Low Complexity Encoding Based on Richardson's LDPC Codes

Low complexity encoding of LDPC codes for high-rate and high-speed communication

“…8, the performance of short length is similar however performance of long length is better than [5], because the H matrices of [5] have many cycle-4. It means that our scheme is more efficient than [5] for t/J =T = I .…”

“…7, the performances of our encoding I and II are the same with IEEE 802.16e LDPC codes. Also we compared proposed scheme I, II with [5] between short length and long length in Fig. 8 using matrix A and C of IEEE 802.16e.…”

“…The complexity of matrix D is focused on many works in [4][6] which has remark ¢ = I and small g [1], because the complexity of Richardson's encoding is O(n+ g2) . Recently, [5] targets on the matrix T and its inverse in order to reduce complexity. In this paper, our goals are to 978-1-4244-2313-2/08/$25.00 ©2008 IEEE approach low complexity encoding of Quasi-Cyclic LDPC Code by using Circulant Permutation Matrices(CPM) [2] for high-rate and fast communication systems.…”

“…In section 3 and section 4, we proposed our low complexity encoding scheme I and II respectively. In section 5, we showed numerical results and compared proposed encoding with [5] and various LOPC. Last section presented remarks and conclusions.…”

“…Unfortunately in parity parts of many cases, the f e -I bterm 0 a a a can cause cycle-4, because from equation (10), b-t+e-(e-t+b)=O ( a b~a t~a e~a et + b~a b ) is caused. In[5], they succeed in ¢ =T =I however their parity parts of H matrix have many cycle-4 due to (10) and (11). So, in this section, we are challenging ¢ =T =I as well as cycleterm a a a + a In an , we will present some conditions.In order to eliminate cycle-4 into parity parts, we can consider matrix D as a zero matrix, then the cycle-4 by parity parts is eliminated.…”