Boris D. Kudryashov

Method and apparatus for speech compression using multi-mode code excited linear predictive coding

An apparatus and method of coding speech. The apparatus includes a first circuit being coupled to receive a first signal, the first signal corresponds to the speech signal. The first circuit is for generating a first set of parameters corresponding to the first frame. The apparatus includes a second circuit, being coupled to receive a second signal and the first set of parameters, the second signal corresponding to the speech signal, and the second circuit is for generating a third signal. The apparatus further includes a pulse train analyzer, being coupled to the second circuit, for generating a third match value, a third set of parameters, and a third excitation value. The apparatus further including a fourth circuit, being coupled to the second circuit, for generating a fourth match value, a fourth set of parameters, and a fourth excitation value. The apparatus further including a fifth circuit, being coupled to the third circuit and the fourth circuit, for selecting a mode corresponding to a match value. The apparatus further including a sixth circuit, being coupled to the fifth circuit, for selecting a selected set of parameters and a selected excitation corresponding to the mode. The apparatus further including a seventh circuit, being coupled to the first circuit and the sixth circuit, for generating an encoded signal responsive to the selected set of parameters and the mode.

Rational rate punctured convolutional codes for soft-decision Viterbi decoding

We present rational rate k/n punctured convolutional codes (n up to 8, k=1, /spl middot//spl middot//spl middot/, n-1, and constraint length /spl nu/ up to 8) with good performance. Many of these codes improve the free distance and (or) weight spectra over previously reported codes with the same parameters. The tabulated codes are found by an exhaustive (or a random) search.

A BEAST for prowling in trees

When searching for convolutional codes and tailbiting codes of high complexity it is of vital importance to use fast algorithms for computing their weight spectra, which corresponds to finding low-weight paths in their code trellises. This can be efficiently done by a combined search in both forward and backward code trees. A bidirectional efficient algorithm for searching such code trees (BEAST) is presented. For large encoder memories, it is shown that BEAST is significantly more efficient than comparable algorithms. BEAST made it possible to find new convolutional and tailbiting codes that have larger free (minimum) distances than the previously best known codes with the same parameters. Tables of such codes are presented.

Searching for Voltage Graph-Based LDPC Tailbiting Codes With Large Girth

The relation between parity-check matrices of quasi-cyclic (QC) low-density parity-check (LDPC) codes and biadjacency matrices of bipartite graphs supports searching for powerful LDPC block codes. Using the principle of tailbiting, compact representations of bipartite graphs based on convolutional codes can be found. Bounds on the girth and the minimum distance of LDPC block codes constructed in such a way are discussed. Algorithms for searching iteratively for LDPC block codes with large girth and for determining their minimum distance are presented. Constructions based on all-one matrices, Steiner Triple Systems, and QC block codes are introduced. Finally, new QC regular LDPC block codes with girth up to 24 are given.

Tailbiting codes: bounds and search results

Tailbiting trellis representations of linear block codes with an arbitrary sectionalization of the time axis are studied. The notations of regular and irregular tailbiting codes are introduced and their maximal state complexities are lower-bounded. The asymptotic behavior of the derived bound is investigated. Furthermore, for regular tailbiting codes the product state complexity is lower-bounded. Tables of new tailbiting trellis representations of linear block codes of rates 1/2, 1/3, and 1/4 are presented. Almost all found trellises are optimal in the sense of the new bound on the state complexity and for most codes with nonoptimal trellises there exist time-varying trellises which are optimal. Five of our newly found tailbiting codes are better than the previously known linear codes with the same parameters. Four of them are also superior to any previously known nonlinear code with the same parameters. Also, more than 40 other quasi-cyclic codes have been found that improve the parameter set of previously known quasi-cyclic codes.

