Flexible rate and punctured zigzag codes

A method for encoding a stream of information bits, comprising:

• determining a coding rate x and a number of information bits J to be encoded in a packet, where J is an integer and x is a real number;
• providing a number K of encoders to be used for encoding, wherein K is a non-zero integer;
• determining a number of parity bits
• K
• *
• I
• =
• B
• x
• -
• B
• ,
• and a number of code segments I;
• selecting a set of values for Ji, where i=1, 2, . . . I, such that
• ∑
• i
• =
• 1
• I
• ⁢
• ⁢
• J
• i
• =
• B
• ;
• building a code segment by appending a parity bit to each string of Ji information bits for all i=1,2, . . . I;
• and
• outputting the I code segments sequentially,
• wherein the coding rate x is other than
• J
• _
• J
• _
• +
• 1
• ,
• J
• _
• J
• _
• +
• 2
• ,
• …
• ⁢
• ⁢
• J
• _
• J
• _
• +
• K
• ,
• where
• J
• _
• =
• B
• I
• .

A method for decoding a stream of information bits, comprising:

• determining a coding rate x, a number of information bits B to be decoded from a packet, and a number K of constituent encoders used in encoding, where B and K are integers and x is a real number;
• determining a number of parity bits
• K
• *
• I
• =
• B
• x
• -
• B
• ,
• and a number of code segments I;
• selecting a set of values for Ji, where i=1, 2, . . . I, such that
• ∑
• i
• =
• 1
• I
• ⁢
• ⁢
• J
• i
• =
• B
• ,
• wherein at least one value for Ji differs from at least one other value for Ji within the set;
• for each ith code segment having Ji information bits and K associated parity bits, checking the Ji information bits against one of the associated parity bits for parity;
• and
• removing from the ith code segment the associated parity bit that was checked.

A method for decoding a stream of information bits, comprising:

• determining a coding rate x, a number of information bits B to be decoded from a packet, and a number K of constituent encoders used in encoding, where B and K are integers and x is a real number and
• x
• ≠
• J
• _
• J
• _
• +
• 1
• ,
• J
• _
• J
• _
• +
• 2
• ,
• …
• ⁢
• ⁢
• J
• _
• J
• _
• +
• K
• ,
• where
• J
• _
• =
• B
• I
• ;
• determining a number of parity bits
• K
• *
• I
• =
• B
• x
• -
• B
• ,
• and a number of code segments I;
• selecting a set of values for Ji, where i=1, 2, . . . I, such that
• ∑
• i
• =
• 1
• I
• ⁢
• ⁢
• J
• i
• =
• B
• ;
• and
• for each ith group of Ji received information bits, checking parity among the Ji information bits and at least one parity bit associated with the Ji information bits, and
• removing the at least one parity bit that was used in the checking.

A method for decoding a received block of data using a decoder of rate xdecode, said received block of data having B information bits and Pencode parity bits encoded at a rate

• x
• encode
• =
• B
• B
• +
• P
• encode
• that differs from xdecode, the method comprising:
• determining a total number of parity bits Pdecode for decoding such that
• P
• decode
• =
• B
• ⁢
• ⁢
• (
• x
• encode
• x
• decode
• -
• 1
• )
• +
• x
• encode
• x
• decode
• ⁢
• P
• encode
• ;
• add a number Pdiff=Pdecode−Pencode of null parity bits to the received block of data;
• and
• decode the received block of data with the added null parity bits in a rate xdecode decoder.

A transmitter comprising:

• K constituent encoders, wherein K is a non-zero integer;
• a memory for storing
• a block size value B of information bits in a block,
• a coding rate x associated with the block size value B,
• a total number K*I of parity bits
• K
• *
• I
• =
• B
• x
• -
• B
• ,
• and
• a set of segment lengths Ji such that
• ∑
• i
• =
• 1
• I
• ⁢
• ⁢
• J
• i
• =
• B
• ⁢
• ⁢
• for
• ⁢
• ⁢
• i
• =
• 1
• ,
• 2
• ,
• …
• ⁢
• ⁢
• I
• ,
• wherein each segment length Ji is not identical;
• a processor coupled to the memory and the K constituent encoders for causing each of the constituent encoders to insert a parity bit to each ith set of length Ji of information bits for all i=1, 2, 3 . . . I segments to achieve the coding rate x for a block of B information bits;
• and
• a transmit antenna having an input coupled to an output of the encoder.

A transmitter comprising:

• K constituent encoders, wherein K is a non-zero integer;
• a memory for storing
• a block size value B of information bits in a block,
• a coding rate x associated with the block size value B, where
• x
• ≠
• J
• _
• J
• _
• +
• 1
• ,
• J
• _
• J
• _
• +
• 2
• ,
• …
• ⁢
• ⁢
• J
• _
• J
• _
• +
• K
• ,
• where
• J
• _
• =
• B
• I
• ,
• a total number K*I of parity bits
• K
• *
• I
• =
• B
• x
• -
• B
• ,
• and
• a set of I segment lengths Ji such that
• ∑
• i
• =
• 1
• I
• ⁢
• ⁢
• J
• i
• =
• B
• for i=1, 2, . . . I;
• a processor coupled to the memory and the K constituent encoders for causing each of the constituent encoder to insert a parity bit to each ith set of length Ji of information bits for all i=1, 2, 3 . . . I segments to achieve the coding rate x for a block of B information bits;
• and
• a transmit antenna having an input coupled to an output of the encoder.

A receiver comprising:

• a receive antenna having an output for receiving a packet;
• a decoder having an input coupled to the output of the receive antenna;
• a memory for storing
• a block size value B of information bits in a block,
• a coding rate x associated with the block size value B,
• a value K of encoders used in encoding a block size value B with a coding rate x,
• a total number K*I of parity bits
• K
• *
• I
• =
• B
• x
• -
• B
• ,
• and
• a set of I segment lengths Ji such that
• ∑
• i
• =
• 1
• I
• ⁢
• ⁢
• J
• i
• =
• B
• ⁢
• ⁢
• for
• ⁢
• ⁢
• i
• =
• 1
• ,
• 2
• ,
• …
• ⁢
• ⁢
• I
• ,
• wherein each segment length Ji is not identical;
• and
• a processor coupled to the memory and the decoder for causing the decoder to delete a parity bit from each ith set of Ji received information bits for all i=1, 2, 3 . . . I segments.

A receiver comprising:

• a receive antenna having an output for receiving a packet;
• a decoder having an input coupled to the output of the receive antenna;
• a memory for storing
• a block size value B of information bits in a block,
• a coding rate x associated with the block size value B, where
• x
• ≠
• J
• _
• J
• _
• +
• 1
• ,
• J
• _
• J
• _
• +
• 2
• ,
• …
• ⁢
• ⁢
• J
• _
• J
• _
• +
• K
• ,
• where
• ⁢
• ⁢
• J
• _
• =
• B
• I
• ,
• a value K of encoders used in encoding a block size value B with a coding rate x,
• a total number K*I of parity bits
• K
• *
• I
• =
• B
• x
• -
• B
• ,
• and
• a set of segment lengths Ji such that
• ∑
• i
• =
• 1
• I
• ⁢
• ⁢
• J
• i
• =
• B
• ⁢
• ⁢
• for
• ⁢
• ⁢
• i
• =
• 1
• ,
• 2
• ,
• …
• ⁢
• ⁢
• I
• ;
• and
• a processor coupled to the memory and the decoder for causing the decoder to delete a parity bit from each ith set of Ji received information bits for all i=1, 2, 3 . . . I segments.