Author: Ilan SutskoverPublisher:
ISBN:
Category :
Languages : en
Pages : 26
Book Description
Iterative Decoding of Low-density Parity Check Codes Over Compound Channels
Author: Ilan SutskoverIterative Decoding Beyond Belief Propagation of Low-Density Parity-Check Codes
Author: Shiva Kumar PlanjeryPublisher:
ISBN:
Category :
Languages : en
Pages : 138
Book Description
The recent renaissance of one particular class of error-correcting codes called low-density parity-check (LDPC) codes has revolutionized the area of communications leading to the so-called field of modern coding theory. At the heart of this theory lies the fact that LDPC codes can be efficiently decoded by an iterative inference algorithm known as belief propagation (BP) which operates on a graphical model of a code. With BP decoding, LDPC codes are able to achieve an exceptionally good error-rate performance as they can asymptotically approach Shannon's capacity. However, LDPC codes under BP decoding suffer from the error floor phenomenon, an abrupt degradation in the error-rate performance of the code in the high signal-to-noise ratio region, which prevents the decoder from achieving very low error-rates. It arises mainly due to the sub-optimality of BP decoding on finite-length loopy graphs. Moreover, the effects of finite precision that stem from hardware realizations of BP decoding can further worsen the error floor phenomenon. Over the past few years, the error floor problem has emerged as one of the most important problems in coding theory with applications now requiring very low error rates and faster processing speeds. Further, addressing the error floor problem while taking finite precision into account in the decoder design has remained a challenge. In this dissertation, we introduce a new paradigm for finite precision iterative decoding of LDPC codes over the binary symmetric channel (BSC). These novel decoders, referred to as finite alphabet iterative decoders (FAIDs), are capable of surpassing the BP in the error floor region at a much lower complexity and memory usage than BP without any compromise in decoding latency. The messages propagated by FAIDs are not quantized probabilities or log-likelihoods, and the variable node update functions do not mimic the BP decoder. Rather, the update functions are simple maps designed to ensure a higher guaranteed error correction capability which improves the error floor performance. We provide a methodology for the design of FAIDs on column-weight-three codes. Using this methodology, we design 3-bit precision FAIDs that can surpass the BP (floating-point) in the error floor region on several column-weight-three codes of practical interest. While the proposed FAIDs are able to outperform the BP decoder with low precision, the analysis of FAIDs still proves to be a difficult issue. Furthermore, their achievable guaranteed error correction capability is still far from what is achievable by the optimal maximum-likelihood (ML) decoding. In order to address these two issues, we propose another novel class of decoders called decimation-enhanced FAIDs for LDPC codes. For this class of decoders, the technique of decimation is incorporated into the variable node update function of FAIDs. Decimation, which involves fixing certain bits of the code to a particular value during decoding, can significantly reduce the number of iterations required to correct a fixed number of errors while maintaining the good performance of a FAID, thereby making such decoders more amenable to analysis. We illustrate this for 3-bit precision FAIDs on column-weight-three codes and provide insights into the analysis of such decoders. We also show how decimation can be used adaptively to further enhance the guaranteed error correction capability of FAIDs that are already good on a given code. The new adaptive decimation scheme proposed has marginally added complexity but can significantly increase the slope of the error floor in the error-rate performance of a particular FAID. On certain high-rate column-weight-three codes of practical interest, we show that adaptive decimation-enhanced FAIDs can achieve a guaranteed error-correction capability that is close to the theoretical limit achieved by ML decoding.
Capacity-approaching Coding Schemes Based on Low-density Parity-check Codes
Author: Jilei HouApplications of Low Density Parity Check Codes for Wiretap Channels and Congestion Localization in Networks
Author: Souvik DihidarPublisher:
ISBN: 9781109870688
Category :
Languages : en
Pages : 98
Book Description
In Chapter 1, we give an introduction to some conventional Cryptographic protocols. Chapter 2 discusses the BB84 protocol in Quantum key Cryptography. The problem of constructing codes for wiretap channels is considered in Chapter 3. Chapter 4 deals with the problem of congestion localization in networks. Chapter 5 summarizes our work in the problem of localizing link failures in networks.
