Error-propagation properties of uniform codes

The problem of error propagation in uniform codes is investigated using the concept of parity-parallelogram submatrices and the threshold-decoding algorithm. A set of optimum orthogonalization rules is presented and it is shown that if these rules are incorporated into the decoder, then sufficient conditions can be found for the return of the decoder to correct operation following a decoding error. These conditions are considerably less stringent than the requirement that the channel be completely free of errors following a decoding error. However, this is not the case if the prescribed orthogonalization rules are not followed, as is demonstrated with a simple example. It is also shown that the syndrome memory required with Massey's orthogonalization procedure for definite decoding of uniform codes is the lowest possible. The results of simulation of the rate
\frac{1}{4}
and
\frac{1}{8}
uniform codes are presented, and these codes are seen to make fewer decoding errors with feedback decoding than with definite decoding. Comparison of the performance of an ordinary feedback decoder with a genie-aided feedback decoder, which never propagates errors, indicates that error propagation with uniform codes is a minor problem if the optimum orthogonalization rules are used, but that the situation is somewhat worse with nonoptimum orthogonalization.