Concatenated and sliding-window polar coding
Methods for encoding and decoding Polar codes are provided, together with apparatuses for performing the methods. An encoding method combines first and second sequences of information bits and CRC bits and a plurality of frozen bits into an input vector. The input vector is multiplied by a generator matrix for a Polar code to produce a concatenated codeword. A decoding method receives such a codeword and produces a decoded vector by generating successive levels of a decision tree. For a first number of levels of the decision tree, paths beyond a first maximum number of most probable paths are discarded. For a second number of levels of the decision tree, paths beyond a second maximum number of most probable paths are discarded. In some cases, the decoding method may have improved performance compared to some decoding methods for non-concatenated codewords.
1. A method for encoding and transmitting a first codeword comprising: with an encoder,
processing K 1 information bits to produce a u 1 -bit error-detecting code (EDC), wherein the K 1 information bits are information bits of a first message;
processing K 2 information bits to produce a u 2 -bit EDC, wherein the K 2 information bits are leading information bits of a second message;
producing an input vector for polar encoding, the input vector including a first sequence of input bits, a second sequence of input bits, and a plurality of frozen hits, wherein
the first sequence of input hits comprises the k 1 information hits and the u 2 -bit EDC, the second sequence of input hits comprises the 1 < 2 information bits and the u 2 -bit EDC,
Polar encoding the input vector to produce the first codeword; and
Polar encoding the second message to produce a second codeword;
with a transmitting device, transmitting, at a first power, the first codeword over a physical channel, the polar encoding being performed to improve a reliability of transmission of the input bits over the physical channel;
with the transmitting device, transmitting, at a second power level, the second codeword,
wherein the first power level is higher than the second power level.
2. The method of claim 1 , wherein Polar encoding comprises multiplying the input vector by a generator matrix for a Polar code and wherein the generator matrix is an m-fold Kronecker product matrix G 2 ® m , where
G
2
=
[
1
0
1
1
]
or
G
2
=
[
1
1
0
1
]
.
3. The method of claim 1 , wherein the u 1 -bit EDC and the u 2 -bit EDC are cyclic redundancy codes (CRC).
4. The method of claim 1 , further comprising:
with the encoder, processing a sequence of K 3 information bits to produce a u 3 -bit EDC,
wherein the produced input vector further comprises a third sequence of input bits, and the third sequence of input bits comprises the sequence of K 3 information bits and the u 3 -bit EDC.
5. The method of claim 1 , wherein the second message contains K 3 information bits after the K 2 information bits, and a u 3 -bit EDC generated from the K 2 and the K 3 information bits in combination.
6. The method of claim 1 , further comprising with the transmitting device, transmitting the first codeword prior to transmitting the second codeword.
7. The method of claim 1 , further comprising with the transmitting device, transmitting the first codeword in temporal proximity to transmitting the second codeword.
8. The method of claim 1 , wherein the method is performed by a base station and wherein the first codeword is transmitted to a user equipment.
9. The method of claim 1 further comprising with the encoder, placing at least one of the u 1 -bit EDC or u 2 -bit EDCs is placed in bit positions of the input vector that satisfy a desired reliability criteria.
10. The method of claim 1 further comprising:
placing the u 1 -bit EDC and K 1 information bits in bit positions of a first group of bit positions of the input vector and
placing the u 2 -bit EDC and K 2 information bits in bit positions of a second group of bit positions of the input vector,
wherein at least one of the u 1 -bit EDC and u 2 -bit EDC is placed in bit positions that satisfy a reliability criterion.
11. The method of claim 10 wherein the u 1 -bit EDC is placed in bit positions in the first group with a highest reliability and the K 1 information bits are placed with a highest remaining reliability in the first group and wherein the u 2 -bit EDC is placed in bit positions of the second group with a highest reliability and the K 2 information bits are placed in bit positions with a highest remaining reliability in the second group.
12. An apparatus comprising:
an encoder configured to produce a first codeword by:
processing K 1 information bits to produce a u 1 bit error-detecting, code (EDC), wherein the K 1 information bits are information bits of a first message;
processing K 2 information bits to produce a u 2 -bit EDC, wherein the K 2 information bits are leading information bits of a second message;
producing an input vector for polar encoding, the input vector including comprising a first sequence of input bits, a. second sequence of input bits, and a plurality of frozen bits, wherein
the first sequence of input bits comprises the K 1 information bits and the ui-bit EDC,
the second sequence of input bits comprises the K 2 information bits and the u 2 -bit EDC, and
Polar encoding the input vector to produce the first codeword;
Polar encoding, the second message to produce a second codeword; and
a transmitting device for transmitting, at a first power, the first codeword over a physical channel, the polar encoding being performed to improve a reliability of transmission of the input bits over the physical channel, and for transmitting, at a second power level, the second codeword, wherein the first power level is higher than the second power level.
13. The apparatus of claim 12 , wherein the encoder is further configured to Polar encode by multiplying the input vector by a generator matrix for a Polar code, wherein the generator matrix is an m-fold Kronecker product matrix G 2 ® m , where
G
2
=
[
1
0
1
1
]
or
G
2
=
[
1
1
0
1
]
.
14. The apparatus of claim 12 , wherein the u 1 -bit EDC and the u 2 -bit EDC are cyclic redundancy codes (CRC).
15. The apparatus of claim 12 wherein the encoder is further configured to:
process a sequence of K 3 information bits to produce a u 3 -bit EDC,
wherein the produced input vector further comprises a third sequence of input bits, and the third sequence of input bits comprises the sequence of K 3 information bits and the u 3 -bit EDC.
16. The apparatus of claim 12 , wherein the second message contains K 3 information bits after the K 2 information bits, and a u 3 -bit EDC generated from the K 2 and the K 3 information bits in combination.
17. The apparatus of claim 12 , wherein the transmitting device is further configured to transmit the first codeword prior to transmitting the second codeword.
18. The apparatus of claim 12 , wherein the transmitting device is further configured to transmit the first codeword in temporal proximity to transmitting the second codeword.
19. The apparatus of claim 12 wherein the apparatus is implemented in a base station and wherein the transmitting device is configured to transmit the first codeword to a User Equipment (UE) device.