A Concatenated Random Error and Burst Erasure Decoding Scheme for Random Noise and Burst Fading or Interference Channels (extended abstract)
Youshi Xu, I. Erasure Decoding · 1997
A concatenated random error correction and burst erasure recovering code scheme is proposed. This will significantly improve the performance of communication systems in some applications. This proposal is based on an efficient erasure decoding al- gorithm for binary block codes and an efficient appli- cation of the presence of fading or interference. In a communication system the receiver may be designed to declare an erasure whenever a received symbol is ambiguous, or when the receiver recognizes the presence of interference, deep fades or some transient malfunction. The traditional erasure decoding capability of binary BCH codes is bounded within the minimum distance of the codes, and decoding oper- ations are in nonbinary finite fields. In the paper we describe an erasure decoding algorithm for binary block codes, such as binary BCH codes. It shows that linear block codes can cor- rect erasures by solving a system of binary linear equations. All the operations of the decoding algorithm are in the binary field, and the decoding process needs only p2 logic XOR oper- ation times, where p is the number of erasures in the received word. More importantly, a computer investigation shows that the number of correctable multi-bursts erasures is approxi- mate to (n-k) for a binary BCH (n, k) code, provided the number of bursts is less than the minimum distance. For ex- ample, the BCH (1023, 513) code with minimum distance 115 is able to correct 25 randomly located bursts, each of which has a length of 20 erasures.