Algebraic soft-decoding of Reed-Solomon codes

1 Foreword This text is divided in two parts. The first one, the prerequisites, introduces all the necessary concepts of coding theory. If the reader is familiar with the basics of information and coding theory, he might skip this part and go directly to the second part, which is the core of this thesis. This second part studies an algorithm which improves the decoding of Reed-Solomon codes. For readers familiar with coding theory, the second part is gently introduced also making it directly accessible. Error-correcting codes are used to add redundancy to data to make it fault tolerant (up to a certain degree). Roughly said, the typical way to do it is to encode sequences of bits to longer sequences of bits by adding structured redundancy in it. That way, even if some bits are corrupted, but not too many, the structured redundancy enables us to retrieve the original data. One of the most efficient and widely used type of error-correcting codes are precisely Reed-Solomon codes. Both because of their good properties and their efficient decoding techniques. The algorithm presented here runs in polynomial time and provides more powerful decoding than conventional decoding algorithms. A more precise and exhaustive description can be found in the introduction of the second part of this text.