Victor V. Zyablov

Decoding of convolutional codes using a syndrome trellis

Soft-decision maximum-likelihood decoding of convolutional codes using the Viterbi algorithm with a syndrome trellis is proposed. The parity check matrix of a convolutional code is used to construct the trellis. This trellis is minimal. The number of operations for the decoding of one block of a q-ary rate k/n convolutional code is /spl sim/nq/sup min(k,n-k)/q/sup /spl nu//, where /spl nu/ is the memory size of the code. When the code rate satisfies k/n> 1/2 , the proposed algorithm is simpler than the classical Viterbi algorithm that has complexity /spl sim/nq/sup k/q/sup /spl nu//. >

Active distances for convolutional codes

A family of active distance measures for general convolutional codes is defined. These distances are generalizations of the extended distances introduced by Thommesen and Justesen (1983) for unit memory convolutional codes. It is shown that the error correcting capability of a convolutional code is determined by the active distances. The ensemble of periodically time-varying convolutional codes is defined and lower bounds on the active distances are derived for this ensemble. The active distances are very useful in the analysis of concatenated convolutional encoders.

Woven convolutional codes .I. Encoder properties

Encoders for convolutional codes with large free distances can be constructed by combining several less powerful convolutional encoders. This paper is devoted to constructions in which the constituent convolutional codes are woven together in a manner that resembles the structure of a fabric. The general construction is called twill and it is described together with two special cases, viz., woven convolutional encoders with outer warp and with inner warp. The woven convolutional encoders inherit many of their structural properties, such as minimality and catastrophicity, from their constituent encoders. For all three types of woven convolutional codes upper and lower bounds on their free distances as well as lower bounds on the active distances of their encoders are derived.

Improved performance of a random OFDMA mobile communication system

In this paper we consider the uplink performance of an OFDMA (orthogonal frequency division multiple access) system for mobile communications. First, we describe the random OFDMA system which is based on MC-FDMA (multicarrier FDMA), and where each user has a set of randomly selected subchannels. We also describe the performance criteria considered for the evaluation of this system and present different system implementations depending on the level of block synchronization assumed. In the last section we describe different methods for improving the system performance, one based on different receiver configurations and another based on different sets of subchannels per user depending on the traffic load. We also show some simulation results for the performance of the system under the different assumptions.

Array codes correcting a two-dimensional cluster of errors

A novel construction method is presented for array codes correcting a single rectangular error cluster of size b/sub 1//spl times/b/sub 2/ or less. Encoding is done in such a way that parity check symbols are calculated row-or columnwise which are a word of a one-dimensional code correcting a phased burst. These parity check symbols are not transmitted but can be calculated by the receiver. Corresponding decoding algorithms are given. A code is constructed with maximum size n/sub 1/=b/sub 1/2/sup b2/, n/sub 2/=b/sub 2/2/sup b1/, and r=3b/sub 1/b/sub 2/ redundancy symbols which is close to the generalized Singleton bound r/spl ges/2b/sub 1/b/sub 2/. Its encoding and decoding complexity are low.

Maximum slope convolutional codes

The slope is an important distance parameter for a convolutional code. It can be used to obtain a lower bound on the active burst distance and in this respect essentially determines the error-correcting capability of the code. An upper bound on the slope of rate R=b/c convolutional codes is derived. A new family of convolutional codes, called the maximum slope (MS) code family, is introduced. Tables for rate R=1/2 MS codes with memory 1/spl les/m/spl les/6 are presented. Additionally, some new rate R=(c-1)/c, 3/spl les/c/spl les/6, punctured convolutional codes with rate R=1/2 optimum free distance (OFD) and MS mother codes are presented. Simulation results for the bit error performance of serially concatenated turbo codes with MS component codes are presented.

On the equivalence of generalized concatenated codes and generalized error location codes

We show that the generator matrix of a generalized concatenated code (GCC code) of order L consists of L submatrices, where the lth submatrix is the Kronecker product of the generator matrices of the lth inner code and the lth outer code. In a similar way we show that the parity-check matrix of a generalized error location code (GEL code) of order L consists of L submatrices, where the lth submatrix is the Gronecker product of the parity-check matrices of the lth inner code and the lth outer code. Then we use these defining matrices to show that for any GCC code there exists an equivalent GEL code and vice versa.

Performance of a random OFDMA system for mobile communications

In this paper we consider the uplink performance of an OFDMA (orthogonal frequency division multiple access) system for mobile communications. We describe the random OFDMA system which is based on MC-FDMA (multicarrier FDMA), and where each user has a set of randomly selected subchannels. We also analyze the problem of block synchronization in an OFDM transmission. Then we describe three different system implementations depending on the underlying level of the block synchronization. We define the considered performance criteria and discuss the influence of the different system implementations. Finally, we show some simulation results for the performance of the different system implementations.

Woven convolutional codes. II: decoding aspects

An iterative decoding scheme for woven convolutional codes is presented. It operates in a window sliding over the received sequence. This exploits the nature of convolutional codewords as infinite sequences and reflects the concept of considering convolutional encoding and decoding as a continuous process. The decoder is analyzed in terms of decoding delay and decoding complexity. Its basic building block is a symbol-by-symbol a posteriori probability (APP) decoder for convolutional codes, which is a windowed variant of the well-known Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm. Additional interleaving for the woven constructions is introduced by employing convolutional scramblers. It is shown that row-wise random interleaving preserves the lower bound on the free distance of the original woven constructions. Based on the properties of the interleavers, new lower bounds on the free distance of woven constructions with both outer warp and inner warp are derived. Simulation results for woven convolutional codes with and without additional interleaving are presented.

Low-complexity GEL codes for digital magnetic storage systems

A class of concatenated block codes, called generalized error-locating (GEL) codes, is proposed for error correction in digital magnetic storage systems. GEL codes are suited for high code rate applications with low-complexity (hard input) decoding algorithms. They offer high flexibility and can be adjusted to a variety of different situations. In this paper, we use as an example a (precoded) PR4 channel and consider GEL codes with BCH and Reed-Solomon component codes. Simulation results give bit error rates with and without constrained codes.