#### DMCA

## Digital Video Broadcasting

### Citations

1341 | Low-Density Parity-Check Codes.
- Gallager
- 1963
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Citation Context ...ll rows in H have the same weight (number of ones) and all columns in H have the same weight; otherwise the code is irregular. LDPC codes were originally proposed by Gallager in his 1960 dissertation =-=[12]-=- along with an iterative process for decoding. Although Gallager proved that the codes were good in theory, they were largely ignored until the advent of turbo codes because the decoder was thought to... |

738 | Good error-correcting codes based on very sparse matrices,
- MacKay
- 1999
(Show Context)
Citation Context ...der was thought to be too complex. However, after turbo codes showed the practicality of iterative decoding, interest in LDPC codes was soon renewed. In the mid-1990’s, MacKay rediscovered LDPC codes =-=[13, 14]-=- and showed that they are capable of approaching the Shannon limit. Soon afterwards, Richardson and Urbanke [15] and Luby et al [16] showed that long irregular LDPC codes can be superior to turbo code... |

629 |
A Recursive Approach to Low Complexity Codes,"
- Tanner
- 1981
(Show Context)
Citation Context ...lation (BICM) [20]. 2.2 Decoding An LDPC code can be decoded iteratively using a message passing algorithm [14] over a graphical representation of the code’s parity check matrix called a Tanner graph =-=[21]-=-. A Tanner graph is a bipartite graph consisting of n variable nodes (v-nodes) and m check nodes (c-nodes). Variable node yj is connected to check node fi if and only if the (i, j) th entry of H is eq... |

550 |
Bit-interleaved coded modulation,”
- Caire, Taricco, et al.
- 1998
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Citation Context ... For the higher order modulations (everything except QPSK), a bit interleaver is placed between the channel encoder and the modulator, and thus the system uses bit interleaved coded modulation (BICM) =-=[20]-=-. 2.2 Decoding An LDPC code can be decoded iteratively using a message passing algorithm [14] over a graphical representation of the code’s parity check matrix called a Tanner graph [21]. A Tanner gra... |

494 | Near Shannon limit performance of low density parity check codes,”
- MacKay, Neal
- 1996
(Show Context)
Citation Context ...der was thought to be too complex. However, after turbo codes showed the practicality of iterative decoding, interest in LDPC codes was soon renewed. In the mid-1990’s, MacKay rediscovered LDPC codes =-=[13, 14]-=- and showed that they are capable of approaching the Shannon limit. Soon afterwards, Richardson and Urbanke [15] and Luby et al [16] showed that long irregular LDPC codes can be superior to turbo code... |

304 | On the Design of Low-Density Parity-Check Codes Within 0.0045 dB of the Shannon Limit,”
- Chung
- 2001
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Citation Context ...ichardson and Urbanke [15] and Luby et al [16] showed that long irregular LDPC codes can be superior to turbo codes of the same length and can approach the Shannon capacity by a fraction of a decibel =-=[17]-=-. 2.1 Encoding The DVB-S2 channel encoder begins by first encoding a length k ′ binary message into a n ′ bit systematic BCH codeword. The k = n ′ BCH codeword is then encoded into a n bit systematic ... |

222 | Improved Low-Density Parity-Check Codes Using Irregular Graphs
- Luby, Mitzenmacher, et al.
- 2001
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Citation Context ...soon renewed. In the mid-1990’s, MacKay rediscovered LDPC codes [13, 14] and showed that they are capable of approaching the Shannon limit. Soon afterwards, Richardson and Urbanke [15] and Luby et al =-=[16]-=- showed that long irregular LDPC codes can be superior to turbo codes of the same length and can approach the Shannon capacity by a fraction of a decibel [17]. 2.1 Encoding The DVB-S2 channel encoder ... |

184 | Efficient encoding of low-density paritycheck codes,”
- Richardson, Urbanke
- 2001
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Citation Context ... k ′ = k − 168 = 16200r − 168 and thus have overall rate r ′ = r − 168/16200. Unlike with turbo codes, the encoding of LDPC codes can be very complex if the code is not designed with encoding in mind =-=[18]-=-. This is especially true for systematic LDPC codes, because a sparse H matrix could require a dense G matrix. In order to facilitate systematic encoding and produce irregular LDPC that are especially... |

154 | Optimal and Sub-Optimal Maximum a Posteriori Algorithms Suitable for Turbo Decoding
- Robertson, Höher, et al.
- 1997
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Citation Context ...s. Eight code rates are supported, ranging from r = 1/3 to r = 6/7. Like the turbo codes used in other standards, a pair of constituent RSC encoders is used along with log-MAP or max-log-MAP decoding =-=[4]-=-. The decoder for each constituent code performs best if the encoder begins and ends in a known state, such as the all-zeros state. This can be accomplished by independently terminating the trellis of... |

63 |
Design of Capacity Approaching Irregular Low-Density Parity Check Codes
- Richardson, Shokrollahi, et al.
- 2001
(Show Context)
Citation Context ...t in LDPC codes was soon renewed. In the mid-1990’s, MacKay rediscovered LDPC codes [13, 14] and showed that they are capable of approaching the Shannon limit. Soon afterwards, Richardson and Urbanke =-=[15]-=- and Luby et al [16] showed that long irregular LDPC codes can be superior to turbo codes of the same length and can approach the Shannon capacity by a fraction of a decibel [17]. 2.1 Encoding The DVB... |

