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We consider coset LDPC codes over GF(q), designed for use over arbitrary channels (particularly nonbinary and asymmetric channels). We show that the random selection of the nonzero elements of the GF(q) parity-check matrix induces a permutation-invariance property on the densities of the messages produced by the decoder. We use this property to show that under a Gaussian approximation, the entire...
Maximum rank distance codes are the equivalent in rank-metric of Reed-Solomon codes whose subcodes have been widely studied. In this paper we characterize subspace subcodes of MRD codes and we show that it is possible to construct efficient polynomial-time encoding-decoding procedures for these subcodes. In a second part we show that subfield subcodes of maximum rank distance codes can be represented...
In a recent paper, Yang et al. presented the class of extended irregular repeat-accumulate (eIRA) codes which are efficiently encodable LDPC codes possessing very low error-rate floors and are appropriate for code rates 1/2 or greater. While efficiently encodable, the left-most (n-k)-by-k submatrix of an eIRA code parity-check matrix is random in nature, making efficient decoder implementation problematic...
The cutoff rate R0(W) of a discrete memoryless channel (DMC) W is often used as a figure of merit, alongside the channel capacity C(W). Given a channel W consisting of two possibly correlated subchannels W1, W2, the capacity function always satisfies C(W1) + C(W2) les C(W), while there are examples for which R0(W1) + R0(W 2) > R0(W). This fact that the cutoff rate can be "created" by...
A generalised Hadamard transform for multiphase or multilevel signals is introduced, which includes the Fourier, generalised, discrete Fourier, Walsh-Hadamard and reverse jacket transforms. The jacket construction is formalised and shown to admit a tensor product decomposition. Primary matrices under this decomposition are identified. New examples of primary jacket matrices of orders 8 and 12 are...
We construct some geometrically dense matrix lattices with good minimum determinants for 4 transmit antenna MISO applications. The construction is based on the theory of rings of algebraic integers and related subrings of the Hamiltonian quaternions. Simulations in a quasi-static Rayleigh fading channel show that our dense quaternionic constructions outperform the earlier rectangular lattices as well...
Based on the normalized diversity product criterion of space-time code designs, we present two optimal 2times2 diagonal algebraic space-time block codes based on field extensions. We then present an ntimesn diagonal space-time code design method directly from 2n real integers based on extended complex lattices. We also present a non-tight upper bound for normalized diversity products of 2times2 diagonal...
We obtain a precise information theoretic upper bound on the rate per communication pair in a one-dimensional ad hoc wireless network. The key ingredient of our result is a uniform upper bound on the determinant of the Cauchy matrix
An ensemble of LDPC convolutional codes with parity-check matrices composed of permutation matrices is considered. The convergence of the iterative belief propagation based decoder for terminated convolutional codes in the ensemble is analyzed for binary-input output-symmetric memoryless channels using density evolution techniques. We observe that the structured irregularity in the Tanner graph of...
This paper describes the synthesis of matrices with good correlation, from cyclic shifts of pseudonoise columns. Optimum matrices result whenever the shift sequence satisfies the constant difference property. Known shift sequences with the constant (or almost constant) difference property are: quadratic (polynomial) and reciprocal shift modulo prime, exponential shift, Legendre shift, Zech logarithm...
This paper shows that several attractive classes of quasi-cyclic (QC) low-density parity-check (LDPC) codes can be obtained from affine planes over finite fields. One class of these consists of duals of one-generator QC codes. Here, for codes contained in this class, the exact minimum-distance and a lower bound on the multiplicity of the minimum-weight codewords are presented. It is shown that the...
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