Turbo product code decoder

A turbo block code decoder for receiving an encoded message having a plurality of bits, and outputting a decoded codeword, the turbo block code decoder comprising:

• a. means for receiving the encoded message, wherein each bit in the plurality of bits in the encoded message is represented by an initial soft decision value in a plurality of initial soft decision values, the initial soft decision values arranged in a first array and in a second array;
• b. means for storing each initial soft decision value in the plurality of initial soft decision values coupled to the means for receiving;
• and
• c. means for iteratively decoding the encoded message coupled to the means for storing, wherein said means for iteratively decoding the encoded message retrieves the plurality of initial soft decision values in the first array and calculates a new soft decision value for each bit in the first array, thereby creating a plurality of new soft decision values, and further wherein the means for iteratively decoding generates a soft difference value for each bit in the first array, thereby creating a plurality of soft difference values, wherein each soft difference value is equal to a numerical difference between the new soft decision value for the bit in the first array and the initial soft decision value for the same bit in the first array, wherein the plurality of soft difference values is combined with the plurality of initial soft decision values in the second array to generate a subsequent soft difference value for each bit in the second array.

A turbo block code decoder for receiving an encoded message having a plurality of bits and outputting a decoded codeword comprising:

• a. an input module for receiving the encoded message, wherein each bit in the encoded message is represented by an initial soft decision value;
• b. an original memory array coupled to the input module for storing the initial soft decision values;
• c. a soft-in/soft-out group coupled to the original memory array for receiving the initial soft decision values in a first predetermined axis and decoding the encoded message, wherein the soft-in/soft-out group calculates a new soft decision value for each bit in the first predetermined axis and generates a soft difference value for each bit in the first predetermined axis, and further wherein the soft difference value is equal to a numerical difference between the new soft decision value and the initial soft decision value in the first predetermined axis;
• and
• d. a difference memory array coupled to the soft-in/soft out group for storing the soft difference values, wherein each soft difference value in the difference memory array is combined with the initial soft decision values in a second predetermined axis to generate a new soft difference value for each bit in the second predetermined axis.

A method of iteratively decoding a received block of data having a plurality of bits represented by a plurality of initial soft decision values, the method comprising the steps of:

• a. storing the plurality of initial soft decision values in a memory array having x-rows and y-columns;
• b. decoding the plurality of initial soft decision values stored in the x-rows, thereby creating a plurality of new x-axis soft decision values;
• c. generating a plurality of x-axis difference values, wherein said plurality of x-axis difference values represent a numerical difference between the plurality of new x-axis soft decision values and the plurality of initial soft decision values stored in the x-rows;
• d. multiplying the plurality of x-axis difference values by an x-axis feedback constant, thereby generating a plurality of x-axis iteration output values, wherein the x-axis feedback constant remains constant for the decoding of the plurality of initial soft decision values stored in the x-rows;
• e. summing the plurality of x-axis iteration output values with the plurality of initial soft decision values stored in the y-columns, thereby generating a plurality of y-axis input values;
• f. decoding the plurality of y-axis input values, thereby creating a plurality of new y-axis soft decision values;
• g. generating a plurality of y-axis difference values, wherein said plurality of y-axis difference values represent a numerical difference between the plurality of new y-axis soft decision values and the plurality of y-axis input values;
• and
• h. multiplying the plurality of y-axis difference values by a y-axis feedback constant, thereby generating a plurality of y-axis iteration output values, wherein the y-axis feedback constant remains constant for the decoding of the plurality of y-axis input values.

A method of iteratively decoding a received block of data having a plurality of bits represented by a plurality of initial soft decision values, the method comprising the steps of:

