Hardware implementations of a quasi-cyclic syndrome decoder

An apparatus for reducing complexity of a decoder, the apparatus comprising:

• at least one processor;
• and
• a non-transitory memory with instructions stored thereon, the instructions upon execution by the at least one processor, causing the at least one processor to:
• receive a noisy codeword that is based on a transmitted codeword generated from a quasi-cyclic linear code;
• compute a plurality of syndromes based on the noisy codeword;
• select a first syndrome from the plurality of syndromes;
• generate a memory cell address as a function of the first syndrome, the memory cell address corresponding to a memory cell that stores one or more coset leaders and excludes syndromes;
• read, based on the memory cell address, a coset leader stored in the memory cell that is accessed using the memory cell address, the coset leader corresponding to the first syndrome;
• and
• determine, based on the noisy codeword and the coset leader, a candidate version of the transmitted codeword.

A non-transitory computer readable storage medium having instructions stored thereupon, the instructions, when executed by a processor, causing the processor to implement a method for reducing complexity of a decoder, comprising:

• instructions for receiving a noisy codeword that is based on a transmitted codeword generated from a quasi-cyclic linear code;
• instructions for computing a plurality of syndromes based on the noisy codeword;
• instructions for selecting a first syndrome from the plurality of syndromes;
• instructions for generating a memory cell address as a function of the first syndrome, the memory cell address corresponding to a memory cell that stores one or more coset leaders and excludes syndromes;
• instructions for reading, based on the memory cell address, a coset leader stored in the memory cell that is accessed using the memory cell address, the coset leader corresponding to the first syndrome;
• and
• instructions for determining, based on the noisy codeword and the coset leader, a candidate version of the transmitted codeword.