| In the practical channel, the methods of interlace and concatenation are often used to reduce the bit error rate. Based on the interlace and concatenation, a new class of error-correcting codes over two-dimension, RS-Complex Rotary Codes, is proposed. RS Codes with a great error-correcting ability is the main structure of the new codes. And Complex Rotary Codes take charge of encoding and decoding the information bits again. Though the rate is a bit lower and the complexity is a bit higher than the original RS Codes, the error-correcting capability of RS-Complex Rotary Codes is improved greatly compared with RS Codes. Because RS-Complex Rotary Codes can be adjusted according to the practical request, it is a class of practical code.A new algorithm of soft decision decoding for the codes over GF(2m) is proposed on the basis of word-by-word decoding algorithm. The new algorithm improves the decoding performance by 2~3dB, and the number of tries sequences is far less than the number of tries sequences of the existing algorithm over GF(2m). So the new algorithm can be applied.Based on the new algorithm mentioned above, two methods of soft decision decoding on RS-Complex Rotary Codes, SDD I and SDD II, are proposed according to the character of encoding and decoding of the codes. By the computer simulation, it is concluded that the complexity of SDD I and SDD II are lower than that of GTC soft decision decoding algorithms over GF(2m). Especially the complexity of SDD II is lowest among the three algorithms.The performance of (7,3,21,9)RS-Complex Rotary Code is superior to (7,3)RS Codes by the computer simulation of (7,3,nc,kc)RS- Complex. It is better than (7,3)RS Code by about 4dB.For the application of RS Codes and the great performance of RS-Complex Rotary Codes, it is believed that RS-Complex RotaryCodes are potential. For the error-correcting capability of RS-Complex Rotary Codes can be adjusted, it can be applied conveniently in the adaptive control system.
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