Can Sequential Decoding Compete with Turbo-codes?

摘要

It has long been known that nearly error-free communication over noisy channels is possible in theory but hard to achieve in practice. Claude Shannon showed in 1948[1] that if the information rate is less than the capacity of the channel, th«n, for any positive value e, there exist codes with decoding error probability less than e. Since Shannon assumed random codes in his proof, whose complexity of decoding was not defined, it soon became apparent that good codes with low enough complexity to allow a practical implementation were difficult to find, particularly for code rates close to capacity. Therefore, until recently, the usual solution to this problem was to design structured codes, making them relatively easy to implement, that yielded moderately low error probabilities at rates significantly lower than capacity. However, in 1993, a French research group[2] presented a class of codes, called Turbo-codes, that achieved moderately low error probabilities with reasonable decoding complexity at rates very close to capacity. Using iterative decoding, a 16-state rate 1/2 Turbo-code can operate at an SNR of 0.7dB (0.7dB greater than the capacity of the AWGN channel) with a decoded bit error rate (BER) of 10~(-5). For comparison, the Big Viterbi Decoder (BVD), designed to decode a much more complex 16384-state code, requires an SNR of 2.4dB to achieve the same BER.