Igor V. Zhilin

Generalized error-locating codes and minimization of redundancy for specified input and output error probabilities

Generalized error-locating codes are discussed. An algorithm for calculation of the upper bound of the probability of erroneous decoding for known code parameters and the input error probability is given. Based on this algorithm, an algorithm for selection of the code parameters for a specified design and input and output error probabilities is constructed. The lower bound of the probability of erroneous decoding is given. Examples of the dependence of the probability of erroneous decoding on the input error probability are given and the behavior of the obtained curves is explained.

High-rate codes for high-reliability data transmission

In this paper we propose to consider a generalized error-locating code (GEL-code) as a possible candidate for data transmission systems that require high code rates along with strict requirements on wrong decoding probability. GEL codes are one of a few that allow analytical computation of code error probability bounds and have practical construction method. The paper describes the construction of the GEL-code and the algorithms for encoding and decoding. It represents the upper and lower bounds on wrong decoding probability. It gives a method for constructing such GEL code (with the minimal redundancy) that guarantees that the probability of wrong decoding will be less than required one (for a given channel error probability). Numerical results for the upper and lower bounds for the various GEL-codes and the analysis of the energy gain for the different signal-code structures are given.

A Binary Block Concatenated Code Based on Two Convolutional Codes

Abstract We propose a concatenated code construction based on convolutional codes. We prove that minimum distance of this construction equals product of free distances of component codes.

Generalized concatenated code constructions with low overhead for optical channels and NAND-flash memory

We propose an error-correcting code construction that allows constructing codes with low overhead (less than 20%) and long length (10000 bits and more) that have good error correction performance and relatively low decoding complexity. A way of reducing decoder latency is proposed. Decoding complexity is estimated and compared to complexity of decoding BCH code.

LDPC code construction as a generalized concatenated code

We propose a construction of general concatenated code that uses low-density parity check codes as component codes. This construction itself can also be considered as low-density parity-check code and decoded using Belief Propagation algorithm. Performances of several decoders are compared; its shown that this code can be efficiently decoded by proposed soft decoding algorithm or combining BP and proposed algorithm.

On the code distance of a woven block code construction

In this paper we propose a woven block code construction based on two convolutional outer codes and a single inner code. We proved lower and upper bounds on this constructions code distance. The lower bound is shown to be higher than the product of the free distances of inner and outer constituent codes. Since this construction uses well-developed convolutional constituent codes, we believe that it would be competitive to turbo codes in the future mobile communication systems.

Generalized error-locating codes with component codes over the same alphabet

We consider generalized error locating (GEL) codes over the same alphabet for both component codes. We propose an algorithm for computing an upper bound on the decoding error probability under known input symbol error rate and code parameters. Is is used to construct an algorithm for selecting code parameters to maximize the code rate for a given construction and given input and output error probabilities. A lower bound on the decoding error probability is given. Examples of plots of decoding error probability versus input symbol error rate are given, and their behavior is explained.

On the Performance of Block Woven Codes Constructions with Row-Wise Permutations.

In this paper we propose a woven block code construction based on two convolutional codes. We also propose a soft-input decoder that allows this construction to have better error correction performance than the turbo codes with a conventional decoder. Computer simulation has showed a 0.1 dB energy gain relative to the LTE turbo code. Asymptotically the proposed code has distance greater than the product of free distances of component codes.

Vectorizing computations at decoding of nonbinary codes with small density of checks

A modification of the decoding q-ary Sum Product Algorithm (q-SPA) was proposed for the nonbinary codes with small check density based on the permutation matrices. The algorithm described has a vector realization and operates over the vectors defined on the field GF(q), rather than over individual symbols. Under certain code parameters, this approach enables significant speedup of modeling.

Effects of belief propagation computational precision on LDPC codes error floors

The influence of the computational precision used in BP decoder on LDPC codes performance is studied. It is shown that an error floor can be lowered and pseudo-codewords are made possible to decode by increasing computational precision.