Design of Non-Binary Quasi-Cyclic LDPC Codes by ACE Optimization

An algorithm for constructing Tanner graphs of non-binary irregular quasi-cyclic LDPC codes is introduced. It employs a new method for selection of edge labels allowing control over the code's non-binary ACE spectrum and resulting in low error-floor. The efficiency of the algorithm is demonstrated by generating good codes of short to moderate length over small fields, outperforming codes generated by the known methods.Comment: Accepted to 2013 IEEE Information Theory Worksho

Evaluation of Channel Coding Methods for Next Generation Mobile Communication Standards

La codificación de canales es crucial para los sistemas de comunicación móvil, y los sistemas de comunicación inalámbrica 5G han decidido utilizar los códigos LDPC como esquema de codificación para sus canales de datos y los códigos Polares como esquema de codificación para sus canales de control. Este estudio se centra en los fundamentos de los códigos LDPC y los códigos Polares, especialmente los nuevos códigos polares, explicando en detalle sus características de polarización y las técnicas de decodificación recursiva. También se estudia las especificaciones de diseño relacionadas con estos dos esquemas de codificación de canales en 5G. Mediante simulaciones, se compara el rendimiento del nuevo esquema de codificación de canales inalámbricos 5G con el de los códigos Turbo a diferentes longitudes de bloque y tasas de código, y se extraen conclusiones relevantes para demostrar la aplicabilidad del esquema de codificación de canales 5G NR.Channel coding is essential for mobile communication systems, and the 5G wireless standardization committees decided to use LDPC codes as the coding scheme of its data channel and Polar codes as the coding scheme of its control channel. This study focuses on the fundamentals of LDPC codes and Polar codes, especially the emerging Polar codes, with detailed explanations of their polarization characteristics and recursive decoding techniques. It is also focused on the design specification related to these two channel coding schemes in 5G. The performance of the 5G New Radio channel coding scheme is compared with that of LTE Turbo codes at different block lengths and code rates through simulations, and relevant conclusions are drawn to demonstrate the suitability of the 5G NR channel coding scheme.Grado en Ingeniería en Sistemas de Telecomunicació

Rate-compatible LDPC Codes based on Primitive Polynomials and Golomb Rulers

We introduce and study a family of rate-compatible Low-Density Parity-Check (LDPC) codes characterized by very simple encoders. The design of these codes starts from simplex codes, which are defined by parity-check matrices having a straightforward form stemming from the coefficients of a primitive polynomial. For this reason, we call the new codes Primitive Rate-Compatible LDPC (PRC-LDPC) codes. By applying puncturing to these codes, we obtain a bit-level granularity of their code rates. We show that, in order to achieve good LDPC codes, the underlying polynomials, besides being primitive, must meet some more stringent conditions with respect to those of classical punctured simplex codes. We leverage non-modular Golomb rulers to take the new requirements into account. We characterize the minimum distance properties of PRC-LDPC codes, and study and discuss their encoding and decoding complexity. Finally, we assess their error rate performance under iterative decoding

Novel Code-Construction for (3, k) Regular Low Density Parity Check Codes

Communication system links that do not have the ability to retransmit generally rely on forward error correction (FEC) techniques that make use of error correcting codes (ECC) to detect and correct errors caused by the noise in the channel. There are several ECC’s in the literature that are used for the purpose. Among them, the low density parity check (LDPC) codes have become quite popular owing to the fact that they exhibit performance that is closest to the Shannon’s limit. This thesis proposes a novel code-construction method for constructing not only (3, k) regular but also irregular LDPC codes. The choice of designing (3, k) regular LDPC codes is made because it has low decoding complexity and has a Hamming distance, at least, 4. In this work, the proposed code-construction consists of information submatrix (Hinf) and an almost lower triangular parity sub-matrix (Hpar). The core design of the proposed code-construction utilizes expanded deterministic base matrices in three stages. Deterministic base matrix of parity part starts with triple diagonal matrix while deterministic base matrix of information part utilizes matrix having all elements of ones. The proposed matrix H is designed to generate various code rates (R) by maintaining the number of rows in matrix H while only changing the number of columns in matrix Hinf. All the codes designed and presented in this thesis are having no rank-deficiency, no pre-processing step of encoding, no singular nature in parity part (Hpar), no girth of 4-cycles and low encoding complexity of the order of (N + g2) where g2«N. The proposed (3, k) regular codes are shown to achieve code performance below 1.44 dB from Shannon limit at bit error rate (BER) of 10 −6 when the code rate greater than R = 0.875. They have comparable BER and block error rate (BLER) performance with other techniques such as (3, k) regular quasi-cyclic (QC) and (3, k) regular random LDPC codes when code rates are at least R = 0.7. In addition, it is also shown that the proposed (3, 42) regular LDPC code performs as close as 0.97 dB from Shannon limit at BER 10 −6 with encoding complexity (1.0225 N), for R = 0.928 and N = 14364 – a result that no other published techniques can reach

Near-capacity fixed-rate and rateless channel code constructions

Fixed-rate and rateless channel code constructions are designed for satisfying conflicting design tradeoffs, leading to codes that benefit from practical implementations, whilst offering a good bit error ratio (BER) and block error ratio (BLER) performance. More explicitly, two novel low-density parity-check code (LDPC) constructions are proposed; the first construction constitutes a family of quasi-cyclic protograph LDPC codes, which has a Vandermonde-like parity-check matrix (PCM). The second construction constitutes a specific class of protograph LDPC codes, which are termed as multilevel structured (MLS) LDPC codes. These codes possess a PCM construction that allows the coexistence of both pseudo-randomness as well as a structure requiring a reduced memory. More importantly, it is also demonstrated that these benefits accrue without any compromise in the attainable BER/BLER performance. We also present the novel concept of separating multiple users by means of user-specific channel codes, which is referred to as channel code division multiple access (CCDMA), and provide an example based on MLS LDPC codes. In particular, we circumvent the difficulty of having potentially high memory requirements, while ensuring that each user’s bits in the CCDMA system are equally protected. With regards to rateless channel coding, we propose a novel family of codes, which we refer to as reconfigurable rateless codes, that are capable of not only varying their code-rate but also to adaptively modify their encoding/decoding strategy according to the near-instantaneous channel conditions. We demonstrate that the proposed reconfigurable rateless codes are capable of shaping their own degree distribution according to the nearinstantaneous requirements imposed by the channel, but without any explicit channel knowledge at the transmitter. Additionally, a generalised transmit preprocessing aided closed-loop downlink multiple-input multiple-output (MIMO) system is presented, in which both the channel coding components as well as the linear transmit precoder exploit the knowledge of the channel state information (CSI). More explicitly, we embed a rateless code in a MIMO transmit preprocessing scheme, in order to attain near-capacity performance across a wide range of channel signal-to-ratios (SNRs), rather than only at a specific SNR. The performance of our scheme is further enhanced with the aid of a technique, referred to as pilot symbol assisted rateless (PSAR) coding, whereby a predetermined fraction of pilot bits is appropriately interspersed with the original information bits at the channel coding stage, instead of multiplexing pilots at the modulation stage, as in classic pilot symbol assisted modulation (PSAM). We subsequently demonstrate that the PSAR code-aided transmit preprocessing scheme succeeds in gleaning more information from the inserted pilots than the classic PSAM technique, because the pilot bits are not only useful for sounding the channel at the receiver but also beneficial for significantly reducing the computational complexity of the rateless channel decoder