61 |
Design of efficiently encodable moderatelength high-rate irregular LDPC codes
- Yang, Ryan, et al.
- 2004
(Show Context)
Citation Context ... facilitate systematic encoding and produce irregular LDPC that are especially suitable for high code rates, DVB-S2 uses a class of LDPC codes called extended irregular repeat accumulate (eIRA) codes =-=[19]-=-. With eIRA codes, the parity check matrix is constrained to be in the form H = [H1 H2] (16) where H1 is a sparse m by k matrix and H2 has the form ⎡ ⎤ 1 ⎢ 1 1 ⎥ ⎢ H2 = ⎢ 1 1 ⎥ ⎢ · · · ⎥ ⎣ 1 1 ⎦ 1 1 (... |

52 |
Tailbiting map decoders
- Anderson, Hladnik
- 1998
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Citation Context ...re must be taken to initialize the forward and backward recursions. Since the starting and stopping states are identical, the code trellis can be visualized as a cylinder (see, for example, Fig. 1 in =-=[10]-=-). The forward recursion can be interpreted as going around the cylinder in the clockwise direction and the backward recursion as going around the cylinder in the counter-clockwise direction. Several ... |

40 | The UMTS Turbo code and an efficient decoder implementation suitable for software defined radios
- Valenti, Sun
- 2002
(Show Context)
Citation Context ... algorithm at a cost of only about 0.1-0.2 dB relative to the optimal log-MAP algorithm. This is in contrast with binary codes, which lose about 0.3-0.4 dB when decoded with the max-log-MAP algorithm =-=[8]-=-. Additionally, duobinary codes are less impacted by the uncertainty of the starting and ending states when using tailbiting and perform better than their binary counterparts when punctured to higher ... |

31 |
On tail biting convolutional codes
- Ma, Wolf
- 1986
(Show Context)
Citation Context ...refore undesirable. As an alternative to terminating the trellis of the code, DVB-RCS uses circular recursive systematic convolutional (CRSC) encoding [5], which is based on the concept of tailbiting =-=[6]-=-. CRSC codes do not use tails, but rather are encoded in such a way that the ending state matches the starting state. Most turbo codes use binary encoders defined over GF(2). However, to facilitate fa... |

26 |
Non-binary convolutional codes for turbo coding
- Berrou, Jezequel
- 1999
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Citation Context ...he starting state. Most turbo codes use binary encoders defined over GF(2). However, to facilitate faster decoding in hardware, the DVB-RCS code uses duobinary constituent encoders defined over GF(4) =-=[7]-=-. During each clock cycle, the encoder takes in two data bits and outputs two parity bits so that, when the systematic bits are included, the code rate is r = 2/4. In order to avoid parallel transitio... |

19 |
Multiple parallel concatenation of circular recursive convolutional (CRSC) codes
- Berrou, Douillard, et al.
- 1999
(Show Context)
Citation Context ... non-negligible reduction in code rate and is therefore undesirable. As an alternative to terminating the trellis of the code, DVB-RCS uses circular recursive systematic convolutional (CRSC) encoding =-=[5]-=-, which is based on the concept of tailbiting [6]. CRSC codes do not use tails, but rather are encoded in such a way that the ending state matches the starting state. Most turbo codes use binary encod... |

16 |
An Introduction to LDPC Codes
- Ryan
- 2004
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Citation Context ...the form of extrinsic information) flow up from the variable nodes to the check nodes and down from the check nodes to the variable nodes. A full description of the decoding algorithm is presented in =-=[22]-=-, so here only the main results are presented. Thesc-nodes f 0 f 1 f 2 Digital Video Broadcasting 15 y 0 y 1 y 2 y 3 y 4 y 5 y 6 v-nodes Fig. 7. Tanner graph for the (7, 4) systematic Hamming code. Ea... |

10 |
Turbo coding for satellite and wireless communications
- Soleymani, Gao, et al.
- 2002
(Show Context)
Citation Context ...is in contrast with the 0.3 − 0.4 dB losses that are incurred when decoding binary turbo codes with the max-log-MAP algorithm, and for this reason many DVB-RCS decoder implementations use max-log-MAP =-=[11]-=-. Fig. 5 shows the influence of the block size. Frame error rate results are shown for blocks of N = {48, 64, 212, 432, 752} message couples, or correspondingly {12, 16, 53, 108, 188} bytes. In each c... |

9 |
An intuitive justification and a simplified implemetation of the MAP decoder for convolutional codes
- Viterbi
- 1998
(Show Context)
Citation Context ...(9) Si→Sj where max∗ is over the four branches Si → Sj exiting state Si at time k. As with α, the β’s are normalized with respect to the metric stored in state zero 1 The max∗ operation is defined in =-=[9]-=- as max∗(x, y) = max(x, y)+log(1+e −|x−y| ). Multiple arguments imply a recursion of pairwise operations, i.e. max∗(x, y, z) = max∗(x, max∗(y, z)).s8 Matthew C. Valenti, Shi Cheng, and Rohit Iyer Sesh... |