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In this paper we describe novel non-statistical Euclidean distance soft-input, soft-output (SISO) decoding algorithms for the three currently most important error-correcting codes: the low-density parity-check (LDPC), turbo and polar codes. The metric is squared Euclidean distance, and the decoders operate using an antilog-log (AL) process. We have investigated the simulated bit-error rate (BER) performance of these non-statistical algorithms on three channel models: the additive White Gaussian noise (AWGN), the Rayleigh fading and Middleton’s Class-A impulsive noise channels, and compare them with the BER performances of the corresponding statistical decoding algorithms for the three codes and channels. In all cases the performance over the AWGN channel of the non-statistical algorithms is almost the same or slightly better than that of the statistical algorithms. In some cases the performance over the two nonGaussian channels of the non-statistical algorithms is worse than that of the statistical algorithms, but the use of a simple signal amplitude limiter placed before the decoder input significantly improves the actual and relative performances of the algorithms. Thus there is no performance loss, and sometimes a significant performance gain, for the proposed decoding algorithms. A major advantage of our algorithms is that estimation of the channel signal-to-noise ratio is not required, which in practice simplifies system implementation. In addition, we have found that the processing complexity of the non-statistical algorithms is similar or slightly less than that of the corresponding statistical algorithms, and is significantly less for the LDPC codes over all of the channels.

Non-statistical Euclidean-distance SISO Decoding of Error-correcting Codes over Gaussian and Other Channels