BEAST decoding for block codes

BEAST is a Bidirectional Efficient Algorithm for Searching code Trees. In this paper, it is used for decoding block codes over a binary-input memoryless channel. If no constraints are imposed on the decoding complexity (in terms of the number of visited nodes during the search), BEAST performs maximum-likelihood (ML) decoding. At the cost of a negligible performance degradation, BEAST can be constrained to perform almost-ML decoding with significantly reduced complexity. The benchmark for the complexity assessment is the number of nodes visited by the Viterbi algorithm operating on the minimal trellis of the code. The decoding complexity depends on the trellis structure of a given code, which is illustrated by three different forms of the generator matrix for the (24, 12, 8) Golay code. Simulation results that assess the error-rate performance and the decoding complexity of BEAST are presented for two longer codes.

Searching for high-rate convolutional codes via binary syndrome trellises

Rate R = (c-1)/c convolutional codes of constraint length ν can be represented by conventional syndrome trellises with a state complexity of s = ν or by binary syndrome trellises with a state complexity of s = ν or s = ν + 1, which corresponds to at most 2s states at each trellis level. It is shown that if the parity-check polynomials fulfill certain conditions, there exist binary syndrome trellises with optimum state complexity s = ν. The BEAST is modified to handle parity-check matrices and used to generate code tables for optimum free distance rate R = (c - 1)=c, c = 3; 4; 5, convolutional codes for conventional syndrome trellises and binary syndrome trellises with optimum state complexity. These results show that the loss in distance properties due to the optimum state complexity restriction for binary trellises is typically negligible.

Searching for Binary and Nonbinary Block and Convolutional LDPC Codes

A unified approach to search for and optimize codes determined by their sparse parity-check matrices is presented. Replacing the nonzero elements of a binary parity-check matrix (the base or parent matrix) either by circulants or by companion matrices of elements from a finite field GF(2m), we obtain quasi-cyclic low-density parity-check (LDPC) block codes and binary images of nonbinary LDPC block codes, respectively. By substituting monomials of a formal variable D, we obtain the polynomial description of an LDPC convolutional code. A set of performance measures applicable to different classes of LDPC codes is considered, and a greedy algorithm for code performance optimization is presented. The heart of the new optimization algorithm is a fast procedure for searching for LDPC codes with large girth of their Tanner graphs. For a few classes of LDPC codes, examples of codes combining good error-correcting performance with compact representation are obtained. In particular, we present optimized convolutional LDPC codes and conclude that the LDPC block codes are still superior to their convolutional counterparts if both decoding complexity and coding delay are considered. Moreover, a specific channel model can easily be embedded into the optimization loop. Thereby, the code can be optimized for a specific channel. The efficiency of such an optimization is demonstrated via an example of faster than Nyquist (FTN) signaling using LDPC codes. The FTN strategy combined with a rate R = 1/2 LDPC code of length 64800 optimized for effective data rate R = 3/4 gains more than 0.5 dB compared with the standard LDPC codes of the same rate and length. The obtained gain corresponds to transmission at the capacity of the binary input additive white Gaussian noise channel. In most numerical examples, we consider codes with bidiagonal structure of the parity-check matrix. This restriction preserves low encoding complexity and allows fair comparison with codes selected for communication standards.

Asymptotically Good Woven Codes with Fixed Constituent Convolutional Codes

A construction of woven graph codes based on constituent convolutional codes is studied. It is shown that within the random ensemble of such codes there exist asymptotically good codes with short fixed constituent codes. An example of a rate R = 1/3 woven graph code with free distance equal to 32 based on rate Rc = 2/3 constituent convolutional codes with overall constraint length 5 is given.

Graph-based convolutional and block LDPC codes

We consider regular block and convolutional LDPC codes determined by paritycheck matrices with rows of a fixed weight and columns of weight 2. Such codes can be described by graphs, and the minimum distance of a code coincides with the girth of the corresponding graph. We consider a description of such codes in the form of tail-biting convolutional codes. Long codes are constructed from short ones using the “voltage graph” method. On this way we construct new codes, find a compact description for many known optimal codes, and thus simplify the coding for such codes. We obtain an asymptotic lower bound on the girth of the corresponding graphs. We also present tables of codes.