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—The average weight distribution of a regular low-density parity-check (LDPC) code ensemble over a finite field is thoroughly analyzed. In particular, a precise asymptotic approximation of the average weight distribution is derived for the small-weight case, and a series of fundamental qualitative properties of the asymptotic growth rate of the average… (More)

The random matrix uniformly distributed over the set of all m-by-n matrices over a finite field plays an important role in many branches of information theory. In this paper a generalization of this random matrix, called k-good random matrices, is studied. It is shown that a k-good random m-by-n matrix with a distribution of minimum support size is… (More)

— The problem of finding good linear codes for joint source-channel coding (JSCC) is investigated in this paper. By the code-spectrum approach, it has been proved in the authors' previous paper that a good linear code for the authors' JSCC scheme is a code with a good joint spectrum, so the main task in this paper is to construct linear codes with good… (More)

Linear codes with good joint spectra are good candidates for lossless joint source-channel coding (JSCC). However, in spite of their existence, it is still unknown how to construct them in practice. This paper is devoted to the construction of such codes. In particular, two families of linear codes are presented and proved to have good joint spectra. The… (More)

This work studies the problem of separate random number generation from correlated general sources with side information at the tester under the criterion of statistical distance. Tight one-shot lower and upper performance bounds are obtained using the random-bin approach. A refined analysis is further performed for two important random-bin maps. One is the… (More)

An information-spectrum approach is applied to solve the multiterminal source coding problem for correlated general sources, where sources may be nonstationary and/or nonergodic, and the distortion measure is arbitrary and may be nonadditive. A general formula for the rate-distortion region of the multiterminal source coding problem with the maximum… (More)

A general lossless joint source-channel coding scheme based on linear codes is proposed and then analyzed in this paper. It is shown that a linear code with good joint spectrum can be used to establish limit-approaching joint source-channel coding schemes for arbitrary sources and channels, where the joint spectrum of the code is a generalization of the… (More)

—A general approach is established for deriving one-shot performance bounds for information-theoretic problems on general alphabets beyond countable alphabets. It is mainly based on the quantization idea and a novel form of " likelihood ratio ". As an example, one-shot lower and upper bounds for random number generation from correlated sources on general… (More)