Abstract: An LFSR module is configured according to a characteristic polynomial for generating an output stream according to an input stream. The LFSR module has several LFSRs coupled together and an output generator. Each LFSR respectively receives a sub-input stream and at least one feedback stream, and respectively generates a sub-output stream and a feedback stream according to the received sub-input stream and the received at least one feedback stream, wherein the sub-input stream is generated according to the input stream, and at least one of the received feedback streams is generated by another LFSR. The output generator generates the output stream according to a plurality of inputs, wherein some of the inputs are the sub-output streams of the LFSRs.

Abstract: Methods and apparatus for generating parity symbols for a data block are disclosed. One of the proposed methods includes: determining a multiplicator polynomial for a first-direction symbol line of the data block, receiving a set of symbols on the first-direction symbol line, multiplying each of the set of symbols by the multiplicator polynomial to generate a set of product polynomials, repeating the determining, receiving, and multiplying steps for a plurality of first-direction symbol lines of the data block to generate a plurality of sets of product polynomials, and summing the plurality of sets of product polynomials to generate a set of parity polynomials. The coefficients of the set of parity polynomials constitute parity symbols of the data block.

Abstract: An LFSR module is configured according to a characteristic polynomial for generating an output stream according to an input stream. The LFSR module has several LFSRs coupled together and an output generator. Each LFSR respectively receives a sub-input stream and at least one feedback stream, and respectively generates a sub-output stream and a feedback stream according to the received sub-input stream and the received at least one feedback stream, wherein the sub-input stream is generated according to the input stream, and at least one of the received feedback streams is generated by another LFSR. The output generator generates the output stream according to a plurality of inputs, wherein some of the inputs are the sub-output streams of the LFSRs.

Abstract: A data recording system and a method of preventing copying data from a recording medium are disclosed. The method comprises an optical recorder receiving modulated bits encoded by EFM/EFM+ (Eight-to-Fourteen Modulation/Eight-to-Fourteen Modulation Plus), the optical recorder converting modulated bits to channel bits, and recording the channel bits to the recording medium. The modulated bits and the channel bits are readable by the optical recorder.

Abstract: Methods and apparatus for generating parity symbols for a data block are disclosed. One of the proposed methods includes: determining a multiplicator polynomial for a first-direction symbol line of the data block, receiving a set of symbols on the first-direction symbol line, multiplying each of the set of symbols by the multiplicator polynomial to generate a set of product polynomials, repeating the determining, receiving, and multiplying steps for a plurality of first-direction symbol lines of the data block to generate a plurality of sets of product polynomials, and summing the plurality of sets of product polynomials to generate a set of parity polynomials. The coefficients of the set of parity polynomials constitute parity symbols of the data block.