Method for performing error corrections of digital information codified as a symbol sequence
A method and system for making error corrections on digital information coded as symbol sequences, for example digital information stored in electronic memory systems or transmitted from and to these systems is described, provides the 5 transmission of sequences incorporating a portion of error corrector code allowing the sequence which is more probably the original transmitted through the calculation of an error syndrome using a parity matrix to be restored when received. Advantageously according to embodiments of the invention, the error code incorporated in the original sequence belongs to a non Boolean group.
1. A method for generating an error correcting code comprising:
receiving at a transmitter/receiver a code word transmitted via a communication channel;
identifying, via an error detection and correction circuit coupled to the transmitter/receiver, an error of a first type when a syndrome value comprises a value of a parity matrix, wherein columns of the parity matrix have additive group values of mod p with p being different from 2 and including numbers p-1, p-2. . . p-2 n-k ;
identifying an error of a second type, via the error detection and correction circuit, when the syndrome value comprises a difference between a modulo value associated with the error correcting code and a value of the parity matrix; and
locating, via the error detection and correction circuit, a position of at least one of the first type or the second type of errors in the code word in response to calculating a scalar product of the parity matrix with the code word and interpreting the scalar product based on the group values of mod p, wherein a position of a value within the parity matrix matching the interpreted scalar product based on the group values of mod p is indicative of the position of the at least one of the first type or second type of errors in the code word.
2. The method of claim 1 , wherein the error correcting code is associated with an asymmetrical channel.
3. The method of claim 1 , wherein the error correcting code is a linear code, wherein said linear code is a code that includes a sum of all vectors in the code.
4. The method of claim 3 , wherein the linear code is generated from a non-binary group of values and data bits to be encoded.
5. The method of claim 4 , wherein the non-binary group of values is generated by performing non-binary addition.
6. The method of claim 1 , wherein the parity matrix comprises an identity matrix having a determinant different from 0 that is utilized in generating the error correcting code.
7. The method of claim 1 , wherein the error of the first type comprises an error wherein a binary value changed from a binary 0 to a binary 1, and wherein the error of the second type comprises an error wherein a binary values changed from a binary 1 to a binary 0.
8. A circuit comprising:
a transmitter receiver to receive a data word;
a plurality of non-binary adder circuits coupled to the transmitter/receiver and configured to develop an error correcting code to correct at least an error in the data word,
wherein the error correcting code is configured to identify an error of a first type when a syndrome value comprises a value of a parity matrix and to identify an error of a second type when the syndrome value comprises a difference between a modulo value associated with the error correcting code and a value of the parity matrix, wherein a position of at least one of the first type or the second type of errors in the data word in response to calculating a scalar product of the parity matrix with the data word and interpreting the scalar product based on the group values of mod p, wherein a position of a value within the parity matrix matching the interpreted scalar product based on the group values of mod p is indicative of the position of the at least one of the first type or second type of errors in the data word.
9. The circuit of claim 8 , wherein the plurality of non-binary adder circuits are further configured to generate a non-binary group of values configured to be applied to a data word being encoded.
10. The circuit of claim 8 , wherein the error correcting code comprises a linear code that includes a sum of all vectors in the code.
11. The circuit of claim 8 , wherein the plurality of non-binary adder circuits operates on binary values.
12. The circuit of claim 8 , wherein the error of the first type comprises an error wherein a binary value changed from a binary 0 to a binary 1 and wherein the error of the second type comprises an error wherein a binary values changed from a binary 1 to a binary 0.
13. The circuit of claim 8 , wherein circuit is configured to correct the error of the first type and the second type based at least in part on the error correcting code.
14. The method of claim 13 , wherein the circuit is configured to correct (d−1)/2 errors, wherein d is a weight of received data bits.
15. A method for generating an error correcting code comprising:
receiving, at a transmitter/receiver, data bits transmitted via a communication channel;
identifying, via an error detection and correction circuit coupled to the transmitter/receiver, an error of a first type when a syndrome value comprises a value of a parity matrix, and based on a comparison of the syndrome value and the received data bits, wherein columns of the parity matrix have additive group values of mod p with p being different from and including numbers p-1, p-2 . . . p-2 n-k ;
identifying an error of a second type, via the error detection and correction circuit, when the syndrome value comprises a difference between a modulo value associated with the error correcting code and a value of the parity matrix; and
locating, via the error detection and correction circuit, a position of at least one of the first type or the second type of errors in the data bits in response to calculating a scalar product of the parity matrix with the data bits and interpreting the scalar product based on the group values of mod p, wherein a position of a value within the parity matrix matching the interpreted scalar product based on the group values of mod p is indicative of the position of the at least one of the first type or second type of errors in the data bits.
16. The method of claim 15 , wherein the error correcting code comprises a non-Boolean group.