Sparse graph-based coding schemes for continuous phase modulations

The use of the continuous phase modulation (CPM) is interesting when the channel represents a strong non-linearity and in the case of limited spectral support; particularly for the uplink, where the satellite holds an amplifier per carrier, and for downlinks where the terminal equipment works very close to the saturation region. Numerous studies have been conducted on this issue but the proposed solutions use iterative CPM demodulation/decoding concatenated with convolutional or block error correcting codes. The use of LDPC codes has not yet been introduced. Particularly, no works, to our knowledge, have been done on the optimization of sparse graph-based codes adapted for the context described here. In this study, we propose to perform the asymptotic analysis and the design of turbo-CPM systems based on the optimization of sparse graph-based codes. Moreover, an analysis on the corresponding receiver will be done

Repeat-Accumulate構造に基づく直列連接信号符号

電気通信大学201

Continuous Transmission of Spatially Coupled LDPC Code Chains

We propose a novel encoding/transmission scheme called continuous chain (CC) transmission that is able to improve the finite-length performance of a system using spatially coupled low-density parity-check (SC-LDPC) codes. In CC transmission, instead of transmitting a sequence of independent code words from a terminated SC-LDPC code chain, we connect multiple chains in a layered format, where encoding, transmission, and decoding are performed in a continuous fashion. The connections between chains are created at specific points, chosen to improve the finite-length performance of the code structure under iterative decoding. We describe the design of CC schemes for different SC-LDPC code ensembles constructed from protographs: a (J,K) -regular SC-LDPC code chain, a spatially coupled repeat-accumulate (SC-RA) code, and a spatially coupled accumulate-repeat-jagged-accumulate (SC-ARJA) code. In all cases, significant performance improvements are reported and it is shown that using CC transmission only requires a small increase in decoding complexity and decoding delay with respect to a system employing a single SC-LDPC code chain for transmission.This material is based upon work supported in part by the National Science Foundation under Grant Nos. CCF-1161754 and CCSS-1710920, in part by NSERC Canada, and in part by the Spanish Ministry of Economy and Competitiveness and the Spanish National Research Agency under grants TEC2016-78434-C3-3-R (AEI/FEDER, EU) and Juan de la Cierva Fellowship IJCI-2014-19150

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

Analysis and Design of Spatially-Coupled Codes with Application to Fiber-Optical Communications

The theme of this thesis is the analysis and design of error-correcting codes that are suitable for high-speed fiber-optical communication systems. In particular, we consider two code classes. The codes in the first class are protograph-based low-density parity-check (LDPC) codes which are decoded using iterative soft-decision decoding. The codes in the second class are generalized LDPC codes with degree-2 variable nodes—henceforth referred to as generalized product codes (GPCs)—which are decoded using iterative bounded-distance decoding (BDD). Within each class, our focus is primarily on spatially-coupled codes. Spatially-coupled codes possess a convolutional structure and are characterized by a wave-like decoding behavior caused by a termination boundary effect. The contributions of this thesis can then be categorized into two topics, as outlined below.First, we consider the design of systems operating at high spectral efficiency. In particular, we study the optimization of the mapping of the coded bits to the modulation bits for a polarization-multiplexed system that is based on the bit-interleaved coded modulation paradigm. As an example, for the (protograph-based) AR4JA code family, the transmission reach can be extended by roughly up to 8% by using an optimized bit mapper, without significantly increasing the system complexity. For terminated spatially-coupled codes with long spatial length, the bit mapper optimization only results in marginal performance improvements, suggesting that a sequential allocation is close to optimal. On the other hand, an optimized allocation can significantly improve the performance of tail-biting spatially-coupled codes which do not possess an inherent termination boundary. In this case, the unequal error protection offered by the modulation bits of a nonbinary signal constellation can be exploited to create an artificial termination boundary that induces a wave-like decoding for tail-biting spatially-coupled codes.As a second topic, we study deterministically constructed GPCs. GPCs are particularly suited for high-speed applications such as optical communications due to the significantly reduced decoding complexity of iterative BDD compared to iterative soft-decision decoding of LDPC codes. We propose a code construction for GPCs which is sufficiently general to recover several well-known classes of GPCs as special cases, e.g., irregular product codes (PCs), block-wise braided codes, and staircase codes. Assuming transmission over the binary erasure channel, it is shown that the asymptotic performance of the resulting codes can be analyzed by means of a recursive density evolution (DE) equation. The DE analysis is then applied to study three different classes of GPCs: spatially-coupled PCs, symmetric GPCs, and GPCs based on component code mixtures

Analysis and Design of Spatially-Coupled Codes with Application to Fiber-Optical Communications

The theme of this thesis is the analysis and design of error-correcting codes that are suitable for high-speed fiber-optical communication systems. In particular, we consider two code classes. The codes in the first class are protograph-based low-density parity-check (LDPC) codes which are decoded using iterative soft-decision decoding. The codes in the second class are generalized LDPC codes with degree-2 variable nodes—henceforth referred to as generalized product codes (GPCs)—which are decoded using iterative bounded-distance decoding (BDD). Within each class, our focus is primarily on spatially-coupled codes. Spatially-coupled codes possess a convolutional structure and are characterized by a wave-like decoding behavior caused by a termination boundary effect. The contributions of this thesis can then be categorized into two topics, as outlined below.First, we consider the design of systems operating at high spectral efficiency. In particular, we study the optimization of the mapping of the coded bits to the modulation bits for a polarization-multiplexed system that is based on the bit-interleaved coded modulation paradigm. As an example, for the (protograph-based) AR4JA code family, the transmission reach can be extended by roughly up to 8% by using an optimized bit mapper, without significantly increasing the system complexity. For terminated spatially-coupled codes with long spatial length, the bit mapper optimization only results in marginal performance improvements, suggesting that a sequential allocation is close to optimal. On the other hand, an optimized allocation can significantly improve the performance of tail-biting spatially-coupled codes which do not possess an inherent termination boundary. In this case, the unequal error protection offered by the modulation bits of a nonbinary signal constellation can be exploited to create an artificial termination boundary that induces a wave-like decoding for tail-biting spatially-coupled codes.As a second topic, we study deterministically constructed GPCs. GPCs are particularly suited for high-speed applications such as optical communications due to the significantly reduced decoding complexity of iterative BDD compared to iterative soft-decision decoding of LDPC codes. We propose a code construction for GPCs which is sufficiently general to recover several well-known classes of GPCs as special cases, e.g., irregular product codes (PCs), block-wise braided codes, and staircase codes. Assuming transmission over the binary erasure channel, it is shown that the asymptotic performance of the resulting codes can be analyzed by means of a recursive density evolution (DE) equation. The DE analysis is then applied to study three different classes of GPCs: spatially-coupled PCs, symmetric GPCs, and GPCs based on component code mixtures