Viktor V. Zyablov

Woven convolutional codes and unequal error protection

Woven convolutional codes with outer warp are used to construct a generator matrix with an effective free distance vector that is lower bounded by the free distances of the component codes. This enables the construction of convolutional codes with unequal error protection.

Encoder and Distance Properties of Woven Convolutional Codes with One Tailbiting Component Code

Woven convolutional codes with one tailbiting component code are studied and their generator matrices are given. It is shown that, if the constituent encoders are identical, a woven convolutional encoder with an outer convolutional warp and one inner tailbiting encoder (WIT) generates the same code as a woven convolutional encoder with one outer tailbiting encoder and an inner convolutional warp (WOT). However, for rate Rtb < 1 tailbiting encoders, the WOT cannot be an encoder realization with a minimum number of delay elements. Lower bounds on the free distance and active distances of woven convolutional codes with a tailbiting component code are given. These bounds are equal to those for woven codes consisting exclusively of unterminated convolutional codes. However, for woven convolutional codes with one tailbiting component code, the conditions for the bounds to hold are less strict.

Distance Approach to Window Decoding

In convolutional coding, code sequences have infinite length; thus, a maximum-likelihood decoder implies an infinite delay. Due to memory and delay constraints in practical coding schemes, convolutional codes often are either terminated or decoded by a window decoder. When a window decoder is used, the convolutional code sequence is not terminated; instead, the window decoder estimates information digits after receiving a finite number of noise-corrupted code symbols, thereby keeping the decoding delay short. An exact characterization of the error-correcting capability of window decoded convolutional codes is given by using active distances of convolutional codes.

On the distribution of the output error burst lengths for Viterbi decoding of convolutional codes

The distribution of the output error burst lengths from a Viterbi decoder is of particular interest in connection with concatenated coding systems, where the inner code is convolutional. From the expurgated, random, and sphere-packing exponents for block codes an upper bound on this distribution for the ensemble of periodically time-varying convolutional codes is obtained. Finally, the distribution obtained from simulating time-invariant convolutional codes is presented.

An upper bound on the slope of convolutional codes

The slope is an important distance parameter of a convolutional code. It essentially determines the error-correcting capability. Here we derive an upper bound on the slope.

On the burst error detecting and erasure correcting capabilities of convolutional codes

In this paper it is shown how a convolutional code can be used either to detect errors or to correct erasures. The erasure correction is related to the error detection. Using the active burst distance lower bounds on the error and erasure correction as well as error detection are obtained for convolutional codes.

Some distance properties of tailbiting codes

The active tailbiting segment distance for convolutional codes is introduced. Together with the earlier defined active burst distance, it describes the error correcting capability of a tailbiting code encoded by a convolutional encoder. Lower bounds on the new active distance as well as an upper bound on the ratio between tailbiting length and memory of the encoder such that its minimum distance d/sub min/ equals the free distance d/sub free/ of the corresponding convolutional code are presented.

Active distances and cascaded convolutional codes

A family of active distances for convolutional codes is introduced. Lower bounds are derived for the ensemble of periodically time-varying convolutional codes.