Nonsystematic convolutional codes for sequential decoding in space applications

Abstract

Previous space applications of sequential decoding have all employed convolutional codes of the systematic type where the information sequence itself is used as one of the encoded sequences. This paper describes a class of rate 1/2 nonsystematic convolutional codes with the following desirable properties: 1) an undetected decoding error probability verified by simulation to be much smaller than for the best systematic codes of the same constraint length; 2) computation behavior with sequential decoding verified by simulation to be virtually identical to that of the best systematic codes; 3) a "quick-look-in" feature that permits recovery of the information sequence from the hard-decisioned received data without decoding simply by modulo-two addition of the received sequences; and 4) suitability for encoding by simple circuitry requiring less hardware than encoders for the best systematic codes of the same constraint length. Theoretical analyses are given to show 1) that with these codes the information sequence is extracted as reliably as possible without decoding for nonsystematic codes and 2) that the constraints imposed to achieve the quicklook-in feature do not significantly limit the error-correcting ability of the codes in the sense that the Gilbert bound on minimum distance can still be attained under these constraints. These codes have been adopted for use in several forthcoming space missions.