In a proposed coding-and-modulation/ demodulation-and-decoding scheme for a free-space optical communication system, an error-correcting code of the low-density parity-check (LDPC) type would be concatenated with a modulation code that consists of a mapping of bits to pulse-position-modulation (PPM) symbols. Hence, the scheme is denoted LDPC-PPM. This scheme could be considered a competitor of a related prior scheme in which an outer convolutional error-correcting code is concatenated with an interleaving operation, a bit-accumulation operation, and a PPM inner code. Both the prior and present schemes can be characterized as serially concatenated pulse-position modulation (SCPPM) coding schemes.

Figure 1. Data Are Encoded, then transmitted as a PPM optical signal. At the receiving end, the optical signal is demodulated and decoded in an iterative process.
Figure 1 represents a free-space optical communication system based on either the present LDPC-PPM scheme or the prior SCPPM scheme. At the transmitting terminal, the original data (u) are processed by an encoder into blocks of bits (a), and the encoded data are mapped to PPM of an optical signal (c). For the purpose of design and analysis, the optical channel in which the PPM signal propagates is modeled as a Poisson point process. At the receiving terminal, the arriving optical signal (y) is demodulated to obtain an estimate (â) of the coded data, which is then processed by a decoder to obtain an estimate (û) of the original data.

Figure 2. The Bit-Error Rate (Pb) was computed as a function of relative signal strength for two coding schemes and for the theoretical channel capacity for the special case of code blocks of ≈8Kb length, nb = 0.2, and M = 64.
The demodulation and decoding subprocesses are iterated to improve the final estimates in an attempt to reconstruct the original data stream (u) exactly. The decoder implements a soft-input/soft-output (SISO) algorithm. This or any SISO decoder receives, as soft inputs, noisy versions (estimates and log- likelihoods of the estimates) of the input and output of the encoder and produces updated log-likelihoods of the estimates of the input, the output, or both. These estimates and their log-likelihoods may then be transmitted to other SISO modules in the receiver, where they are treated as noisy inputs.

In comparison with non-iterative alternatives, both the present LDPC-PPM scheme and the prior SCPPM scheme offer better performance. In comparison with iterative alternatives, both schemes afford better performance with less complexity. In comparison of these schemes with each other, each is partly advantageous and partly disadvantageous: For example, computational simulations have shown that for a block length of about 8Kb, the performance of the prior SCPPM scheme is about 0.8 dB away from the theoretical channel capacity, while the performance of the LDPC-PPM scheme is expected to be about 1.2 dB away from the theoretical channel capacity at a bit-error rate of about 2 × 10–5 (see Figure 2); in other words, the performance of the LDPC-PPM scheme is expected to be about 0.4 dB below that of the prior SCPPM scheme. On the other hand, unlike the prior SCPPM scheme, the LDPC-PPM scheme is lends itself very well to low-latency parallel processing. Either scheme could serve as the basis of design of an optical communication system, depending on requirements pertaining to the PPM order, latency, and architecture of the system.

This work was done by Maged Barsoum, Bruce Moision, Dariush Divsalar, and Jon Hamkins of Caltech and Michael Fitz of UCLA for NASA’s Jet Propulsion Laboratory. NPO-44408

This Brief includes a Technical Support Package (TSP).
LDPC-PPM Coding Scheme for Optical Communication

(reference NPO-44408) is currently available for download from the TSP library.

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