Figure 1.
Channel model: CI-WTBC.
Figure 1.
Channel model: CI-WTBC.
Figure 2.
Graphical representation of the sets in (10)–(19). The indices inside the soft and dark gray area form and respectively. The indices that form are those inside the red curve, while those inside the blue curve form .
Figure 2.
Graphical representation of the sets in (10)–(19). The indices inside the soft and dark gray area form and respectively. The indices that form are those inside the red curve, while those inside the blue curve form .
Figure 3.
For Case A, graphical representation of the encoding that leads to the construction of when . Consider the Block 2: , , , and are those areas filled with yellow squares, blue circles, blue and yellow diamonds, pink crosses, and gray pentagons, respectively, and the set is the green filled area. At Block , is represented by symbols of the same color (e.g., red symbols at Block 2), and , and are represented by squares, circles and triangles respectively. Furthermore, and are denoted by squares and triangles, respectively, with a line through them. At Block , the diamonds denote . In Block , is stored into those entries whose indices belong to the green area. For , is denoted by crosses (e.g., purple crosses at Block 2), and is repeated in . The sequence is represented by gray pentagons and is replicated in all blocks. The sequences and are those entries inside the red at Block 1 and the blue curve at Block L, respectively.
Figure 3.
For Case A, graphical representation of the encoding that leads to the construction of when . Consider the Block 2: , , , and are those areas filled with yellow squares, blue circles, blue and yellow diamonds, pink crosses, and gray pentagons, respectively, and the set is the green filled area. At Block , is represented by symbols of the same color (e.g., red symbols at Block 2), and , and are represented by squares, circles and triangles respectively. Furthermore, and are denoted by squares and triangles, respectively, with a line through them. At Block , the diamonds denote . In Block , is stored into those entries whose indices belong to the green area. For , is denoted by crosses (e.g., purple crosses at Block 2), and is repeated in . The sequence is represented by gray pentagons and is replicated in all blocks. The sequences and are those entries inside the red at Block 1 and the blue curve at Block L, respectively.
Figure 4.
For Case B, graphical representation of the encoding that leads to the construction of when . Consider the Block 2: the sets , , , , , and are those areas filled with yellow squares, yellow triangles, blue circles, blue triangles, blue and yellow diamonds, pink crosses, and gray pentagons, respectively, and is the green filled area with purple crosses. At Block , is represented by symbols of the same color (e.g., red symbols at Block 2), and , and are represented by squares, circles, and triangles, respectively. Furthermore, and are denoted by squares and triangles, respectively, with a line through them. At Block , the diamonds denote . In Block , is stored into those entries whose indices belong to the green area. For , and, therefore, is repeated entirely into . The sequence from is represented by gray pentagons and is repeated in all blocks. The sequences and are the entries inside the red curve at Block 1 and the blue curve at Block L, respectively.
Figure 4.
For Case B, graphical representation of the encoding that leads to the construction of when . Consider the Block 2: the sets , , , , , and are those areas filled with yellow squares, yellow triangles, blue circles, blue triangles, blue and yellow diamonds, pink crosses, and gray pentagons, respectively, and is the green filled area with purple crosses. At Block , is represented by symbols of the same color (e.g., red symbols at Block 2), and , and are represented by squares, circles, and triangles, respectively. Furthermore, and are denoted by squares and triangles, respectively, with a line through them. At Block , the diamonds denote . In Block , is stored into those entries whose indices belong to the green area. For , and, therefore, is repeated entirely into . The sequence from is represented by gray pentagons and is repeated in all blocks. The sequences and are the entries inside the red curve at Block 1 and the blue curve at Block L, respectively.
Figure 5.
For Case C, graphical representation of the encoding that leads to the construction of when . Consider the Bloc 2: , , and are those areas filled with yellow squares, blue circles, blue and yellow diamonds, and gray pentagons, respectively, and is the green filled area. At Block , is represented by symbols of the same color (e.g., red symbols at Block 2), and , and are represented by squares, circles, and triangles, respectively. Furthermore, and are denoted by squares and triangles, respectively, with a line through them. At Block , the diamonds denote . For , is stored into those entries belonging to the green area. The sequence is represented by gray pentagons and is repeated in all blocks. The sequences and are the entries inside the red curve at Block 1 and the blue curve at Block L, respectively.
Figure 5.
For Case C, graphical representation of the encoding that leads to the construction of when . Consider the Bloc 2: , , and are those areas filled with yellow squares, blue circles, blue and yellow diamonds, and gray pentagons, respectively, and is the green filled area. At Block , is represented by symbols of the same color (e.g., red symbols at Block 2), and , and are represented by squares, circles, and triangles, respectively. Furthermore, and are denoted by squares and triangles, respectively, with a line through them. At Block , the diamonds denote . For , is stored into those entries belonging to the green area. The sequence is represented by gray pentagons and is repeated in all blocks. The sequences and are the entries inside the red curve at Block 1 and the blue curve at Block L, respectively.
Figure 6.
For Case D, graphical representation of the encoding that leads to the construction of when . Consider the Block 2: , , , and are those areas filled with yellow squares, blue circles, blue and yellow diamonds, yellow squares overlapped by blue circles, and gray pentagons, respectively, and the set is the green filled area. At Block , is represented by symbols of the same color (e.g., red symbols at Block 2), and , and are represented by squares, circles, and triangles, respectively. Furthermore, and are denoted by squares and triangles, respectively, with a line through them. At Block , is represented by diamonds, and by squares overlapped by circles. At Block , is stored into those entries that belong to the green area. Sequence is denoted by gray pentagons and is repeated in all blocks. Sequences and are the entries inside the red curve at Block 1 and the blue curve at Block L, respectively.
Figure 6.
For Case D, graphical representation of the encoding that leads to the construction of when . Consider the Block 2: , , , and are those areas filled with yellow squares, blue circles, blue and yellow diamonds, yellow squares overlapped by blue circles, and gray pentagons, respectively, and the set is the green filled area. At Block , is represented by symbols of the same color (e.g., red symbols at Block 2), and , and are represented by squares, circles, and triangles, respectively. Furthermore, and are denoted by squares and triangles, respectively, with a line through them. At Block , is represented by diamonds, and by squares overlapped by circles. At Block , is stored into those entries that belong to the green area. Sequence is denoted by gray pentagons and is repeated in all blocks. Sequences and are the entries inside the red curve at Block 1 and the blue curve at Block L, respectively.
Figure 7.
Graphical representation (Bayesian graph) of the dependencies between random variables involved in the polar coding scheme. Independent random variables are indicated by white nodes, whereas those that are dependent are indicated by gray nodes.
Figure 7.
Graphical representation (Bayesian graph) of the dependencies between random variables involved in the polar coding scheme. Independent random variables are indicated by white nodes, whereas those that are dependent are indicated by gray nodes.