Rotationally invariant coding

Receiver apparatus for processing a received data-bearing signal which was generated by applying a stream of data to a differential encoder, applying at least a portion of an output of said differential encoder to a non-binary redundancy encoder implementing a non-binary redundancy code comprising a plurality of valid code words, and generating said data-bearing signal representative of channel symbols selected from a predetermined signal constellation in response at least to the output of said non-binary redundancy encoder, said receiver apparatus comprising:

• means for recovering from said data-bearing signal a recovered signal representing said output of said non-binary redundancy encoder,
• means for redundancy decoding said recovered signal to generate a redundancy decoded signal, and
• means for differentially decoding said redundancy decoded signal in order to recover said stream of data,
• wherein said constellation exhibits at least one phase symmetry, and a rotation of said channel symbols by an amount corresponding to said phase symmetry converts at least one of said valid code words into an invalid code word.

A method comprising the steps of:

• applying a first stream of data to a differential encoder,
• applying at least a portion of an output of said differential encoder to a non-binary redundancy encoder implementing:
• a non-binary redundancy code comprising a plurality of valid code words,
• selecting channel symbols from a predetermined signal constellation in response at least to the output of said non-binary redundancy encoder, and
• transmitting to a receiver a signal representing the selected channel symbols,
• wherein said constellation exhibits at least one phase symmetry, and a rotation of said channel symbols by an amount corresponding to said phase symmetry converts at least one of said valid code words into an invalid code word.

A method comprising the steps of:

• applying a stream of data to a differential encoder,
• applying at least a portion of an output of said differential encoder to a non-binary redundancy encoder implementing a non-binary redundancy code comprising a plurality of valid code words,
• generating a data-bearing signal which represents channel symbols selected from a predetermined signal constellation in response at least to the output of said non-binary redundancy encoder,
• recovering from said data-bearing signal a recovered signal representing said output of said non-binary redundancy encoder,
• redundancy decoding said recovered signal to generate a redundancy decoded signal, and
• differentially decoding said redundancy decoded signal in order to recover said stream of data,
• wherein said constellation exhibits at least one phase symmetry, and a rotation of said channel symbols by an amount corresponding to said phase symmetry converts at least one of said valid code words into an invalid code word.

A method for processing a signal transmitted over a transmission channel, said signal representing a sequence of shortened Reed-Solomon frames that may have been subjected to a deterministic complementation of bits in one or more bit positions of each word of said frames, each frame being comprised of a number, n, of m-bit words, said method including the use of standard syndromes computed for said frame and modified syndromes computed for an augmented frame comprised of a) (2.sup.m -1- n ) m-bit stuffing words whose value is that arrived at by subjecting a m-bit null word to said deterministic complementation and b) the words of said received frame, said method comprising the steps of:

• receiving said signal from said transmission channel, and Reed-Solomon decoding the sequence of shortened Reed-Solomon frames therefrom,
• said Reed-Solomon decoding step comprising the steps, performed in repetitive alternation, of
• a) initiating the use of said standard syndromes to carry out error correction/detection for ones of said received frames until it is determined that said shortened Reed-Solomon frames are being subjected to said deterministic complementation, and
• b) thereupon initiating the use of said modified syndromes to carry out error correction/detection for subsequent frames of said sequence until it is determined that said shortened Reed-Solomon frames are no longer being subjected to said predetermined complementation.

A method for processing a signal transmitted over a transmission channel, said signal representing a sequence of shortened Reed-Solomon frames that may have been subjected to a deterministic complementation of bits in one or more bit positions of each word of said frames, each frame being comprised of a number, n, of m-bit words, said method comprising the steps of:

• receiving said signal from said channel,
• Reed-Solomon decoding each frame of said sequence in response to the received signal,
• computing, for each frame being decoded, modified syndromes for an augmented frame comprised of a) (2.sup.m -1- n) m-bit stuffing words whose value is that arrived at by subjecting an m-bit null word to said deterministic complementation and b) the words of the frame being decoded, and
• if said modified syndromes are zero syndromes for a particular one of said frames, thereupon subjecting subsequent frames of said sequence to a further such complementation prior to said Reed-Solomon decoding step.

A method for processing a signal transmitted over a transmission channel, said transmitted signal having been coded with use of a non-binary redundancy encoder for implementing error correction, said method comprising the steps of:

• receiving a signal corresponding to said transmitted signal from said transmission channel,
• determining whether said received signal is different than said transmitted signal,
• if said received signal is different than said transmitted signal, determining whether the difference therebetween is due to an occurrence of a rotation in said transmission channel,
• if said difference is due to said occurrence of said rotation, correcting said received signal by compensating therefor,
• if said received signal is different than said transmitted signal, determining whether the difference therebetween is due to a bit error in said received signal, and
• if said difference is due to said bit error, correcting said bit error in said received signal with use of a non-binary redundancy decoder corresponding to said non-binary redundancy encoder.

A receiver apparatus for processing a signal transmitted over a transmission channel, said transmitted signal having been coded with use of a non-binary redundancy encoder for implementing error correction, said receiver apparatus comprising:

• means for receiving a signal corresponding to said transmitted signal from said transmission channel,
• means for determining whether said received signal is different than said transmitted signal,
• means for determining whether the difference between said received signal and said transmitted signal is due to an occurrence of a rotation in said transmission channel,
• means for correcting said received signal by compensating for said rotation,
• means for determining whether the difference between said received signal and said transmitted signal is due to a bit error in said received signal, and
• a non-binary redundancy decoder corresponding to said non-binary redundancy encoder and adapted to correct said bit error in said received signal.