Coding Theory and its Applications in Communication systems

Error control coding has been used extensively in digital communication systems because of its cost-effectiveness in achieving efficient, reliable digital transmission. Coding now plays an important role in the design of modern communication systems. This paper reviews the development of basic coding theory and state-of-art coding techniques. The applications of coding to communication systems and future trends are also discussed

Simplified decoding techniques for linear block codes

Error correcting codes are combinatorial objects, designed to enable reliable transmission of digital data over noisy channels. They are ubiquitously used in communication, data storage etc. Error correction allows reconstruction of the original data from received word. The classical decoding algorithms are constrained to output just one codeword. However, in the late 50’s researchers proposed a relaxed error correction model for potentially large error rates known as list decoding. The research presented in this thesis focuses on reducing the computational effort and enhancing the efficiency of decoding algorithms for several codes from algorithmic as well as architectural standpoint. The codes in consideration are linear block codes closely related to Reed Solomon (RS) codes. A high speed low complexity algorithm and architecture are presented for encoding and decoding RS codes based on evaluation. The implementation results show that the hardware resources and the total execution time are significantly reduced as compared to the classical decoder. The evaluation based encoding and decoding schemes are modified and extended for shortened RS codes and software implementation shows substantial reduction in memory footprint at the expense of latency. Hermitian codes can be seen as concatenated RS codes and are much longer than RS codes over the same aphabet. A fast, novel and efficient VLSI architecture for Hermitian codes is proposed based on interpolation decoding. The proposed architecture is proven to have better than Kötter’s decoder for high rate codes. The thesis work also explores a method of constructing optimal codes by computing the subfield subcodes of Generalized Toric (GT) codes that is a natural extension of RS codes over several dimensions. The polynomial generators or evaluation polynomials for subfield-subcodes of GT codes are identified based on which dimension and bound for the minimum distance are computed. The algebraic structure for the polynomials evaluating to subfield is used to simplify the list decoding algorithm for BCH codes. Finally, an efficient and novel approach is proposed for exploiting powerful codes having complex decoding but simple encoding scheme (comparable to RS codes) for multihop wireless sensor network (WSN) applications

Algorithm Development and VLSI Implementation of Energy Efficient Decoders of Polar Codes

With its low error-floor performance, polar codes attract significant attention as the potential standard error correction code (ECC) for future communication and data storage. However, the VLSI implementation complexity of polar codes decoders is largely influenced by its nature of in-series decoding. This dissertation is dedicated to presenting optimal decoder architectures for polar codes. This dissertation addresses several structural properties of polar codes and key properties of decoding algorithms that are not dealt with in the prior researches. The underlying concept of the proposed architectures is a paradigm that simplifies and schedules the computations such that hardware is simplified, latency is minimized and bandwidth is maximized. In pursuit of the above, throughput centric successive cancellation (TCSC) and overlapping path list successive cancellation (OPLSC) VLSI architectures and express journey BP (XJBP) decoders for the polar codes are presented. An arbitrary polar code can be decomposed by a set of shorter polar codes with special characteristics, those shorter polar codes are referred to as constituent polar codes. By exploiting the homogeneousness between decoding processes of different constituent polar codes, TCSC reduces the decoding latency of the SC decoder by 60% for codes with length n = 1024. The error correction performance of SC decoding is inferior to that of list successive cancellation decoding. The LSC decoding algorithm delivers the most reliable decoding results; however, it consumes most hardware resources and decoding cycles. Instead of using multiple instances of decoding cores in the LSC decoders, a single SC decoder is used in the OPLSC architecture. The computations of each path in the LSC are arranged to occupy the decoder hardware stages serially in a streamlined fashion. This yields a significant reduction of hardware complexity. The OPLSC decoder has achieved about 1.4 times hardware efficiency improvement compared with traditional LSC decoders. The hardware efficient VLSI architectures for TCSC and OPLSC polar codes decoders are also introduced. Decoders based on SC or LSC algorithms suffer from high latency and limited throughput due to their serial decoding natures. An alternative approach to decode the polar codes is belief propagation (BP) based algorithm. In BP algorithm, a graph is set up to guide the beliefs propagated and refined, which is usually referred to as factor graph. BP decoding algorithm allows decoding in parallel to achieve much higher throughput. XJBP decoder facilitates belief propagation by utilizing the specific constituent codes that exist in the conventional factor graph, which results in an express journey (XJ) decoder. Compared with the conventional BP decoding algorithm for polar codes, the proposed decoder reduces the computational complexity by about 40.6%. This enables an energy-efficient hardware implementation. To further explore the hardware consumption of the proposed XJBP decoder, the computations scheduling is modeled and analyzed in this dissertation. With discussions on different hardware scenarios, the optimal scheduling plans are developed. A novel memory-distributed micro-architecture of the XJBP decoder is proposed and analyzed to solve the potential memory access problems of the proposed scheduling strategy. The register-transfer level (RTL) models of the XJBP decoder are set up for comparisons with other state-of-the-art BP decoders. The results show that the power efficiency of BP decoders is improved by about 3 times

