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SiPS ... design and implementation - IEEE Workshop on Signal Processing Systems

Overlapped Decoding for a Class of Quasi-Cyclic LDPC Codes

Sang-Min Kim, Keshab K. Parhi

Published Dec 23, 2004• 12 citations
Publisher

Abstract

In low-density parity-check (LDPC) code decoding with the iterative sum-product algorithm (SPA), due to the randomness of the parity-check matrix, H, the overlapping of the check node processing unit (CNU) and variable node processing unit (VNU) in the same clock cycle is difficult. The paper demonstrates that overlapped decoding can be exploited as long as the LDPC matrix is composed of identity matrices and their cyclic-shifted matrices, i.e., the parity-check matrix, H, belongs to a class of quasi-cyclic LDPC codes. It is shown that the number of clock cycles required for decoding can be reduced by 50% when overlapped decoding is applied to a (3,6)-regular LDPC code decoder.

DOI
10.1109/sips.2004.1363034

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In low-density parity-check (LDPC) code decoding with the iterative sum-product algorithm (SPA), due to the randomness of the parity-check matrix, H, the overlapping of the check node processing unit (CNU) and variable node processing unit (VNU) in the same clock cycle is difficult. The paper demonstrates that overlapped decoding can be exploited as long as the LDPC matrix is composed of identity matrices and their cyclic-shifted matrices, i.e., the parity-check matrix, H, belongs to a class of quasi-cyclic LDPC codes. It is shown that the number of clock cycles required for decoding can be reduced by 50% when overlapped decoding is applied to a (3,6)-regular LDPC code decoder.
In this paper, the authors propose an efficient highly-parallel decoder architecture using partially overlapped decoding scheme for quasi-cyclic (QC) low-density parity-check (LDPC) codes, which leads to reduction in hardware complexity and power consumption. Generally, due to the regularly structured parity-check matrix H of QC LDPC codes, the message updating computations in the check node unit (CNU) and the variable node unit (VNU) can be efficiently overlapped, which increases the decoding throughput by maximizing the hardware utilization efficiency (HUE). However, the partially overlapped decoding scheme cannot be used to design a highly-parallel decoding architecture for high-throughput applications. For (3, 5)-regular QC LDPC codes, our proposed method could reduce the hardware complexity by approximately 33% for the CNU and 20% for the VNU in the highly-parallel decoder architecture without any performance degradation. In addition, the power consumption can be minimized by reducing the total number of memory accesses for updated messages.
In this paper, we propose a low-complexity entirely-overlapped partially-parallel decoder architecture for quasi-cyclic low-density parity-check (QC-LDPC) codes. For a (c, t)-regular QC-LDPC decoder, this decoder can achieve approximate 100% hardware utilization efficiency (HUE) and entirely overlapped decoding by using only one check node process unit group (CNUG) to process c groups of check node messages sequentially. Compared with traditional partially-parallel decoder, the quantities of check node process unit (CNU), barrel shifters and counters can be decreased prominently. Moreover, it is flexible in code rate and code length.
In this paper, a combined Low-Density Parity-Check (LDPC) code decoding design method, called modified Block-Type LDPC (B-LDPC), for realistic LDPC coding system architectures is presented. The B-LDPC code, which is a special class of quasi-cyclic LDPC (QC-LDPC), has an efficient encoding algorithm owing to the simple structure of their parity-check matrices. A proposed distribution of irregular parity-check matrix for the modified B-LDPC is developed so that we can obtain an area-efficient decoder design, good error correction performance, and achievable architecture implementation. The modified B-LDPC code decoding utilizes the iterative min-sum algorithm (MSA) and its decoding architecture design employs the non-overlapping operations of bit node unit (BNU) and check node unit (CNU). Different block matrix sizes for parity-check matrix can be adopted so that the modified B-LDPC code decoding improves the throughput without obvious performance degradation.
This paper presents a reduced-complexity iterative decoding scheme for quasi-cyclic (QC) low-density parity-check (LDPC) codes which is devised based on the section-wise cyclic structure of their parity-check matrices. The decoding scheme significantly reduces the hardware implementation complexity of a QC-LDPC code decoder in terms of the number of message processing units and the number of wires required to connect the message processing units. A long high-rate high-performance QC-LDPC code is used to demonstrate the effectiveness of the proposed decoding scheme. Using this long code as the mother code, descendant QC-LDPC codes of various lengths and rates can be constructed by puncturing and masking the columns and rows of the parity-check matrix of the mother code. These descendant codes can be decoded by deactivating specific sets of message processing units of the mother decoder.
There are many low-density parity-check (LDPC) decoder architectures in the literature most of which are based on structured codes. Besides been specific to a particular class of codes, suggested architectures are limited in scalability. The major challenge in decoder design and implementation is the consideration of several strongly interrelated factors. These factors affect decoder computation and communication complexity, and error-correcting performance. In this paper we present a low-complexity, flexible and scalable LDPC decoder architecture for quasi-cyclic codes that supports multiple code designs (size, weights, rates, regular and irregular). The architecture is a result of a combination of flexible code construction and computation overlapping techniques. The architecture is based on overlapping techniques that allow sequential processing of check and variable nodes. The overlapping techniques lead to a low-complexity decoder interconnect compared to the existing techniques as they allow serial processing of code sub-matrices as compared to parallel processing of all sub-matrices in the existing overlapping technique. Although the architecture is based on quasi-cyclic codes, it can also be applied to random or other structured codes making it the most flexible, scalable and high-throughput partly-parallel LDPC decoder architecture.