Efficient Bit-to-Symbol Likelihood Mappings

A new algorithm that increases decoder speed contributes to the development of high-speed optical communications links.

This innovation is an efficient algorithm designed to perform bit-to-symbol and symbol-to-bit likelihood mappings that represent a significant portion of the complexity of an error-correction code decoder for high-order constellations. Recent implementation of the algorithm in hardware has yielded an 8-percent reduction in overall area relative to the prior design. This gain resulted from changing just two operations in a complex decoder. Larger gains are possible for larger constellations that are of interest for deep-space optical communications. The algorithm structures the bit-to-symbol/symbol-to-bit operations like a tree that forms a portion of a Fast-Fourier-Transform (FFT). Much like an FFT, the parallel computation may be structured in order to reduce repeated computations. Symmetry in the values was noted and allowed for the reduction of the bit-to-symbol mapping by a factor of 2.

This method computes bit-to-symbol likelihood mappings for a soft-in/soft-out decoder that operates over M-ary symbols, but receives and transmits bit-log likelihoods. There are two bit-to-symbol mappings. The first requires M – 2 operations and log₂ M – 1 clock cycles. The second requires O(M log₂ M) operations and log₂log₂ M clock cycles. The symbol-to-bit mapping requires log₂ M clock cycles and 3M – log₂ M – 4 operations. In a pipelined architecture, the reduced operation counts also translate into reduced memory requirement.

This technology can apply to communications channels that use high-order constellations and decode over symbols from that constellation. This would potentially include a large number of communications channels, such as cable modems, disk drives, etc., as well as being a direct improvement to the Optical Communications End-to-End Testbed, which is currently in use to demonstrate, test, and develop deep-space optical communications technology.

This work was done by Bruce E. Moision of Caltech and Michael A. Nakashima of Skillstorm, Incorporated for NASA’s Jet Propulsion Laboratory.

In accordance with Public Law 96-517, the contractor has elected to retain title to this invention. Inquiries concerning rights for its commercial use should be addressed to:

Innovative Technology Assets Management
JPL
Mail Stop 202-233
4800 Oak Grove Drive
Pasadena, CA 91109-8099
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Refer to NPO-44987, volume and number of this NASA Tech Briefs issue, and the page number.