Serial-concatenated turbo codes

A method comprising the steps of

• encoding a current one of a sequence of input bit groups using a first redundancy code to generate an expanded group of first redundancy encoder output bits, each of which is a function of at least one bit from the current input bit group and at least one previous input bit group,
• encoding a predetermined number of said first redundancy encoder output bits using a second redundancy code to generate an expanded group of second redundancy encoder output bits,
• selecting a data symbol from a predetermined signal constellation as a function of a plurality of bits, said plurality of bits including any remaining ones of said first redundancy encoder output bits and said second redundancy encoder output bits, said data symbol being represented by at least one signal space coordinate which is a function of more than one of said plurality of bits,
• wherein in said selecting step, each different pattern of said plurality of bits identifies a corresponding subset of symbols of said signal constellation, and the minimum Euclidian distance between any two of said subsets is not a function of the Hamming distance between the two corresponding bit patterns,
• wherein said expanded group of second redundancy encoder output bits includes all of said predetermined number of said first redundancy encoder output bits as well as a redundant bit, and
• wherein said constellation is partitioned into two subconstellations with the intra-subconstellation minimum distance being maximized, wherein each of said subconstellations comprises a plurality of subsets, wherein said first redundancy encoder is a finite state machine defined by a trellis diagram having a plurality of current states, a plurality of next states and a plurality of state transitions connecting ones of said current states to ones of said next states, wherein each of said state transitions has an assigned one of said subsets, and wherein said selecting and said first redundancy code are such that, for each subconstellation, the inter-subset minimum distance between the subsets assigned to the state transitions that originate from a given current state or merge into a given next state of said trellis diagram is maximized.

A method comprising the steps of

• receiving a sequence of input bit groups,
• selecting a data symbol from a predetermined signal constellation as a function of a plurality of data-symbol-determining bits, said data symbol being represented by at least one signal space coordinate which is a function of more than one of said data-symbol-determining bits, said data-symbol-determining bits being generated by the steps of
• using a first redundancy code to generate an expanded group of first redundancy encoder output bits, each of which is a function of at least one bit from a current one of said input bit groups or a previous one of said input bit groups, and
• using a second redundancy code to generate an expanded group of second redundancy encoder output bits which are a function of a predetermined number of said first redundancy encoder output bits,
• said data-symbol-determining bits including any remaining ones of said first redundancy encoder output bits and said second redundancy encoder output bits,
• wherein said predetermined number of first redundancy encoder output bits is less than the number of bits in said expanded group of said first redundancy encoder output bits.

A method comprising the steps of

• receiving a sequence of input bit groups,
• selecting a data symbol from a predetermined signal constellation as a function of a plurality of data-symbol-determining bits, said data symbol being represented by at least one signal space coordinate which is a function of more than one of said data-symbol-determining bits, said data-symbol-determining bits being generated by the steps of
• using a first redundancy code to generate an expanded group of first redundancy encoder output bits, each of which is a function of at least one bit from a current one of said input bit groups and a previous one of said input bit groups,
• interleaving the expanded groups of said first redundancy encoder output bits on a bit-group-by-bit-group basis, and
• using a second redundancy code to generate an expanded group of second redundancy encoder output bits which are a function of a predetermined number of the interleaved first redundancy encoder output bits,
• said data-symbol-determining bits including any remaining ones of said first redundancy encoder output bits and said second redundancy encoder output bits,
• wherein each of said redundancy codes implements a finite state machine having a current state, and
• wherein both the output bits generated by each redundancy encoder and a next state of said each redundancy encoder are each a function of said current state and of the bits then being encoded.

A method for use in digital data transmission comprising the steps of

• receiving a sequence of input bit groups,
• selecting a data symbol from a predetermined signal constellation as a function of a plurality of data-symbol-determining bits, said data symbol being represented by at least one signal space coordinate which is a function of more than one of said data-symbol-determining bits, said data-symbol-determining bits being generated by the steps of
• using a first redundancy code to generate an expanded group of first redundancy encoder output bits, each of which is a function of at least one bit from a current one of said input bit groups and at least one previous one of said input bit groups,
• using a second redundancy code to generate an expanded group of second redundancy encoder output bits which are a function of a predetermined number of said first redundancy encoder output bits,
• said data-symbol-determining bits including any remaining ones of said first redundancy encoder output bits and said second redundancy encoder output bits,
• wherein said signal constellation includes more than four data symbols,
• wherein in said selecting step, each different pattern of said data-symbol-determining bits identifies a corresponding subset of the symbols of said signal constellation, and the minimum Euclidian distance between any two of said subsets is not a function of the Hamming distance between the two corresponding bit patterns,
• wherein said expanded group of second redundancy encoder output bits includes all of said first redundancy encoder output bits as well as a redundant bit, and
• wherein said constellation is partitioned into two subconstellations with the intra-subconstellation minimum distance being maximized, wherein each of said subconstellations comprises a plurality of subsets, wherein said first redundancy encoder is a finite state machine defined by a trellis diagram having a plurality of current states, a plurality of next states and a plurality of state transitions connecting ones of said current states to ones of said next states, wherein each of said state transitions has an assigned one of said subsets, and wherein said selecting and said first redundancy code are such that, for each subconstellation, the inter-subset minimum distance between the subsets assigned to the state transitions that originate from a given current state or merge into a given next sate of said trellis diagram is maximized.

