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55. 55 all at the same finite field lengths as the BPSK modulation simulations. Those results are shown in Figs. 9. As expected, the coding gain difference between BPSK and QPSK is minimal. For the 16QAM modulation scheme over AWGN channels, gains are more significant especially at lower code rates. 3 dBs are achieved at BER of 10−6 with code rates equal to the QPSK code rates. These gains are shown in Figs. 12. 5 6 Eb/N0(dB) Fig. 6 BER of AG-BTC(64,39) versus RS-BTC(31,23) using BPSK over AWGN Considering the highest modulation scheme, 64QAM allows us to examine the performance gains at higher probability of channel error rate over an AWGN channel.

In: IEEE ICC’93, vol 2, pp 1064–1070. 1993. 397441 24. Pyndiah R, Glavieux A, Picart A, Jacq S (1994) Near optimum decoding of product codes. In: IEEE GLOBECOM ’94, pp 339–343. 513494 25. Picart A, Pyndiah R (1999) Adapted iterative decoding of product codes. In: IEEE GLOBECOM ’99, vol 5, pp 2357–2362. 831724 26. Hirst SA, Honary B, Markarian G (2001) Fast chase algorithm with an application in turbo decoding. IEEE Trans Commun 49(10):1693–1699. 957387 27. Martin P, Taylor D (2002) Distance based adaptive scaling in suboptimal iterative decoding.

In 1993, Feng and Rao [10] introduced a simple MV scheme in order to overcome the shortcoming of all previous decoding algorithms which can be summarized as an inability of these algorithms to correct a number of errors up to the maximum number that can be achieved by the algorithm. The purpose of Feng and Rao’s work was to simplify the concept of AG codes and introduce a decoding algorithm. The idea of their algorithm was to apply Gaussian elimination on a matrix of known syndromes and use the MV scheme in order to find the values of unknown syndromes.

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