Size Compatible (SC)-Array LDPC Codes

Abstract

Array low density parity check (LDPC) codes are high-rate codes that can achieve good error rate performance in additive white Gaussian noise (AWGN) channels. However, array LDPC codes do not support arbitrary code lengths, because the code length of an array LDPC code with good error rate performance is limited to a multiple of a prime number. This paper proposes Size Compatible (SC)-array LDPC codes; they achieve good error rate performance while supporting arbitrary code lengths. We conduct computer simulations to evaluate the block error rate (BLER) performance of SC-array LDPC codes in AWGN channels. We also evaluate the corresponding performance of SC-array LDPC coded multiband OFDM systems for data transmission rates over 1 Gbps in the UWB multipath channel model CM 3. We show that if the submatrix size is a nonprime number, SC-array LDPC codes achieve better error rate performance than the conventional array LDPC codes in AWGN channels. We also show that the SC-array LDPC codes achieve better error rate performance than the punctured array LDPC codes in AWGN channels. We also show that if the submatrix size is a prime number, SC-array LDPC codes achieve the same error rate performance as conventional array LDPC codes in AWGN channels. Moreover, we show that for multiband OFDM systems with data transmission rates of over 1 Gbps, SC-array LDPC codes achieve better error rate performance than conventional array LDPC codes.

Soft decoding method for systematic raptor codes

“…3 shows the BER performance comparison of systematic and non‐systematic raptor codes using binary phase‐shift keying (BPSK) over an additive white Gaussian noise (AWGN) channel according to R −1 = n / k in (a) and E s / N 0 in (b), respectively. In both the systematic and non‐systematic codes, the (1176, 1078) size‐compatible (SC)‐array LDPC code [22] is used as the outer code, and the LT code with the distribution in [20] was used as the inner code.…”

Compressive Sensing Measurement Matrix Generator Based on Improved SC-Array LDPC Code

“…We propose the shift index distribution to reflect the above phenomena, namely the elements in two adjacent vertices of a rectangle are the same and the elements in the other two adjacent vertices of the rectangle are also the same. Formula (1) shows the calculation method of the shift indices [1], where i ∈ [1, r ] is the row index and j ∈ [1, l] is the column index. This means that every permutation matrix is cyclically right-shifted according to the shift index.…”

“…All repetitive row numbers are obtained in this way. The shift indices of repetitive rows are calculated by formula (2), and the remaining rows are calculated by formula (1). Once all shift indices are calculated, 4-cycles are further removed by the right cyclic shift operation applied according to formula (3).…”

Construction of regular quasi-cyclic LDPC codes based on cosets

“…As we see on Fig.1, various lengths are realizable by our construction. Certainly, the codes with specific length or rate can be obtained by choosing a part of the square matrices in (4) and some columns of other square matrices.…”

“…To construct an array LDPC code with girth at least 6, the circulant permutation matrices (shortly, circulants) size has to be prime to eliminate the short cycles. A modified construction to array LDPC codes was presented for supporting arbitrary circulants size by Abematsu et al [4], while such codes probably contain a few short cycles. In [5], Tanner et al proposed a construction method for QC LDCP codes based on the multiplicative structure of a group.…”