Binary Linear Block Codes
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Decoding Error Probability of Binary Linear Block Codes
The performance of maximum-likelihood (ML) decoded binary linear block codes is addressed via the derivation of tightened upper bounds on their decoding error probability. The upper bounds on the block and bit error probabilities are valid for any memoryless, binary-input and outputsymmetric communication channel, and their effectiveness is exemplified for various ensembles of turbo-like codes ...
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The paper introduces new bounds on the asymptotic density of parity-check matrices and the achievable rates under ML decoding of binary linear block codes transmitted over memoryless binary-input output-symmetric channels. The lower bounds on the parity-check density are expressed in terms of the gap between the channel capacity and the rate of the codes for which reliable communication is achi...
متن کاملOn the Parity-Check Density and Achievable Rates of LDPC Codes for Memoryless Binary-Input Output-Symmetric Channels
We introduce upper bounds on the achievable rates of binary linear block codes under maximum-likelihood (ML) decoding, and lower bounds on the asymptotic density of their parity-check matrices; the transmission of these codes is assumed to take place over an arbitrary memoryless binary-input output-symmetric channel. The bounds hold for every sequence of binary linear block codes. The new bound...
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Unequal error protection (UEP) codes find applications in broadcast cbannels, as well as in otber digital communication systems, where messages bave ditTerent degrees of importance, In this correspon dence, binary linear UEP (LUEP) codes combined with a Gray mapped QPSK signal set are used to obtain new efficient QPSK block-modulation codes for unequal error protection. Several examples of QPS...
متن کاملBinary Linear Codes with Optimal Scaling and Quasi-Linear Complexity
We present the first family of binary codes that attains optimal scaling and quasi-linear complexity, at least for the binary erasure channel (BEC). In other words, for any fixed δ > 0, we provide codes that ensure reliable communication at rates within ε > 0 of the Shannon capacity with block length n = O(1/ε2+δ), construction complexity Θ(n), and encoding/decoding complexity Θ(n log n). Furth...
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We derive bounds on the asymptotic density of parity-check matrices and the achievable rates of binary linear block codes transmitted over memoryless binary-input output-symmetric (MBIOS) channels. The lower bounds on the density of arbitrary parity-check matrices are expressed in terms of the gap between the rate of these codes for which reliable communication is achievable and the channel cap...
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