A method comprising the steps of

• trellis encoding a current one of a sequence of input bit groups to generate an expanded group of first trellis encoder output bits,
• trellis encoding a predetermined number of said first trellis encoder output bits to generate an expanded group of second trellis encoder output bits, and
• selecting a data symbol from a predetermined signal constellation as a function of any remaining ones of said first trellis encoder output bits and said second trellis encoder output bits,
• wherein said data symbol is selected as a further function of at least one other bit.

A method comprising the steps of

• trellis encoding a current one of a sequence of input bit groups to generate an expanded group of first trellis encoder output bits,
• trellis encoding a predetermined number of said first trellis encoder output bits to generate an expanded group of second trellis encoder output bits, and
• selecting a data symbol from a predetermined signal constellation as a function of any remaining ones of said first trellis encoder output bits and said second trellis encoder output bits,
• wherein said predetermined number of first trellis encoder output bits is less than the number of bits in said expanded group of said first trellis encoder output bits.

A method comprising the steps of

• trellis encoding a current one of a sequence of input bit groups to generate an expanded group of first trellis encoder output bits,
• trellis encoding a predetermined number of said first trellis encoder output bits to generate an expanded group of second trellis encoder output bits,
• selecting a data symbol from a predetermined signal constellation as a function of any remaining ones of said first trellis encoder output bits and said second trellis encoder output bits, and
• interleaving the expanded groups of said first trellis encoder output bits prior to the second trellis encoding step,
• wherein said interleaving step is performed on a bit-group-by-bit-group basis.

Apparatus comprising

• a first redundancy encoder adapted to encode a current one of a sequence of input bit groups using a first redundancy code to generate an expanded group of first redundancy encoder output bits, each of which is a function of at least one bit from the current input bit group or at least one previous input bit group,
• a second redundancy encoder adapted to encode a predetermined said first redundancy encoder output bits using a second redundancy code to generate an expanded group of second redundancy encoder output bits, and
• a mapper adapted to select a data symbol from a predetermined signal constellation as a function of a plurality of bits, said plurality of bits including any remaining ones of said first redundancy encoder output bits and said second redundancy encoder output bits, said data symbol being represented by at least one signal space coordinate which is a function of more than one of said plurality of bits,
• wherein said predetermined number of first redundancy encoder output bits is less than the number of bits in said expanded group of first redundancy encoder output bits.

Apparatus comprising

• a first redundancy encoder adapted to encode a current one of a sequence of input bit groups using a first redundancy code to generate an expanded group of first redundancy encoder output bits, each of which is a fiction of at least one bit from the current input bit group or at least one previous input bit group,
• a second redundancy encoder adapted to encode a predetermined number of the interleaved first redundancy encoder output bits using a second redundancy code to generate an expanded group of second redundancy encoder output bits, and
• a mapper adapted to select a data symbol from a predetermined signal constellation as a function of a plurality of bits, said plurality of bits including any remaining ones of said first redundancy encoder output bits and said second redundancy encoder output bits, said data symbol being represented by at least one signal space coordinate which is a function of more than one of said plurality of bits,
• wherein said mapper selects said data symbol in such a way that each different pattern of said plurality of bits identifies a corresponding subset of the symbols of said signal constellation, and the minimum Euclidian distance between any two of said subsets is not a function of the Hamming distance between the two corresponding bit patterns,
• wherein said expanded group of second redundancy encoder output bits includes all of said predetermined number of said first redundancy encoder output bits as well as a redundant bit, and
• wherein said constellation is partitioned into two subconstellations with the intra-subconstellation minimum distance being maximized, wherein each of said subconstellations comprises a plurality of subsets, wherein said first redundancy encoder is a finite state machine defined by a trellis diagram having a plurality of current states, a plurality of next states and a plurality of state transitions connecting ones of said current states to ones of said next states, wherein each of said state transitions has an assigned one of said subsets, and wherein said selecting and said first redundancy code are such that, for each subconstellation, the inter-subset minimum distance between the subsets assigned to the state transitions that originate from a given current state or merge into a given next state of said trellis diagram is maximized.

Apparatus comprising

• a first redundancy encoder adapted to encode a current one of a sequence of input bit groups using a first redundancy code to generate an expanded group of first redundancy encoder output bits, each of which is a function of at least one bit from the current input bit group and at least one previous input bit group,
• means for interleaving the expanded groups of said first redundancy encoder output bits, the interleaving being on a bit-group-by-bit-group basis,
• a second redundancy encoder adapted to encode a predetermined number of the interleaved first redundancy encoder output bits using a second redundancy code to generate an expanded group of second redundancy encoder output bits, and
• a mapper adapted to select a data symbol from a predetermined signal constellation as a function of a plurality of bits, said plurality of bits including any remaining ones of said first redundancy encoder output bits and said second redundancy encoder output bits, said data symbol being represented by at least one signal space coordinate which is a function of more than one of said plurality of bits,
• wherein said predetermined number of first redundancy encoder output bits includes at least one bit which is a function of at least one bit from said at least one previous input bit group.