Low-density Parity-check Codes and Iterative Decoding Algorithms for Input-constrained Channels and Channels with Memory
Author: Wongkot VijacksungsithiPublisher:
ISBN:
Category :
Languages : en
Pages : 454
Book Description
Construction, Decoding and Application of Low-density Parity-check Codes
Author: Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
In this doctoral dissertation, a construction of binary and nonbinary low-density parity-check (LDPC) codes with quasi-cyclic (QC) structures is presented. First, a general construction of RC-constrained arrays of circulant permutation matrices is introduced, then a specific construction method based on additive subgroups of finite fields is presented. Array masking is also proposed to improve the waterfall-region performance of the QC-LDPC codes, where an algorithm to construct irregular masking matrices is introduced for low error floors. Simulations show that all the above-constructed codes perform well on AWGN channels. Also presented in this dissertation is an LDPC-based error control scheme in a multicast network where a well-known network coding is used. With this scheme, error performance of the system can be improved and equal error protection can be achieved. Finally, an iterative decoding with backtracking is presented. This decoding algorithm greatly lowers the error floors of many regular and irregular LDPC codes of different constructions, and in many cases can push the error floors down to a level limited by the codes' minimum distances. Performance analysis and error floor estimation for the proposed algorithm are also performed.
Generalized Low-Density Parity-Check Codes
Author: Sherif ElsanadilyPublisher:
ISBN:
Category : Computers
Languages : en
Pages : 0
Book Description
Scientists have competed to find codes that can be decoded with optimal decoding algorithms. Generalized LDPC codes were found to compare well with such codes. LDPC codes are well treated with both types of decoding; HDD and SDD. On the other hand GLDPC codes iterative decoding, on both AWGN and BSC channels, was not sufficiently investigated in the literature. This chapter first describes its construction then discusses its iterative decoding algorithms on both channels so far. The SISO decoders, of GLDPC component codes, show excellent error performance with moderate and high code rate. However, the complexities of such decoding algorithms are very high. When the HDD BF algorithm presented to LDPC for its simplicity and speed, it was far from the BSC capacity. Therefore involving LDPC codes in optical systems using such algorithms is a wrong choice. GLDPC codes can be introduced as a good alternative of LDPC codes as their performance under BF algorithm can be improved and they would then be a competitive choice for optical communications. This chapter will discuss the iterative HDD algorithms that improve decoding error performance of GLDPC codes. SDD algorithms that maintain the performance but lowering decoding simplicity are also described.
Iterative Decoding of Low Density Parity Check Codes and Turbo Codes
Author: Juntan ZhangPublisher:
ISBN:
Category : Error-correcting codes (Information theory)
Languages : en
Pages : 288
Book Description
Low-density Parity-check Codes with Reduced Decoding Complexity
Author: Benjamin SmithPublisher:
ISBN: 9780494273289
Category :
Languages : en
Pages : 156
Book Description
This thesis presents new methods to design low-density parity-check (LDPC) codes with reduced decoding complexity. An accurate measure of iterative decoding complexity is introduced. In conjunction with extrinsic information transfer (EXIT) chart analysis, an efficient optimization program is developed, for which the complexity measure is the objective function, and its utility is demonstrated by designing LDPC codes with reduced decoding complexity. For long block lengths, codes designed by these methods match the performance of threshold-optimized codes, but reduce the decoding complexity by approximately one-third. The performance of LDPC codes is investigated when the decoder is constrained to perform a sub-optimal decoding algorithm. Due to their practical relevance, the focus is on the design of LDPC codes for quantized min-sum decoders. For such a decoder, codes designed for the sum-product algorithm are sub-optimal, and an alternative design strategy is proposed, resulting in gains of more than 0.5 dB.
Low Density Parity Check Code for Next Generation Communication System
Author: Mayank ArdeshanaPublisher: LAP Lambert Academic Publishing
ISBN: 9783845420417
Category :
Languages : en
Pages : 72
Book Description
Channel coding provides the means of patterning signals so as to reduce their energy or bandwidth consumption for a given error performance. LDPC codes have been shown to have good error correcting performance which enables efficient and reliable communication. LDPC codes have linear decoding complexity but performance approaching close to shannon capacity with iterative probabilistic decoding algorithm. In this dissertation, the performance of different error correcting code such as convolution, Reed Solomon(RS), hamming, block code are evaluated based on different parameters like code rate, bit error rate (BER), Eb/No, complexity, coding gain and compare with LDPC code. In general, message passing algorithm and the sum-product algorithm are used to decode the message. We showed that logarithmic sum-product algorithm with long block length code reduces multiplication to addition by introducing logarithmic likelihood ratio so that it achieves the highest BER performance among all the decoding algorithms. The astonishing performance combined with proposed modified MS decoding algorithm make these codes very attractive for the next generations digital broadcasting system (ABS - S).