occasional channel errors. This non-ideal behavior requires a nontraditional use of fountain codes. With a carefully constructed architecture, fountain codes provide the desired efficient error correction to the photon-counting PPM receiver.