Programmable redundancy/syndrome generator

Apparatus for generating redundancy symbols during encoding of data comprising groups of binary bits into codewords of polynomial codes, each codeword c(x) being formed by dividing a data polynomial D(x) of degree less than k by a generator polynomial g(x) of degree n-k to obtain a redundancy polynomial r(x) of degree less than n-k, and appending r(x) to D(x) to yield c(x) of degree less than n, each symbol having a predetermined plurality of binary bits m, and for generating syndromes during decoding of codewords which may contain errors, comprising:

• (a) a plurality of cells, each cell having;
• an m bit wide adder having first and second adder inputs and an output;
• an m bit wide resettable register having its output connected as one input to said adder;
• an m bit wide finite field constant multiplier having its output connected to said resettable register;
• (b) connection means for selectively connecting each said cell as a first-order polynomial divider having a current output and a current input, in which the current output of each said m bit wide adder is the current input to the respective said cell added to the output of the respective said register in said divider, the register having an input comprising the current output of the respective said adder multiplied by a finite field constant;
• (c) connection means for selectively connecting each said cell as a first-order polynomial multiplier having a current output and a current input, in which the current output is the current input added to the output of a register in said multiplier, the register having an input comprising the current input multiplied by a constant, said cells being ordered in a cascade of first-order polynomial multipliers in opposite order from their respective order in the cascade of first-order polynomial dividers:
• (d) connection means for selectively connecting said plurality of cells either as a cascade of said first-order polynomial dividers or a cascade of said first-order polynomial multipliers;
• (e) connection means enabling transmittal data to be connected to an input stage of the divider cascade;
• (f) a connection means enabling the output of an output stage of the said multiplier cascade to be output to an information channel as the redundancy symbols;
• and,
• (g) a connection means enabling each said cell to be connected as separate first-order polynomial dividers so that each said divider may be used to divide received data in order to generate one of the syndromes.

Apparatus for generating redundancy symbols during encoding of data symbols consisting of groups of binary bits into codewords of polynomial codes, each codeword c(x) being formed by dividing a data polynomial D(x) of degree less than k by a generator polynomial g(x) of degree n-k to obtain a redundancy polynomial r(x) of degree less than n-k, and appending r(x) to D(x) to yield c(x) of degree less than n, each symbol having a predetermined plurality of binary bits m, comprising:

• a plurality of cells, each cell having a register, a finite field multiplier and an adder, each cell being selectively connectable as a first order polynomial divider and as a first order polynomial multiplier;
• means for connecting each cell to form a first order polynomial divider, and for coupling said first order polynomial dividers together to form a cascade of first order polynomial dividers;
• means for sequentially inputting data symbols for a codeword to the cascade of first-order polynomial dividers;
• means for connecting each cell to form a first order polynomial multiplier, and for coupling said first order polynomial multipliers together to form a cascade of first order polynomial multipliers, said registers being ordered in said cascade of first-order polynomial multipliers in opposite order from their respective order in the cascade of first-order polynomial dividers;
• and,
• means for holding the input to said multiplier cascade to zero and clocking said registers to clock out the redundancy symbols associated with the data symbols.

A method of generating redundancy symbols during encoding of data symbols consisting of groups of binary bits into codewords of polynomial codes, each codeword c(x) being formed by dividing a data polynomial D(x) of degree less than k by a generator polynomial g(x) of degree n-k to obtain a redundancy polynomial r(x) of degree less than n-k, and appending r(x) to D(x) to yield c(x) of degree less than n, each symbol having a predetermined plurality of binary bits m, comprising the steps of:

