SOFT-IN, SOFT-OUT (SISO) DECODING WITH THE EUCLIDEAN METRIC

FARRELL, P. G.; CASTIÑEIRA MOREIRA, J.

Ambleside

Congreso; Tenth International Symposium in Communications Theory and Applications; 2009

LANCASTER UNIVERSITY, UK

Soft-in, hard-out (SIHO) decoding of linear error correcting codes, using only a quantised or real number soft metric such as Euclidean distance, has been well understood for over 40 years. This is minimum soft distance (MSD) decoding, and it can be implemented optimally by applying the Viterbi algorithm (VA) to the code trellis [1], for example. The output of a minimum soft distance decoder is the codeword (in the case of a block code) or code sequence (for a convolutional code) closest in distance to the soft word or sequence received from the channel and input to the decoder, so that MSD decoding minimises the average output word or sequence error rate. Conceptually, but not in practice except in the case of a rather simple code, the codeword or code sequence closest in soft distance to the received word is found by determining the soft distances between the received word and all the words or sequences in the code, and then selecting the closest. If the second closest distance is significantly different from the closest distance, then the decision of the decoder is a confident one; if not, then the confidence of the decision is lower. In practice, it is often possible to obtain an estimate of the confidence in a decoder decision; for example, when applying the VA to a block code, by comparing the soft distances of all the paths which reach the terminating node of the trellis.