• a. storing the plurality of initial soft decision values in a memory having x-rows, y-columns and z-columns;
• b. decoding the plurality of initial soft decision values stored in the x-rows, thereby creating a plurality of new x-axis soft decision values;
• c. generating a plurality of x-axis difference values, wherein said plurality of x-axis difference values represent a numerical difference between the plurality of new x-axis soft decision values and the plurality of initial soft decision values stored in the x-rows;
• d. multiplying the plurality of x-axis difference values by an x-axis feedback constant, thereby generating a plurality of x-axis iteration output values;
• e. summing the plurality of x-axis iteration output values with the plurality of initial soft decision values stored in the y-columns, thereby generating a plurality of y-axis input values;
• f. decoding the plurality of y-axis input values, thereby creating a plurality of new y-axis soft decision values;
• g. generating a plurality of y-axis difference values, wherein said plurality of y-axis difference values represent a numerical difference between the plurality of new y-axis soft decision values and the plurality of y-axis input values;
• h. multiplying the plurality of y-axis difference values by a y-axis feedback constant, thereby generating a plurality of y-axis iteration output values;
• i. summing the plurality of y-axis iteration output values with the plurality of x-axis iteration output values and plurality of initial soft decision values stored in the z-columns, thereby generating a plurality of z-axis input values;
• j. decoding the plurality of z-axis input values, thereby creating a plurality of new z-axis soft decision values;
• k. generating a plurality of z-axis difference values, wherein said plurality of z-axis difference values represent a numerical difference between the plurality of new z-axis soft decision values and the plurality of z-axis input values;
• and
• l. multiplying the plurality of z-axis difference values by a z-axis feedback constant, thereby generating a plurality of z-axis iteration output values.

A method for decoding a linear block encoded string of information bits comprising the steps of:

• a. receiving the linear block encoded string of information bits and converting the string into codewords of length N;
• b. performing hard and soft decisions on each codeword in order to generate a hard decision vector h of length N and a soft decision vector c of length N, wherein the soft decision vector represents the reliability of the information in the hard decision vector;
• c. computing the syndrome of the hard decision vector h;
• d. computing the 1 bit parity of the hard decision vector h;
• e. if the syndrome calculation indicates that there is an error in the hard decision vector, correcting the error by inverting the appropriate hard decision bit value in the hard decision vector and 2's complementing the soft decision value in the same bit position in the soft decision vector;
• f. if the parity was correct and step e. required the hard decision bit value to be inverted, or if the parity was incorrect and step e did not require the hard decision bit value to be inverted, inverting the appropriate hard decision bit value in the hard decision vector and 2's complementing the soft decision value for the last bit position in the soft decision vector;
• g. finding the location of the two minimum values in the soft decision vector and designating these locations as LOW1 and LOW2, then replacing the soft decision value at location LOW1 with the 2's complement of the soft decision value at location LOW2 and replacing the soft decision value at location LOW2 with the 2's complement of the soft decision value at location LOW1;
• h. finding the sum of the new soft decision values at locations LOW1 and LOW2 in the soft decision vector for later use;
• i. computing the set of nearby valid codewords with Hamming weight 4 which have 1's in locations LOW1 and LOW2;
• for (n, k) codes, this will yield a set of (n/2−1) codewords with each of these nearby valid codewords having a 1 in locations LOW1 and LOW2 and two other locations which are designated Nc1 and Nc2;
• j. finding the sum of the soft decision values in locations Nc1 and Nc2 in the soft decision vector;
• k. swapping the soft decision value at location Nc1 with the soft decision value at location Nc2 and repeat steps j and k for each of the nearby valid codewords which were computed in step i;
• l. from the sums computed in steps h and j, determining which soft decision value sum is the lowest and designate this as Min1;
• m. determining which two bit locations created Min1, and designate these two bit locations as MinA and MinB;
• additionally, determine the next lowest soft value sum from steps i and k, and designate this as Min2;
• n. replacing the value at bit location MinA in the soft decision vector with the value of Min2 minus the current value at bit location MinA, and replacing the value at bit location MinB in the soft decision vector with the value of Min2 minus the current value at bit location MinB;
• o. subtracting the value of Min1 from the values in all other bit locations in the soft decision vector in order to generate an output codeword—if the locations of Min1 and Min2 are the same as the locations of LOW1 and LOW2 (independent of order), then the output codeword is the center codeword and if the locations Min1 and Min2 are not the same as the locations of LOW1 and LOW2 (independent of order) then invert the hard decision bits in the hard decision vector at locations MinA, MinB, LOW1 and LOW2;
• and
• p. for each bit in the output codeword generating a new signed soft value vector, this accomplished by 2's complementing all soft values in the output codeword at bit locations which correspond with bit locations in the hard decision vector having a 0 in their location and creating the new signed soft value vector.