Table Look-Up Decoding

Abstract

It is desirable to develop a decoding scheme with speed comparable to that of majority-logic decoding, and error-correcting capability approaching that of Viterbi or sequential decoding. For a given encoding rate and constraint length, this requirement can be met by using table look-up decoding. For systematic encoders, it achieves the full feedback error-correcting capability t _min without any requirements such as orthogonalizability. Hence, encoders with much smaller constraint lengths can be used. For instance, rate one-half completely orthogonalizable encoders with the same d _min have larger m than rate one-half OMD encoders, and rate one-half self-orthogonal encoders have even larger m. Table look-up decoding can also be used with nonsystematic encoders, and error-correcting capability t _j ≥ t _min is achievable if received subsequences larger than one output constraint length are used in each decoding step.