Algorithm Development and VLSI Implementation of Energy Efficient Decoders of Polar Codes

With its low error-floor performance, polar codes attract significant attention as the potential standard error correction code (ECC) for future communication and data storage. However, the VLSI implementation complexity of polar codes decoders is largely influenced by its nature of in-series decoding. This dissertation is dedicated to presenting optimal decoder architectures for polar codes. This dissertation addresses several structural properties of polar codes and key properties of decoding algorithms that are not dealt with in the prior researches. The underlying concept of the proposed architectures is a paradigm that simplifies and schedules the computations such that hardware is simplified, latency is minimized and bandwidth is maximized. In pursuit of the above, throughput centric successive cancellation (TCSC) and overlapping path list successive cancellation (OPLSC) VLSI architectures and express journey BP (XJBP) decoders for the polar codes are presented. An arbitrary polar code can be decomposed by a set of shorter polar codes with special characteristics, those shorter polar codes are referred to as constituent polar codes. By exploiting the homogeneousness between decoding processes of different constituent polar codes, TCSC reduces the decoding latency of the SC decoder by 60% for codes with length n = 1024. The error correction performance of SC decoding is inferior to that of list successive cancellation decoding. The LSC decoding algorithm delivers the most reliable decoding results; however, it consumes most hardware resources and decoding cycles. Instead of using multiple instances of decoding cores in the LSC decoders, a single SC decoder is used in the OPLSC architecture. The computations of each path in the LSC are arranged to occupy the decoder hardware stages serially in a streamlined fashion. This yields a significant reduction of hardware complexity. The OPLSC decoder has achieved about 1.4 times hardware efficiency improvement compared with traditional LSC decoders. The hardware efficient VLSI architectures for TCSC and OPLSC polar codes decoders are also introduced. Decoders based on SC or LSC algorithms suffer from high latency and limited throughput due to their serial decoding natures. An alternative approach to decode the polar codes is belief propagation (BP) based algorithm. In BP algorithm, a graph is set up to guide the beliefs propagated and refined, which is usually referred to as factor graph. BP decoding algorithm allows decoding in parallel to achieve much higher throughput. XJBP decoder facilitates belief propagation by utilizing the specific constituent codes that exist in the conventional factor graph, which results in an express journey (XJ) decoder. Compared with the conventional BP decoding algorithm for polar codes, the proposed decoder reduces the computational complexity by about 40.6%. This enables an energy-efficient hardware implementation. To further explore the hardware consumption of the proposed XJBP decoder, the computations scheduling is modeled and analyzed in this dissertation. With discussions on different hardware scenarios, the optimal scheduling plans are developed. A novel memory-distributed micro-architecture of the XJBP decoder is proposed and analyzed to solve the potential memory access problems of the proposed scheduling strategy. The register-transfer level (RTL) models of the XJBP decoder are set up for comparisons with other state-of-the-art BP decoders. The results show that the power efficiency of BP decoders is improved by about 3 times

Easily decoded error-correcting codes and techniques for their generation

Imperial Users onl

Error control techniques for satellite and space communications

Shannon's capacity bound shows that coding can achieve large reductions in the required signal to noise ratio per information bit (E sub b/N sub 0 where E sub b is the energy per bit and (N sub 0)/2 is the double sided noise density) in comparison to uncoded schemes. For bandwidth efficiencies of 2 bit/sym or greater, these improvements were obtained through the use of Trellis Coded Modulation and Block Coded Modulation. A method of obtaining these high efficiencies using multidimensional Multiple Phase Shift Keying (MPSK) and Quadrature Amplitude Modulation (QAM) signal sets with trellis coding is described. These schemes have advantages in decoding speed, phase transparency, and coding gain in comparison to other trellis coding schemes. Finally, a general parity check equation for rotationally invariant trellis codes is introduced from which non-linear codes for two dimensional MPSK and QAM signal sets are found. These codes are fully transparent to all rotations of the signal set

