Methods and systems for bit error determination and correction

A computer-implemented method for correcting a data packet comprising a payload d(x) and cyclic redundancy check (CRC) information, calculated using a generator polynomial g(x), the method comprising:

• calculating a syndrome value according to said data packet and said generator polynomial g(x);
• generating a list of potential error vectors EN according to one of the following:
• A)
• initializing an error vector e using said syndrome value;
• determining that the error vector e is a potential error vector according to a number of bits in the error vector e that have a value that is indicative of an error;
• adding the error vector e to the list of potential error vectors EN according to the determining;
• generating an additional error vector e′ by adding a shifted version of a vector g to the error vector e at a bit position, where the bit position is determined according to a bit value of the error vector e and according to previously determined bit positions, the vector g being associated with the generator polynomial g(x);
• and
• repeating the determining, the adding and the generating by using the additional error vector e′ as the error vector e, for each said bit position of said data packet;
• B)
• providing a lookup table comprising a plurality of syndrome value indexes and entries each entry corresponding to a relative distance to a single error and a next normalized syndrome value, the entries being associated to one of the plurality of syndrome value indexes in accordance with previously determined possible syndrome values for said generator polynomial g(x);
• identifying a relative distance to a single error and a next normalized syndrome value from the entries of the lookup table according to one of the plurality of syndrome value indexes corresponding to the syndrome value;
• generating an error vector e according to said identified relative distance to a single error;
• determining that said error vector e is a potential error vector according to said relative distance to the single error;
• adding said identified error vector e to the list of potential error vectors EN, according to the determining;
• and
• repeating the previous four steps for each bit in said payload d(x), using the identified next normalized syndrome value as the syndrome value;
• returning the list EN;
• selecting a potential error vector e from the list EN;
• and
• correcting the packet based on the selected potential error vector e.