# US 10,312,947 B2 · Concatenated and sliding-window polar coding

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- Number: US 10,312,947 B2
- Document ID: US10312947B2
- Status: Granted
- Kind: B2
- Application number: 15/003,184
- Filed: 2016-01-21
- Published: 2017-07-27
- Granted: 2019-06-04
- Earliest claimed: 2016-01-21
- Assignees: Huawei Technologies Co., Ltd.
- Applicants: Yiqun Ge; Wuxian Shi
- Inventors: Yiqun Ge; Wuxian Shi
- Web page: https://patentgrep.com/patent/US10312947B2

## CPC

- H03M 13/3972: {using sliding window techniques or parallel windows}
- H03M 13/09: Error detection only, e.g. using cyclic redundancy check [CRC] codes or single parity bit
- H03M 13/13: Linear codes
- H03M 13/2927: {Decoding strategies}
- H03M 13/616: {Matrix operations, especially for generator matrices or check matrices, e.g. column or row permutations}
- H03M: CODING; DECODING; CODE CONVERSION IN GENERAL (using fluidic means F15C4/00; optical analogue/digital converters G02F7/00; coding, decoding or code conversion, specially adapted for particular applications, see the relevant subclasses, e.g. G01D, G01R, G06F, G06T, G09G, G10L, G11B, G11C, H04B, H04L, H04M, H04N; ciphering or deciphering for cryptography or other purposes involving the need for secrecy G09C)

## Abstract

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.

## Claims

### Claim 1

A method for encoding and transmitting a first codeword comprising: with an encoder,
processing K1 information bits to produce a u1-bit error-detecting code (EDC), wherein the K1 information bits are information bits of a first message;
processing K2 information bits to produce a u2-bit EDC, wherein the K2 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 k1 information hits and the u2-bit EDC, the second sequence of input hits comprises the 1<2 information bits and the u2-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.

### Claim 2 (depends on 1)

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 G2®m, where
G
2
=
[
1
0
1
1
]
⁢
⁢
or
⁢
⁢
G
2
=
[
1
1
0
1
]
.

### Claim 3 (depends on 1)

The method of claim 1, wherein the u1-bit EDC and the u2-bit EDC are cyclic redundancy codes (CRC).

### Claim 4 (depends on 1)

The method of claim 1, further comprising:
with the encoder, processing a sequence of K3 information bits to produce a u3-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 K3 information bits and the u3-bit EDC.

### Claim 5 (depends on 1)

The method of claim 1, wherein the second message contains K3 information bits after the K2 information bits, and a u3-bit EDC generated from the K2 and the K3 information bits in combination.

### Claim 6 (depends on 1)

The method of claim 1, further comprising with the transmitting device, transmitting the first codeword prior to transmitting the second codeword.

### Claim 7 (depends on 1)

The method of claim 1, further comprising with the transmitting device, transmitting the first codeword in temporal proximity to transmitting the second codeword.

### Claim 8 (depends on 1)

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.

### Claim 9 (depends on 1)

The method of claim 1 further comprising with the encoder, placing at least one of the u1-bit EDC or u2-bit EDCs is placed in bit positions of the input vector that satisfy a desired reliability criteria.

### Claim 10 (depends on 1)

The method of claim 1 further comprising:
placing the u1-bit EDC and K1 information bits in bit positions of a first group of bit positions of the input vector and
placing the u2-bit EDC and K2 information bits in bit positions of a second group of bit positions of the input vector,
wherein at least one of the u1-bit EDC and u2-bit EDC is placed in bit positions that satisfy a reliability criterion.

### Claim 11 (depends on 10)

The method of claim 10 wherein the u1-bit EDC is placed in bit positions in the first group with a highest reliability and the K1 information bits are placed with a highest remaining reliability in the first group and wherein the u2-bit EDC is placed in bit positions of the second group with a highest reliability and the K2 information bits are placed in bit positions with a highest remaining reliability in the second group.

### Claim 12

An apparatus comprising:
an encoder configured to produce a first codeword by:
processing K1 information bits to produce a u1 bit error-detecting, code (EDC), wherein the K1 information bits are information bits of a first message;
processing K2 information bits to produce a u2-bit EDC, wherein the K2 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 K1 information bits and the ui-bit EDC,
the second sequence of input bits comprises the K2 information bits and the u2-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.

### Claim 13 (depends on 12)

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 G2®m, where
G
2
=
[
1
0
1
1
]
⁢
⁢
or
⁢
⁢
G
2
=
[
1
1
0
1
]
.

### Claim 14 (depends on 12)

The apparatus of claim 12, wherein the u1-bit EDC and the u2-bit EDC are cyclic redundancy codes (CRC).

### Claim 15 (depends on 12)

The apparatus of claim 12 wherein the encoder is further configured to:
process a sequence of K3 information bits to produce a u3-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 K3 information bits and the u3-bit EDC.

### Claim 16 (depends on 12)

The apparatus of claim 12, wherein the second message contains K3 information bits after the K2 information bits, and a u3-bit EDC generated from the K2 and the K3 information bits in combination.

### Claim 17 (depends on 12)

The apparatus of claim 12, wherein the transmitting device is further configured to transmit the first codeword prior to transmitting the second codeword.

### Claim 18 (depends on 12)

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.

### Claim 19 (depends on 12)

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.