According to the properties found in the algebraic complete decoding method for triple-error-correcting binary Bose-Chaudhuri-Hocquenghem (BCH) codes, a step-by-step complete decoding algorithm of this code is presented.

Similar to algebraic decoding schemes, the (23, 12, 7) Golay code can be decoded by applying the step-by-step decoding algorithm. In this work, a modified step-by-step algorithm for decoding the Golay code is presented. Logical analysis yielded a simple rule for directly determining whether a bit in the received word is correct. The computational complexity can be reduced significantly using this scheme.

In this letter, we propose a simplified step-by-step decoding algorithm for t-error-correcting binary Bose-Chaudhuri- Hocquenghem (BCH) codes based on logical analysis. Compared to the conventional step-by-step decoding algorithm, the computation complexity of this decoder is much less, since it significantly reduces the matrix calculation and the operations of multiplication.

A low-complexity step-by-step decoding algorithm for t-error-correcting binary Bose-Chaudhuri-Hocquenghem (BCH) codes is proposed. Using logical analysis, we obtained a simple rule which can directly determine whether a bit in the received word is correct. The computational complexity of this decoder is less than the conventional step-by-step decoding algorithm, since it reduces at least half of the matrix computations and the most complex element in the conventional step-by-step decoder is the "matrix-computing" element.

Based on a modified step-by-step decoding procedure, a high-speed pipelined Reed-Solomon decoder is presented. The decoder requires only the delay time of three 2-input XOR gates for decoding each coded symbol. The decoder can be operated in a bit rate of Gbits/sec order and thus suitable for the very high speed data transmission systems.