Figure 5

The factor graphs of different ECCs. (a) Irregular LDPC codes. (b) MET-LDPC codes. (c) Trellis of polar codes with \(N = 8\). Variable nodes and check nodes are denoted by circle and square, respectively. The number of variable nodes is 4 and the frozen variable nodes are drawn in orange circle. (d) Raptor codes. (e) Puncturing and shortening technology that applied to the [8,4] LDPC codes with rate \(R = 1/2\). In the puncturing example (left), one symbol is deleted from the word and a [8,4] code, with rate \(R = 1/2\), is converted to a [7,4] code and its rate increased to \(R = 4/7\). In the shortening example (right), one symbol is deleted from the word and the same [8,4] code is converted to a [7,3] code, the rate now decreases to \(R = 3/7\)