Wireless Communications

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Convex Analysisの二,三の進展について

This paper investigates the maximal channel coding rate achievable at a given blocklength and error probability. For general classes of channels new achievability and converse bounds are given, which are tighter than existing bounds for wide ranges of parameters of interest, and lead to tight approximations of the maximal achievable rate for blocklengths n as short as 100. It is also shown analytically that the maximal rate achievable with error probability ? isclosely approximated by C - ?(V/n) Q-1(?) where C is the capacity, V is a characteristic of the channel referred to as channel dispersion , and Q is the complementary Gaussian cumulative distribution function.

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Channel Coding Rate in the Finite Blocklength Regime

Information Theory and Reliable Communication

Zehavi (1992) showed that the performance of coded modulation over a Rayleigh fading channel can be improved by bit-wise interleaving the encoder output and by using an appropriate soft-decision metric as an input to a Viterbi decoder. The goal of this paper is to present in a comprehensive fashion the theory underlying bit-interleaved coded modulation, to provide tools for evaluating its performance, and to give guidelines for its design.

/pdf/bit-interleaved-coded-modulation-2ld6uk564f.pdf

Bit-Interleaved Coded Modulation

In this paper, we are concerned with the finite-length analysis of low-density parity-check (LDPC) codes when used over the binary erasure channel (BEC). The main result is an expression for the exact average bit and block erasure probability for a given regular ensemble of LDPC codes when decoded iteratively. We also give expressions for upper bounds on the average bit and block erasure probability for regular LDPC ensembles and the standard random ensemble under maximum-likelihood (ML) decoding. Finally, we present what we consider to be the most important open problems in this area.

/pdf/finite-length-analysis-of-low-density-parity-check-codes-on-4jld71f17q.pdf

Finite-length analysis of low-density parity-check codes on the binary erasure channel

The mismatch capacity of a channel is the highest rate at which reliable communication is possible over the channel with a given (possibly suboptimal) decoding rule. This quantity has been studied extensively for single-letter decoding rules over discrete memoryless channels (DMCs). Here we extend the study to memoryless channels with general alphabets and to channels with memory with possibly non-single-letter decoding rules. We also study the wide-band limit, and, in particular, the mismatch capacity per unit cost, and the achievable rates on an additive-noise spread-spectrum system with single-letter decoding and binary signaling.

/pdf/mismatched-decoding-revisited-general-alphabets-channels-46a1y3izit.pdf

Mismatched decoding revisited: general alphabets, channels with memory, and the wide-band limit

Burnashev in 1976 gave an exact expression for the reliability function of a discrete memoryless channel (DMC) with noiseless feedback. A coding scheme that achieves this exponent needs, in general, to know the statistics of the channel. Suppose now that the coding scheme is designed knowing only that the channel belongs to a family Q of DMCs. Is there a coding scheme with noiseless feedback that achieves Burnashev's exponent uniformly over Q at a nontrivial rate? We answer the question in the affirmative for two families of channels (binary symmetric, and Z). For these families we show that, for any given fraction, there is a feedback coding strategy such that for any member of the family: i) guarantees this fraction of its capacity as rate, and ii) guarantees the corresponding Burnashev's exponent. Therefore, for these families, in terms of delay and error probability, the knowledge of the channel becomes asymptotically irrelevant in feedback code design: there are blind schemes that perform as well as the best coding scheme designed with the foreknowledge of the channel under use. However, a converse result shows that, in general, even for families that consist of only two channels, such blind schemes do not exist.

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Variable length coding over an unknown channel

Several models of wide-band broadcast communication scenarios are studied with an emphasis on conditions under which, as the bandwidth tends to infinity, time sharing is asymptotically optimal. The models include the Gaussian channel, the Poisson channel, the "very noisy" channel, and the average-power limited fading channel. Only stochastically degraded scenarios are studied.

On wide-band broadcast channels

A transmitter and receiver need to be designed to guarantee reliable communication on any channel belonging to a given family of finite-state channels defined over common finite input, output, and state alphabets. Both the transmitter and receiver are assumed to be ignorant of the channel over which transmission is carried out and also ignorant of its initial state. For this scenario we derive an expression for the highest achievable rate. As a special case we derive the compound channel capacity of a class of Gilbert-Elliott channels.

/pdf/the-compound-channel-capacity-of-a-class-of-finite-state-30fire7e3c.pdf

I.E. Telatar

Papers

Finite-length analysis of low-density parity-check codes on the binary erasure channel

Mismatched decoding revisited: general alphabets, channels with memory, and the wide-band limit

Variable length coding over an unknown channel

On wide-band broadcast channels

The compound channel capacity of a class of finite-state channels