Convolutional codes for iterative decoding

Abstract

This paper gives an overview of three different classes of convolutional codes that are suitable for iterative decoding. They are characterized by the type of component codes that are used to construct the overall codes, which can be trivial parity-check constraints, block component codes, or convolutional component codes. Distance properties and iterative decoding performance are considered. All three classes of codes are asymptotically good, allow simple encoding, and can be decoded efficiently using iterative pipeline decoding architectures. I. INTRODUCTION Error correcting codes defined by sparse parity-check ma- trices in combination with iterative decoding have proved to be very efficient in both theory and practice. The most prominent representatives of iteratively decodable codes are the low-density parity-check (LDPC) block codes invented by Gallager (1) and the turbo codes introduced by Berrou, Glavieux, and Thitimajshima (2). Also, convolutional codes designed for iterative decoding combine excellent bit error rate (BER) performance with the additional advantage that their structure allows linear time encoding based on shift-registers, a parallel pipeline implementation of iterative decoding, and block transmission in frames of arbitrary size, which makes them attractive for practical implementation. In this paper, we consider three different classes of con- volutional codes. First, the convolutional code counterpart of Gallager's LDPC block codes is described in Section II. Then, in Section III, we introduce convolutional codes with block components, called braided block codes (BBCs). A similar construction based on convolutional components, braided con- volutional codes (BCCs), are considered in Section IV. The distance properties and iterative decoding performance of the different code classes are presented in Sections V and VI, respectively. Section VII concludes the paper.