The Telecommunications and Data Acquisition Report

Tracking and ground-based navigation; communications, spacecraft-ground; station control and system technology; capabilities for new projects; networks consolidation program; and network sustaining are described

System Development and VLSI Implementation of High Throughput and Hardware Efficient Polar Code Decoder

Polar code is the first channel code which is provable to achieve the Shannon capacity. Additionally, it has a very good performance in terms of low error floor. All these merits make it a potential candidate for the future standard of wireless communication or storage system. Polar code is received increasing research interest these years. However, the hardware implementation of hardware decoder still has not meet the expectation of practical applications, no matter from neither throughput aspect nor hardware efficient aspect. This dissertation presents several system development approaches and hardware structures for three widely known decoding algorithms. These algorithms are successive cancellation (SC), list successive cancellation (LSC) and belief propagation (BP). All the efforts are in order to maximize the throughput meanwhile minimize the hardware cost. Throughput centric successive cancellation (TCSC) decoder is proposed for SC decoding. By introducing the concept of constituent code, the decoding latency is significantly reduced with a negligible decoding performance loss. However, the specifically designed computation unites dramatically increase the hardware cost, and how to handle the conventional polar code sets and constituent codes sets makes the hardware implementation more complicated. By exploiting the natural property of conventional SC decoder, datapaths for decoding constituent codes are compatibly built via computation units sharing technique. This approach does not incur additional hardware cost expect some multiplexer logic, but can significantly increase the decoding throughput. Other techniques such as pre-computing and gate-level optimization are used as well in order to further increase the decoding throughput. A specific designed partial sum generator (PSG) is also investigated in this dissertation. This PSG is hardware efficient and timing compatible with proposed TCSC decoder. Additionally, a polar code construction scheme with constituent codes optimization is also presents. This construction scheme aims to reduce the constituent codes based SC decoding latency. Results show that, compared with the state-of-art decoder, TCSC can achieve at least 60% latency reduction for the codes with length n = 1024. By using Nangate FreePDK 45nm process, TCSC decoder can reach throughput up to 5.81 Gbps and 2.01 Gbps for (1024, 870) and (1024, 512) polar code, respectively. Besides, with the proposed construction scheme, the TCSC decoder generally is able to further achieve at least around 20% latency deduction with an negligible gain loss. Overlapped List Successive Cancellation (OLSC) is proposed for LSC decoding as a design approach. LSC decoding has a better performance than LS decoding at the cost of hardware consumption. With such approach, the l (l > 1) instances of successive cancellation (SC) decoder for LSC with list size l can be cut down to only one. This results in a dramatic reduction of the hardware complexity without any decoding performance loss. Meanwhile, approaches to reduce the latency associated with the pipeline scheme are also investigated. Simulation results show that with proposed design approach the hardware efficiency is increased significantly over the recently proposed LSC decoders. Express Journey Belief Propagation (XJBP) is proposed for BP decoding. This idea origins from extending the constituent codes concept from SC to BP decoding. Express journey refers to the datapath of specific constituent codes in the factor graph, which accelerates the belief information propagation speed. The XJBP decoder is able to achieve 40.6% computational complexity reduction with the conventional BP decoding. This enables an energy efficient hardware implementation. In summary, all the efforts to optimize the polar code decoder are presented in this dissertation, supported by the careful analysis, precise description, extensively numerical simulations, thoughtful discussion and RTL implementation on VLSI design platforms

System Development and VLSI Implementation of High Throughput and Hardware Efficient Polar Code Decoder

