A note on soft decision decoding with successive erasures (Corresp.)

This paper deals with soft decision as a means to bridge the gap in performance between a receiver using hard decision symbol estimation followed by an algebraic decoder and a maximum-likelihood receiver. A measure of the reliability of the code symbol estimates is introduced to facilitate the decoding process. The decoding operation studied erases the least reliable received symbols and then applies an algorithm capable of correcting errors and erasures. This procedure, termed successive-erasure decoding (SED), was introduced by G. D. Forney in connection with general minimum-distance decoding (GMD). It is studied for binary and nonbinary transmission using polyphase signals on the additive white Gaussian noise (AWGN) channel. The exponential behavior of the error probability at high signal-to-noise ratio (SNR) is calculated and is supplemented by computer simulations. The results indicate that soft decision by successive erasures for binary transmission has properties not present in the nonbinary case. In the binary case the procedure is asymptotically optimum for increasing SNR's. On the nonbinary channel, however, the procedure is only capable of bridging part of the gap in performance between maximum-likelihood decoding (MLD) and hard decision decoding (HDD).