In one embodiment of the present invention, the efficiency of an encoder can be maintained while reducing the complexity of a decoder. In one embodiment, the invention includes a communication system in which a transmitter has a pipelined encoder that includes a controller that does not access a look-up table to encode a block of data bits into a binary codeword, and in which a receiver has a decoder to receive the binary codeword after transmission through a communications medium, and to correct an error in the binary codeword introduced during transmission without using a look-up table.

 
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