09-04-2012, 04:02 PM
Splitting of RA-Type LDPC
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 [1] and various fast-encodable LDPC codes with dual-diagonal parity structure have been proposed [2], [3], 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) [4], puncturing [5]-[9], extending [10], [11], and splitting [12] have been proposed to construct rate-compatible (RC) LDPC codes.
. COMPARISON OF VARIOUS RATE-COMPATIBLE RA-Types LDPC CODE
In this section, we will compare the decoding convergence speed and the decoding complexity when splitting, puncturing, and extending & puncturing are used to construct RA-Type LDPC codes. Note that extending & puncturing is the scheme to obtain high-rate codes by puncturing mother code and to obtain low-rate codes by extending mother code. Also, the performances of RC RA-Type LDPC codes obtained by splitting, puncturing, and extending & puncturing are compared through simulation
A. 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. Since the punctured nodes are assigned the initial LLR value 0 and their degrees are 2, at each iteration, the messages are only passed through the punctured nodes make the decoding convergence speed slow and the convergence speed of punctured RA-type LDPC code of the same code rate even if both codes have the same threshold. Therefore, among three rate control schemes for the same code rate, splitting gives the fast convergence speed and puncturing gives the slow convergence speed, which is confirmed through simulation in Fig. 3.
B. Construction of RC Block- Type LDPC Codes for various Rate-Control Schemes
In this subsection, the degree distributions of mother block- type LDPC (B-LDPC) codes [3], a class of RA-Type LDPC codes, are obtained for splitting, puncturing, and extending & puncturing. We assume that the target code rates are 1/3, 1/2, 2/3 and 4/5. For the mother code of rate 1/3 for puncturing, the degree distributions from [15] are used. For the mother code of rate 4/5 for splitting, we obtained the degree distributions by using density evolution such that the RC B-LDPC codes obtained by splitting and puncturing have the same degree distribution for the lowest code rate 1/3 for fair comparison.
Simulation Results
In this subsection, three rate-control schemes are compared through simulation using the RC B-LDPC codes given in III.B. For the simulation, BPSK modulation, AWGN channel, 1056 information bits, and belief propagation algorithm are used. When the number of iterations is 20, Fig. 3(a) shows that, at rates between 1/2 and 4/5, splitting gives about O.ldB- 0.25dB and 0.5dB-1.2dB gains at FER=10~2 over extending & puncturing and puncturing, respectively, as. expected from the result in subsection Ilt-A. Fig. 3(b) shows that as the number of iterations increases, the performance gaps become smaller. In Fig. 3, by comparing with the performances of the mother code of rate 2/3 from IEEE 802.16e standard and other mother code*. we can conclude that the splitting can give good performance comparable to well-designed mother code.