Exploiting Locality for Improved Decoding of Binary Cyclic Codes

In this paper, we show how the presence of locality within a binary cyclic code can be exploited to improve decoding performance and to reduce decoding complexity. We pursue two approaches. Under the first approach, we show how the ordered statistics decoding (OSD) method can be modified by inserting a simple single round belief-propagation step at the start that involves only the local codes. The resultant locality-aware OSD algorithm yields an appreciable signal-to-noise ratio (SNR) gain for a given level of reliability and essentially the same level of decoder complexity. Under the second, trellis decoding approach, we show that the careful introduction of locality results in the creation of a cyclic subcode that possesses lower maximum state complexity. In addition, we present a simple means of deriving an upper bound to the state complexity profile of any cyclic code that is based only on the zeros of the code. Furthermore, we show how the decoding speed of either locality-aware OSD or trellis decoding can be significantly increased in the presence of locality, in the moderate-to-high SNR regime, by making the use of a quick-look decoder that often returns the maximum likelihood code word.