Seho Myung

Quasi-cyclic LDPC codes for fast encoding

In this correspondence we present a special class of quasi-cyclic low-density parity-check (QC-LDPC) codes, called block-type LDPC (B-LDPC) codes, which have an efficient encoding algorithm due to the simple structure of their parity-check matrices. Since the parity-check matrix of a QC-LDPC code consists of circulant permutation matrices or the zero matrix, the required memory for storing it can be significantly reduced, as compared with randomly constructed LDPC codes. We show that the girth of a QC-LDPC code is upper-bounded by a certain number which is determined by the positions of circulant permutation matrices. The B-LDPC codes are constructed as irregular QC-LDPC codes with parity-check matrices of an almost lower triangular form so that they have an efficient encoding algorithm, good noise threshold, and low error floor. Their encoding complexity is linearly scaled regardless of the size of circulant permutation matrices.

A combining method of quasi-cyclic LDPC codes by the Chinese remainder theorem

In this paper we propose a method of constructing quasi-cyclic low-density parity-check (QC-LDPC) codes of large length by combining QC-LDPC codes of small length as their component codes, via the Chinese remainder theorem. The girth of the QC-LDPC codes obtained by the proposed method is always larger than or equal to that of each component code. By applying the method to array codes, we present a family of high-rate regular QC-LDPC codes with no 4-cycles. Simulation results show that they have almost the same performance as random regular LDPC codes.

Low-Density Parity-Check Codes for ATSC 3.0

In this paper, we introduce the overview and detailed structure of low-density parity-check (LDPC) codes, which are adopted for the physical layer standard of Advanced Television Systems Committee (ATSC) 3.0. As one of the features to mitigate channel errors efficiently, LDPC codes are used as a main part of forward error correction scheme within the bit interleaved coded modulation chain. This paper presents two different structures of LDPC codes in the ATSC 3.0 standard: 1) irregular repeat accumulate structure and 2) multi-edge type structure. After the detailed encoding methods for the two structures are introduced, the performance results including comparison studies with other broadcasting standards such as DVB-T2 and DVB-S2 are shown.

Lifting methods for quasi-cyclic LDPC codes

In this paper, we present two simple methods to construct a quasi-cyclic LDPC (QC-LDPC) code of larger length by lifting a given QC-LDPC code. We show that its girth is always larger than or equal to that of the given QC-LDPC code. Applying the methods recursively, it is possible to construct a sequence of QC-LDPC codes generated from a single exponent matrix by proper floor or modulo operations. Simulation results show that they have no serious performance degradation, as compared with randomly constructed LDPC codes

Flexible and Robust Transmission for Physical Layer Signaling of ATSC 3.0

The physical layer [layer-1 (L1)] signaling (L1 signaling) of Advanced Television Systems Committee (ATSC) 3.0 is studied. In the new digital broadcasting system, ATSC 3.0, L1 signaling is designed to be more efficient but still robust compared with preceding standards such as DVB-T2. We introduce the error protection scheme of ATSC 3.0 in detail. Especially advanced methods newly employed in ATSC 3.0 are investigated with regard to its purpose and benefit in comparison to conventional DVB-T2.

Extension of quasi-cyclic LDPC codes by lifting

In this paper, we analyze some cycle properties of quasi-cyclic low-density parity-check (QC-LDPC) codes and show that the girth of a QC-LDPC code is upper bounded by a certain number introduced by the structure of its mother matrix. We also propose a simple method to extend QC-LDPC codes of large length by lifting QC-LDPC codes of smaller length. In particular, it is possible to generate them from a single exponent matrix by a proper modulo-operation. Simulation results show that the more we apply the lifting to QC-LDPC codes, the more memory efficiency becomes better, but it may induce a little performance degradation

A Combining Method of Structured LDPC Codes from Affine Permutation Matrices

In this paper we present a class of structured low-density parity-check (LDPC) codes from affine permutation matrices, called the APM-LDPC codes, which are a generalization of quasi-cyclic LDPC codes. We give a necessary and sufficient condition under which an APM-LDPC code has a cycle and introduce a simple method to construct APM-LDPC codes of large length by combining those of small length based on the Chinese remainder theorem. In particular, we show that the girth of APM-LDPC codes obtained in this method is always larger than or equal to those of given APM-LDPC codes

Design of LDPC Coded BICM in DVB Broadcasting Systems With Block Permutations

A new simplified structure of bit-interleaved coded modulation (BICM) for second generation digital video broadcasting (DVB) standards, such as DVB-T2, DVB-C2, and DVB-NGH is proposed. In the BICM of the DVB standards, parity and column-twist interleavers are employed in order to avoid possible performance degradation due to the structural weaknesses of the BICM scheme. In this paper, a new method is proposed of finding permutation-equivalent low-density parity-check codes that eliminate the BICM weaknesses without the column-twist interleaver, thereby simplifying the BICM structure of the DVB standards. The new code descriptions are found by applying a column permutation to the parity check matrices of the original codes in the DVB standards. The codes generated by these new descriptions have the same error correcting capability individually for a binary memoryless channel. However, the resulting BICM has a different structure that is free of weakness, called the less-capable check node.

Efficient Decoding Schemes of LDPC Codes for the Layered-Division Multiplexing Systems in ATSC 3.0

A low-complexity decoding scheme of low-density parity-check codes for the layered-division multiplexing (LDM) systems in ATSC 3.0 is proposed. Based on the unique characteristic of the LDM and the special structure of a parity-check matrix (PCM) for the core layer, the proposed scheme applies the sum-product algorithm (SPA) to only a part of the PCM. For this reason, it is referred to as “the partial SPA,” compared with the conventional scheme, denoted by “the full SPA.” Clearly, it has a significantly lower complexity than the full SPA. Furthermore, we propose hybrid decoders employing both the full SPA and the partial SPA to achieve a better performance, while maintaining their complexity low. Numerical results show that the proposed schemes have a good performance enough to perform successive interference cancellation for the enhanced layer of the LDM systems in ATSC 3.0 as well as they have a low-complexity merit depending on system parameters. Since they only schedule the decoding procedure without modifying the decoder structure, they also have a benefit in the implementation of decoders.

Efficient modulation and coding scheme based on low-density parity-check codes

A repetition coding can provide coding and diversity gains, however, the transmission rate is severely decreased. Therefore, the repetition diversity scheme has been recognized as an inefficient coding technique. In the paper, we present some performance results of LDPC codes with a repetition coding over AWGN and Rayleigh channels for given transmission rates. Simulation results show that the repetition scheme with QPSK modulation always provides a good coding gain over a Rayleigh fading channel due to diversity effect, as compared with the case of BPSK modulation without repetition. Furthermore, we observe the performance of LDPC coded modulation with non-uniform constellation over AWGN and Rayleigh channels. Finally, we present that the best modulation and coding strategy for given channel condition can be determined by adjusting code-rate, modulation and repetition schemes.