High Order Modulation Protograph Codes

Digital communication coding methods for designing protograph-based bit-interleaved code modulation that is general and applies to any modulation. The general coding framework can support not only multiple rates but also adaptive modulation. The method is a two stage lifting approach. In the first stage, an original protograph is lifted to a slightly larger intermediate protograph. The intermediate protograph is then lifted via a circulant matrix to the expected codeword length to form a protograph-based low-density parity-check code

The Design of Efficiently-Encodable Rate-Compatible LDPC Codes

We present a new class of irregular low-density parity-check (LDPC) codes for moderate block lengths (up to a few thousand bits) that are well-suited for rate-compatible puncturing. The proposed codes show good performance under puncturing over a wide range of rates and are suitable for usage in incremental redundancy hybrid-automatic repeat request (ARQ) systems. In addition, these codes are linear-time encodable with simple shift-register circuits. For a block length of 1200 bits the codes outperform optimized irregular LDPC codes and extended irregular repeat-accumulate (eIRA) codes for all puncturing rates 0.6~0.9 (base code performance is almost the same) and are particularly good at high puncturing rates where good puncturing performance has been previously difficult to achieve.Comment: Accepted subject to minor revision to IEEE Trans. on Com

Development of rate-compatible structured LDPC CODEC algorithms and hardware IP

Issued as final reportSamsung Advanced Institute of Technolog

A Balanced Tree Approach to Construction of Length-Compatible Polar Codes

From the perspective of tree, we design a length-flexible coding scheme. For an arbitrary code length, we first construct a balanced binary tree (BBT) where the root node represents a transmitted codeword, the leaf nodes represent either active bits or frozen bits, and a parent node is related to its child nodes by a length-adaptive (U+V|V) operation. Both the encoding and the successive cancellation (SC)-based decoding can be implemented over the constructed coding tree. For code construction, we propose a signal-to-noise ratio (SNR)-dependent method and two SNR-independent methods, all of which evaluate the reliabilities of leaf nodes and then select the most reliable leaf nodes as the active nodes. Numerical results demonstrate that our proposed codes can have comparable performance to the 5G polar codes. To reduce the decoding latency, we propose a partitioned successive cancellation (PSC)-based decoding algorithm, which can be implemented over a sub-tree obtained by pruning the coding tree. Numerical results show that the PSC-based decoding can achieve similar performance to the conventional SC-based decoding.Comment: 30 pages, 10 figure

Randomly Punctured LDPC Codes

In this paper, we present a random puncturing analysis of low-density parity-check (LDPC) code ensembles. We derive a simple analytic expression for the iterative belief propagation (BP) decoding threshold of a randomly punctured LDPC code ensemble on the binary erasure channel (BEC) and show that, with respect to the BP threshold, the strength and suitability of an LDPC code ensemble for random puncturing is completely determined by a single constant that depends only on the rate and the BP threshold of the mother code ensemble. We then provide an efficient way to accurately predict BP thresholds of randomly punctured LDPC code ensembles on the binary- input additive white Gaussian noise channel (BI-AWGNC), given only the BP threshold of the mother code ensemble on the BEC and the design rate, and we show how the prediction can be improved with knowledge of the BI-AWGNC threshold. We also perform an asymptotic minimum distance analysis of randomly punctured code ensembles and present simulation results that confirm the robust decoding performance promised by the asymptotic results. Protograph-based LDPC block code and spatially coupled LDPC code ensembles are used throughout as examples to demonstrate the results

Low Complexity Rate Compatible Puncturing Patterns Design for LDPC Codes

In contemporary digital communications design, two major challenges should be addressed: adaptability and flexibility. The system should be capable of flexible and efficient use of all available spectrums and should be adaptable to provide efficient support for the diverse set of service characteristics. These needs imply the necessity of limit-achieving and flexible channel coding techniques, to improve system reliability. Low Density Parity Check (LDPC) codes fit such requirements well, since they are capacity-achieving. Moreover, through puncturing, allowing the adaption of the coding rate to different channel conditions with a single encoder/decoder pair, adaptability and flexibility can be obtained at a low computational cost.In this paper, the design of rate-compatible puncturing patterns for LDPCs is addressed. We use a previously defined formal analysis of a class of punctured LDPC codes through their equivalent parity check matrices. We address a new design criterion for the puncturing patterns using a simplified analysis of the decoding belief propagation algorithm, i.e., considering a Gaussian approximation for message densities under density evolution, and a simple algorithmic method, recently defined by the Authors, to estimate the threshold for regular and irregular LDPC codes on memoryless binary-input continuous-output Additive White Gaussian Noise (AWGN) channels