Generation and application of a sub-codebook of an error control coding codebook
View Patent ↗There is provided a method of encoding and decoding data using an error control code having a codebook G. The codebook G is a sub-codebook of a codebook P. Each codeword g in the sub-codebook G has an autocorrelation amplitude that is different from and higher than each correlation amplitude between g and each of the other codewords in the sub-codebook G. In one specific embodiment in which the codebook P is that of a Reed-Muller code, using G instead of P reduces the likelihood of the presence of more than one maximum correlation amplitude when computing the non-coherent decision metric during decoding.
1. A method of encoding data using an error control code, the method being performed in a transmitter and comprising:
mapping a sequence of the data to a codeword from a codebook G of the error control code; and
forwarding the codeword for transmission over a channel;
wherein the codebook G is a sub-codebook of another codebook P, wherein each codeword g in the sub-codebook G has an autocorrelation amplitude that is different from and higher than each correlation amplitude between g and each of the other codewords in the sub-codebook G, and
wherein the sub-codebook G was generated from the codebook P by:
(a) establishing an empty sub-codebook G;
(b) selecting a codeword from codebook P and including the codeword from codebook P in sub-codebook G;
(c) computing the autocorrelation amplitude of the codeword from codebook P;
(d) computing the correlation amplitude between the codeword from codebook P and each codeword in codebook P, and deleting from codebook P each codeword in codebook P for which the correlation amplitude is equal to the auto-correlation amplitude; and
(e) repeating operations (b) to (d) until all of the plurality of codewords are deleted from codebook P.
2. The method of claim 1 wherein the codebook P is a codebook of a Reed-Muller code.
3. The method of claim 1 wherein the autocorrelation amplitude is computed as
∑
t
p
t
2
,
and wherein the correlation amplitude is computed as
∑
t
p
t
*
p
~
t
,
where p t , t=1, 2, . . . T, is a data symbol of a set of T data symbols associated with the codeword from codebook P included in sub-codebook G, where p t * is the complex conjugate of p t , and where {tilde over (p)} t is a data symbol of a set of T data symbols associated with a codeword in code book P.
4. The method of claim 3 wherein the codeword is transmitted using Orthogonal Frequency-Division Multiplexing (OFDM).
5. The method of claim 1 wherein the sequence of data comprises a control packet.
6. The method of claim 1 wherein forwarding the codeword for transmission over a channel further comprises:
modulating the codeword using Quadrature Phase Shift Key (QPSK) modulation; and
transmitting the modulated codeword.
7. The method of claim 1 , wherein the channel is associated with a cellular communication network.
8. A method of decoding a sequence of data received over a communication channel, the sequence having been encoded using an error control code prior to transmission over the communication channel, the method being performed in a receiver and comprising:
obtaining the sequence of data that was received over the communication channel;
for each codeword in a codebook G of the error control code, computing a correlation value between the sequence and the codeword; and
selecting a codeword in the codebook G associated with the highest correlation value of the computed correlation values;
wherein the codebook G is a sub-codebook of another codebook P, wherein each codeword g in the sub-codebook G has an autocorrelation amplitude that is different from and higher than each correlation amplitude between g and each of the other codewords in the sub-codebook G, and
wherein the sub-codebook G was generated from the codebook P by:
(a) establishing an empty sub-codebook G;
(b) selecting a codeword from codebook P and including the codeword from codebook P in sub-code book G;
(c) computing the autocorrelation amplitude of the codeword from codebook P;
(d) computing the correlation amplitude between the codeword from codebook P and each codeword in codebook P, and deleting from codebook P each codeword in codebook P for which the correlation amplitude is equal to the auto-correlation amplitude; and
(e) repeating operations (b) to (d) until all of the plurality of codewords are deleted from codebook P.
9. The method of claim 8 wherein the method is performed in a receiver that implements non-coherent detection and wherein the codebook P is a codebook of a Reed-Muller code.
10. The method of claim 9 wherein the sequence of data is received using Orthogonal Frequency-Division Multiplexing (OFDM), and wherein the correlation value is computed as
∑
i
,
k
∑
j
p
ij
*
y
ijk
2
,
where p ij is a data symbol of a tile i and a data tone j, and y ijk is the value of p ij received at an antenna k of the receiver.
11. The method of claim 8 wherein the autocorrelation amplitude is computed as
∑
t
p
t
2
,
and wherein the correlation amplitude is computed as
∑
t
p
t
*
p
~
t
,
where p t , t=1, 2, . . . T, is a data symbol of a set of T data symbols associated with the codeword from codebook P included in sub-codebook G, where p t * is the complex conjugate of p t , and where {tilde over (p)} t is a data symbol of a set of T data symbols associated with a codeword in code book P.
12. The method of claim 8 further comprising decoding the sequence of data utilizing the selected codeword in the codebook G resulting in the highest correlation value.
13. The method of claim 12 further comprising forwarding the decoded sequence of data to a descrambling logic module effective to descramble the decoded sequence of data and recover alternate data associated with the sequence of data.
14. The method of claim 13 , wherein the decoded sequence of data includes a cyclic redundancy check (CRC) checksum.
15. A device in a data communication system configured to encode data using an error control code, the device comprising:
memory for storing a codebook G of the error control code;
an encoder configured to map a sequence of the data to a codeword from the codebook G; and
transmit circuitry for transmitting the codeword over a channel;
wherein the codebook G is a sub-codebook of another codebook P, wherein each codeword g in the sub-codebook G has an autocorrelation amplitude that is different from and higher than each correlation amplitude between g and each of the other codewords in the sub-codebook G, and
wherein the sub-codebook G stored in the memory was previously generated from the code book P by:
(a) establishing an empty sub-codebook G;
(b) selecting a codeword from codebook P and including the codeword from codebook P in sub-code book G;
(c) computing the autocorrelation amplitude of the codeword from codebook P;
(d) computing the correlation amplitude between the codeword from codebook P and each codeword in codebook P, and deleting from codebook P each codeword in codebook P for which the correlation amplitude is equal to the auto-correlation amplitude; and
(e) repeating operations (b) to (d) until all of the plurality of codewords are deleted from codebook P.
16. The device of claim 15 wherein the codebook P is a codebook of a Reed-Muller code.
17. The device of claim 16 further comprising a plurality of transmit antennas, and wherein the transmit circuitry is configured to transmit the codeword over the channel using Orthogonal Frequency-Division Multiplexing (OFDM).
18. The device of claim 15 , wherein the sequence of data comprises a control packet.
19. The device of claim 15 , the device further configured to:
modulate the codeword using Quadrature Amplitude modulation; and
transmit the modulated codeword utilizing the transmit circuitry.
20. The device of claim 15 , wherein the device comprises a mobile terminal associated with at least one wireless communication system.