New convolutional code constructions and a class of asymptotically good time-varying codes

New Convolutional Code Constructions and a C lass of Asymptotically Good T ime-Varying Codes

Asymptotically Good Convolutional Codes

In this paper, we construct new sequences of asymptotically good convolutional codes (AGCC). These sequences are obtained from sequences of transitive, self-orthogonal and self-dual algebraic geometry (AG) codes attaining the Tsfasman-Vladut-Zink bound. Furthermore, by applying the techniques of expanding, extending, puncturing, direct sum, the 〈u|u+ v〉 construction and the product code constru...

On classes of convolutional codes that are not asymptotically catastrophic

Denote by w 0 the minimum average weight per edge over all nonzero cycles in the state diagram for a convolutional code, and assume that a technique is available for generating canonical parity-check matrices for codes with increasing degree m. The obtained class of codes is asymptotically catastrophic if w 0 approaches zero for large m. In this paper we prove the existence of convolutional cod...

A New Construction for Low Density Parity Check Convolutional Codes

Low density parity check (LDPC) block codes have been shown to achieve near capacity performance for binary transmission over noisy channels. Block codes, however, require splitting the data to be transmitted into frames, which can be a disadvantage in some applications. Convolutional codes, on the other hand, have no such requirement, and are hence well suited for continuous transmission. In [...

Linear-Time Encodable Error-Correcting Codes Decodable

We present a new class of asymptotically good, linear error-correcting codes. These codes can be both encoded and decoded in linear time. They can also be encoded by logarithmicdepth circuits of l inear size and decoded by logarithmic depth circuits of size O(n log n). W e present both randomized and explicit constructions of these codes. a generator matrix. The second complexity is the time it...