Algebraic codes for Slepian-Wolf code design

Practical constructions of lossless distributed source codes (for the Slepian-Wolf problem) have been the subject of much investigation in the past decade. In particular, near-capacity achieving code designs based on LDPC codes have been presented for the case of two binary sources, with a binary-symmetric correlation. However, constructing practical codes for the case of non-binary sources with arbitrary correlation remains by and large open. From a practical perspective it is also interesting to consider coding schemes whose performance remains robust to uncertainties in the joint distribution of the sources. In this work we propose the usage of Reed-Solomon (RS) codes for the asymmetric version of this problem. We show that algebraic soft-decision decoding of RS codes can be used effectively under certain correlation structures. In addition, RS codes offer natural rate adaptivity and performance that remains constant across a family of correlation structures with the same conditional entropy. The performance of RS codes is compared with dedicated and rate adaptive multistage LDPC codes (Varodayan et al. '06), where each LDPC code is used to compress the individual bit planes. Our simulations show that in classical Slepian-Wolf scenario, RS codes outperform both dedicated and rate-adaptive LDPC codes under $q$-ary symmetric correlation, and are better than rate-adaptive LDPC codes in the case of sparse correlation models, where the conditional distribution of the sources has only a few dominant entries. In a feedback scenario, the performance of RS codes is comparable with both designs of LDPC codes. Our simulations also demonstrate that the performance of RS codes in the presence of inaccuracies in the joint distribution of the sources is much better as compared to multistage LDPC codes.Comment: 5 pages, accepted by ISIT 201

Efficient Joint Network-Source Coding for Multiple Terminals with Side Information

Consider the problem of source coding in networks with multiple receiving terminals, each having access to some kind of side information. In this case, standard coding techniques are either prohibitively complex to decode, or require network-source coding separation, resulting in sub-optimal transmission rates. To alleviate this problem, we offer a joint network-source coding scheme based on matrix sparsification at the code design phase, which allows the terminals to use an efficient decoding procedure (syndrome decoding using LDPC), despite the network coding throughout the network. Via a novel relation between matrix sparsification and rate-distortion theory, we give lower and upper bounds on the best achievable sparsification performance. These bounds allow us to analyze our scheme, and, in particular, show that in the limit where all receivers have comparable side information (in terms of conditional entropy), or, equivalently, have weak side information, a vanishing density can be achieved. As a result, efficient decoding is possible at all terminals simultaneously. Simulation results motivate the use of this scheme at non-limiting rates as well

Algebraic approaches to distributed compression and network error correction

Algebraic codes have been studied for decades and have extensive applications in communication and storage systems. In this dissertation, we propose several novel algebraic approaches for distributed compression and network error protection problems. In the first part of this dissertation we propose the usage of Reed-Solomon codes for compression of two nonbinary sources. Reed-Solomon codes are easy to design and offer natural rate adaptivity. We compare their performance with multistage LDPC codes and show that algebraic soft-decision decoding of Reed-Solomon codes can be used effectively under certain correlation structures. As part of this work we have proposed a method that adapts list decoding for the problem of syndrome decoding. This in turn allows us to arrive at improved methods for the compression of multicast network coding vectors. When more than two correlated sources are present, we consider a correlation model given by a system of linear equations. We propose a transformation of correlation model and a way to determine proper decoding schedules. Our scheme allows us to exploit more correlations than those in the previous work and the simulation results confirm its better performance. In the second part of this dissertation we study the network protection problem in the presence of adversarial errors and failures. In particular, we consider the usage of network coding for the problem of simultaneous protection of multiple unicast connections, under certain restrictions on the network topology. The proposed scheme allows the sharing of protection resources among multiple unicast connections. Simulations show that our proposed scheme saves network resources by 4%-15% compared to the protection scheme based on simple repetition codes, especially when the number of primary paths is large or the costs for establishing primary paths are high

Studies on Physical Layer Cryptography in Free Space Optical Communications

早大学位記番号:新7517早稲田大

Bridging Hamming Distance Spectrum with Coset Cardinality Spectrum for Overlapped Arithmetic Codes

Overlapped arithmetic codes, featured by overlapped intervals, are a variant of arithmetic codes that can be used to implement Slepian-Wolf coding. To analyze overlapped arithmetic codes, we have proposed two theoretical tools: Coset Cardinality Spectrum (CCS) and Hamming Distance Spectrum (HDS). The former describes how source space is partitioned into cosets (equally or unequally), and the latter describes how codewords are structured within each coset (densely or sparsely). However, until now, these two tools are almost parallel to each other, and it seems that there is no intersection between them. The main contribution of this paper is bridging HDS with CCS through a rigorous mathematical proof. Specifically, HDS can be quickly and accurately calculated with CCS in some cases. All theoretical analyses are perfectly verified by simulation results

Algebraic Codes for Slepian-Wolf code design

Practical constructions of lossless distributed source codes (for the Slepian-Wolf problem) have been the subject of much investigation in the past decade. In particular, near-capacity achieving code designs based on LDPC codes have been presented for the case of two binary sources, with a binary-symmetric correlation. However, constructing practical codes for the case of non-binary sources with arbitrary correlation remains by and large open. From a practical perspective it is also interesting to consider coding schemes whose performance remains robust to uncertainties in the joint distribution of the sources. In this work we propose the usage of Reed-Solomon (RS) codes for the asymmetric version of this problem. We show that algebraic soft-decision decoding of RS codes can be used effectively under certain correlation structures. In addition, RS codes offer natural rate adaptivity and performance that remains constant across a family of correlation structures with the same conditional entropy. The performance of RS codes is compared with dedicated and rate adaptive multistage LDPC codes (Varodayan et al. '06), where each LDPC code is used to compress the individual bit planes. Our simulations show that in classical Slepian-Wolf scenario, RS codes outperform both dedicated and rate-adaptive LDPC codes under q-ary symmetric correlation, and are better than rate-adaptive LDPC codes in the case of sparse correlation models, where the conditional distribution of the sources has only a few dominant entries. In a feedback scenario, the performance of RS codes is comparable with both designs of LDPC codes. Our simulations also demonstrate that the performance of RS codes in the presence of inaccuracies in the joint distribution of the sources is much better as compared to multistage LDPC codes.This is a manuscript of a proceeding from the IEEE International Symposium on Information Theory (2011): 1861, doi:10.1109/ISIT.2011.6033873. Posted with permission.</p