13-06-2012, 12:18 PM
Design Of Rate Compatible RA-Type Low-Density Parity-Check Codes Using Splitting
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INTRODUCTION
IT is known that the encoding complexity of LDPC codes is quadratic in the block length resulting in slow encoding. Therefore, efficient encoding algorithm has been studied and various fast-encodable LDPC codes with dual-diagonal parity structure have been proposed which are called repeat accumulate-type (RA-Type) LDPC codes. The dual diagonal parity structure can allow many degree-2 parity nodes while keeping the stability and enables the linear time encoding. Many rate-control schemes such as data puncturing (shortening) puncturing extending and splitting have been proposed to construct rate-compatible (RC) LDPC codes. These schemes have several problems such as slow decoding convergence speed, high decoding complexity, and performance degradation. To overcome such shortcomings, we proposed the rate-control scheme called splitting and in this paper we extend the result in by providing complexity analysis and further simulation results
Low Density Parity-Check Codes
In information theory, a low-density parity-check (LDPC) code is a linear error correcting code, a method of transmitting a message over a noisy transmission channel, and is constructed using a sparse bipartite graph. Low-density parity-check (LDPC) codes are a class of linear block codes. The name comes from the characteristic of their parity-check matrix which contains only a few 1s in comparison to the amount of 0s. Their main advantage is that they provide a performance which is very close to the capacity for a lot of different channels and linear time complex algorithms for decoding
New Rate-Control Scheme of LDPC Codes: SPLITTING
In this section, we propose a new rate-control scheme Called splitting. Assume that u set A = {B1, B2,… BI, C1, C2, …., CJ} of binary elements satisfies the even parity. Then, by adding the same binary element D to the sets B = { B1, B2, …, Bi} and C = {C1, C2, …, Cj, D}, two sets {B1, B2, …, Bi, D} and {C1, C2, …, Cj, D} can be made to satisfy the even partly. It is clear that all the elements in those two sets also satisfy even parity because A satisfies the even parity. By using this concept, a degree - k check node can be split into a degree - i check node and a degree - j check node, i + j = k + 2, by adding a new degree-2 parity node. Fig. 1 shows an example of splitting where upper and lower black circle nodes denote the parity and information nodes, respectively, and square nodes denote the check nodes. Since the variable nodes 1, 2, 3, 4, 5, and 6 satisfies the even parity, the check node a can be split into two check nodes b and v connected to {1, 4, 5} and {2, 3, 6), respectively, by introducing a common degree-2 parity node 7.
Decoding Convergence Speed of Various Rate-Control Scheme
In this subsection, we compare the decoding convergence speeds of three rate control schemes, puncturing, splitting, and extending & puncturing, for RA-Type LDPC codes. It is assumed that only degree-2 parity bits are punctured.
It implies that punctured modes make the decoding convergence speed slow and the convergence speed of RA-type LDPC code is slower than that of unpunctured one, even if both codes have same threshold.
Therefore among the three splitting gives the fast convergence speed and puncturing gives the slow.
[attachment=24288]
INTRODUCTION
IT is known that the encoding complexity of LDPC codes is quadratic in the block length resulting in slow encoding. Therefore, efficient encoding algorithm has been studied and various fast-encodable LDPC codes with dual-diagonal parity structure have been proposed which are called repeat accumulate-type (RA-Type) LDPC codes. The dual diagonal parity structure can allow many degree-2 parity nodes while keeping the stability and enables the linear time encoding. Many rate-control schemes such as data puncturing (shortening) puncturing extending and splitting have been proposed to construct rate-compatible (RC) LDPC codes. These schemes have several problems such as slow decoding convergence speed, high decoding complexity, and performance degradation. To overcome such shortcomings, we proposed the rate-control scheme called splitting and in this paper we extend the result in by providing complexity analysis and further simulation results
Low Density Parity-Check Codes
In information theory, a low-density parity-check (LDPC) code is a linear error correcting code, a method of transmitting a message over a noisy transmission channel, and is constructed using a sparse bipartite graph. Low-density parity-check (LDPC) codes are a class of linear block codes. The name comes from the characteristic of their parity-check matrix which contains only a few 1s in comparison to the amount of 0s. Their main advantage is that they provide a performance which is very close to the capacity for a lot of different channels and linear time complex algorithms for decoding
New Rate-Control Scheme of LDPC Codes: SPLITTING
In this section, we propose a new rate-control scheme Called splitting. Assume that u set A = {B1, B2,… BI, C1, C2, …., CJ} of binary elements satisfies the even parity. Then, by adding the same binary element D to the sets B = { B1, B2, …, Bi} and C = {C1, C2, …, Cj, D}, two sets {B1, B2, …, Bi, D} and {C1, C2, …, Cj, D} can be made to satisfy the even partly. It is clear that all the elements in those two sets also satisfy even parity because A satisfies the even parity. By using this concept, a degree - k check node can be split into a degree - i check node and a degree - j check node, i + j = k + 2, by adding a new degree-2 parity node. Fig. 1 shows an example of splitting where upper and lower black circle nodes denote the parity and information nodes, respectively, and square nodes denote the check nodes. Since the variable nodes 1, 2, 3, 4, 5, and 6 satisfies the even parity, the check node a can be split into two check nodes b and v connected to {1, 4, 5} and {2, 3, 6), respectively, by introducing a common degree-2 parity node 7.
Decoding Convergence Speed of Various Rate-Control Scheme
In this subsection, we compare the decoding convergence speeds of three rate control schemes, puncturing, splitting, and extending & puncturing, for RA-Type LDPC codes. It is assumed that only degree-2 parity bits are punctured.
It implies that punctured modes make the decoding convergence speed slow and the convergence speed of RA-type LDPC code is slower than that of unpunctured one, even if both codes have same threshold.
Therefore among the three splitting gives the fast convergence speed and puncturing gives the slow.