• (a) providing a plurality of cells, each cell having:
• an m bit wide resettable register, each register having a register input and a register output,
• an m bit wide finite field constant multiplier having a multiplier input and a multiplier output connected to said register input;
• (b) connecting the register output of each of the plurality of cells as one of two adder inputs of a respective m bit wide adder, and connecting the input of said m bit wide finite field constant multiplier so that the current output of each said m bit wide adder is the current input to the respective said adder added to the output of the respective said register whose input is the current output of the respective said adder multiplied by a finite field constant to form a first order polynomial divider, and coupling said first order polynomial dividers together to form a cascade of first order polynomial dividers;
• (c) sequentially inputting data symbols for a codeword to the cascade of first-order polynomial dividers formed in step (b);
• (d) connecting the register output of each of the plurality of cells as one of two adder inputs of a respective m bit wide adder, and connecting the input of said m bit wide finite field constant multiplier so that the current output of each of the last named said m bit wide adders is the current input to the respective said adder added to the output of the respective said register whose input is the current input of the respective said adder multiplied by a finite field constant to form a first order polynomial multiplier, and coupling said first order polynomial multipliers together to form a cascade of first order polynomial multipliers, said cells formed by the resettable registers and respective finite field multipliers being ordered in said cascade of first-order polynomial multipliers in opposite order from their respective order in the cascade of first-order polynomial dividers;
• and,
• (e) holding the input to said multiplier cascade to zero and clocking said resettable registers to clock out the redundancy symbols associated with the data symbols of step (c).

A method of generating redundancy symbols during encoding of data symbols consisting of groups of binary bits into codewords of polynomial codes, each codeword c(x) being formed by dividing a data polynomial D(x) of degree less than k by a generator polynomial g(x) of degree n-k to obtain a redundancy polynomial r(x) of degree less than n-k, and appending r(x) to D(x) to yield c(x) of degree less than n, each symbol having a predetermined plurality of binary bits m, comprising the steps of:

• (a) providing a plurality of cells, each cell having a register, a finite field multiplier and an adder, each cell being selectively connectable as a first order polynomial divider and as a first order polynomial multiplier;
• (b) connecting each cell to form a first order polynomial divider, and coupling said first order polynomial dividers together to form a cascade of first order polynomial dividers;
• (c) sequentially inputting data symbols for a codeword to the cascade of first-order polynomial dividers formed in step (b);
• (d) connecting each cell to form a first order polynomial multiplier, and coupling said first order polynomial multipliers together to form a cascade of first order polynomial multipliers, said registers being ordered in said cascade of first-order polynomial multipliers in opposite order from their respective order in the cascade of first-order polynomial dividers;
• and,
• (e) holding the input to said multiplier cascade to zero and clocking said resettable registers to clock out the redundancy symbols associated with the data symbols of step (c).

Apparatus for generating redundancy symbols during encoding of data symbols consisting of groups of binary bits into codewords of polynomial codes, each codeword c(x) being formed by dividing a data polynomial D(x) of degree less than k by a generator polynomial g(x) of degree n-k to obtain a redundancy polynomial r(x) of degree less than n-k, and appending r(x) to D(x) to yield c(x) of degree less than n, each symbol having a predetermined plurality of binary bits m, comprising:

• a plurality of cells, each cell having a register, a finite field multiplier and an adder, said cells being selectively connectable to function as a cascade of first order polynomial dividers and as a cascade of first order polynomial multipliers, said registers being ordered in said cascade of first-order polynomial multipliers to function in opposite order from their respective order in the cascade of first-order polynomial dividers;
• means for connecting said cells to function as said cascade of first order polynomial dividers;
• means for sequentially inputting data symbols for a codeword to the cascade of first-order polynomial dividers;
• means for connecting said cells to function as said cascade of first order polynomial multipliers;
• and,
• means for holding the input to said multiplier cascade to zero and clocking said resettable registers to clock out the redundancy symbols associated with the data symbols.

A method of generating redundancy symbols during encoding of data symbols consisting of groups of binary bits into codewords of polynomial codes, each codeword c(x) being formed by dividing a data polynomial D(x) of degree less than k by a generator polynomial g(x) of degree n-k to obtain a redundancy polynomial r(x) of degree less than n-k, and appending r(x) to D(x) to yield c(x) of degree less than n, each symbol having a predetermined plurality of binary bits m, comprising:

• providing a plurality of cells, each cell having a register, a finite field multiplier and an adder, said cells being selectively connectable to function as a cascade of first order polynomial dividers and as a cascade of first order polynomial multipliers, said registers being ordered in said cascade of first-order polynomial multipliers to function in opposite order from their respective order in the cascade of first-order polynomial dividers;
• connecting said cells to function as said cascade of first order polynomial dividers;
• sequentially inputting data symbols for a codeword to the cascade of first-order polynomial dividers;
• connecting said cells to function as said cascade of first order polynomial multipliers, and,
• holding the input to said multiplier cascade to zero and clocking said resettable registers to clock out the redundancy symbols associated with the data symbols.