Polar code is the first channel code which is provable to achieve the Shannon capacity. Additionally, it has a very good performance in terms of low error floor. All these merits make it a potential candidate for the future standard of wireless communication or storage system. Polar code is received increasing research interest these years. However, the hardware implementation of hardware decoder still has not meet the expectation of practical applications, no matter from neither throughput aspect nor hardware efficient aspect. This dissertation presents several system development approaches and hardware structures for three widely known decoding algorithms. These algorithms are successive cancellation (SC), list successive cancellation (LSC) and belief propagation (BP). All the efforts are in order to maximize the throughput meanwhile minimize the hardware cost. Throughput centric successive cancellation (TCSC) decoder is proposed for SC decoding. By introducing the concept of constituent code, the decoding latency is significantly reduced with a negligible decoding performance loss. However, the specifically designed computation unites dramatically increase the hardware cost, and how to handle the conventional polar code sets and constituent codes sets makes the hardware implementation more complicated. By exploiting the natural property of conventional SC decoder, datapaths for decoding constituent codes are compatibly built via computation units sharing technique. This approach does not incur additional hardware cost expect some multiplexer logic, but can significantly increase the decoding throughput. Other techniques such as pre-computing and gate-level optimization are used as well in order to further increase the decoding throughput. A specific designed partial sum generator (PSG) is also investigated in this dissertation. This PSG is hardware efficient and timing compatible with proposed TCSC decoder. Additionally, a polar code construction scheme with constituent codes optimization is also presents. This construction scheme aims to reduce the constituent codes based SC decoding latency. Results show that, compared with the state-of-art decoder, TCSC can achieve at least 60% latency reduction for the codes with length n = 1024. By using Nangate FreePDK 45nm process, TCSC decoder can reach throughput up to 5.81 Gbps and 2.01 Gbps for (1024, 870) and (1024, 512) polar code, respectively. Besides, with the proposed construction scheme, the TCSC decoder generally is able to further achieve at least around 20% latency deduction with an negligible gain loss. Overlapped List Successive Cancellation (OLSC) is proposed for LSC decoding as a design approach. LSC decoding has a better performance than LS decoding at the cost of hardware consumption. With such approach, the l (l > 1) instances of successive cancellation (SC) decoder for LSC with list size l can be cut down to only one. This results in a dramatic reduction of the hardware complexity without any decoding performance loss. Meanwhile, approaches to reduce the latency associated with the pipeline scheme are also investigated. Simulation results show that with proposed design approach the hardware efficiency is increased significantly over the recently proposed LSC decoders. Express Journey Belief Propagation (XJBP) is proposed for BP decoding. This idea origins from extending the constituent codes concept from SC to BP decoding. Express journey refers to the datapath of specific constituent codes in the factor graph, which accelerates the belief information propagation speed. The XJBP decoder is able to achieve 40.6% computational complexity reduction with the conventional BP decoding. This enables an energy efficient hardware implementation. In summary, all the efforts to optimize the polar code decoder are presented in this dissertation, supported by the careful analysis, precise description, extensively numerical simulations, thoughtful discussion and RTL implementation on VLSI design platforms

A STUDY OF ERASURE CORRECTING CODES

This work focus on erasure codes, particularly those that of high performance, and the related decoding algorithms, especially with low computational complexity. The work is composed of different pieces, but the main components are developed within the following two main themes. Ideas of message passing are applied to solve the erasures after the transmission. Efficient matrix-representation of the belief propagation (BP) decoding algorithm on the BEG is introduced as the recovery algorithm. Gallager's bit-flipping algorithm are further developed into the guess and multi-guess algorithms especially for the application to recover the unsolved erasures after the recovery algorithm. A novel maximum-likelihood decoding algorithm, the In-place algorithm, is proposed with a reduced computational complexity. A further study on the marginal number of correctable erasures by the In-place algoritinn determines a lower bound of the average number of correctable erasures. Following the spirit in search of the most likable codeword based on the received vector, we propose a new branch-evaluation- search-on-the-code-tree (BESOT) algorithm, which is powerful enough to approach the ML performance for all linear block codes. To maximise the recovery capability of the In-place algorithm in network transmissions, we propose the product packetisation structure to reconcile the computational complexity of the In-place algorithm. Combined with the proposed product packetisation structure, the computational complexity is less than the quadratic complexity bound. We then extend this to application of the Rayleigh fading channel to solve the errors and erasures. By concatenating an outer code, such as BCH codes, the product-packetised RS codes have the performance of the hard-decision In-place algorithm significantly better than that of the soft-decision iterative algorithms on optimally designed LDPC codes