International Journal of Computer Applications (0975 – 8887) Volume 9– No.1, November 2010 1 An HARQ based Optimized Error Correction Technique Kaustuv Kunal Indian Institute of Information Technology, Allahabad, India R. C. Tripathi Indian Institute of Information Technology, Allahabad, India Vrijendra Singh Indian Institute of Information Technology, Allahabad, India ABSTRACT Errors during data communication are inevitable. Noise in the channel leads to bit error. The paper proposes a matrix based novel bits encoding technique, aim to achieve error correction capability with optimize redundancy. Furthermore an efficient software based decoding algorithm to detect and correct transmission errors is introduced. Here errors include single bit error, multiple bits error and burst errors. The proposed technique maintains high code rate, provides multiple bit error correction capability and can best be implemented as hybrid automatic repeat request (HARQ). General Terms Error correcting codes, bits encoding, decoding Keywords Error detection, error correction, forward error correction, automatic repeat request, hybrid automatic repeat request 1. INTRODUCTION Data communication over the data networks comprising of various carriers like repeater, hub, gateways etc is prone to errors because of reasons such as traffic congestion, delay, network components getting down, packet drop, non receipt of acknowledgements and signaling factors. Automatic repeat request (ARQ) and forward error correction (FEC) are strategies to combat error. ARQ proposes retransmission. Retransmission is not a desirable option particularly in long distance and wireless communication such as through satellite. In FEC, redundancy is added for error prevention. Redundant bits are encapsulated with data bits to form encoded information. However this increases the payload for transmission. Addition of redundant bit is known as channel coding. Error correcting codes (ECC) are used for this purpose. Reliability can be enhanced by combining FEC and ARQ as Hybrid-ARQ (HARQ). First significant ECC as a way of systematic codes was introduced by Hamming [1].He corrected one error per block of code using parity and adjusted it to detect up to two bit error. Elias [2] improved the efficiency with his second order check product codes (figure 1) and further emphasized that it is not necessary to use the same kind of code at each stage of iterative process. BCH code[3,4,5],a multiple bit ECC, is a further generalization of hamming code where 2m-1 bits comprising of mt redundant bits enable correction up to t-bits error. Other significant ECC include Reed Muller code [6, 7], Low density parity check code (LDPC) [8, 9, 10] and turbo code [11, 12]. FEC has reliability issues and ARQ suffers with degrading throughput. A solution is to combine both. Such a scheme is termed as hybrid ARQ [13, 14]. The proposed technique achieves multiple bit correction capability after encoding with high code rate. It uses outlines of product codes and encode message in the form of matrix. Row and column encoding method are dissimilar with an objective to achieve maximum correction capability with minimum redundancy. Our proposed technique when used as HARQ is able to archive high throughput as well as high reliability. Proposed technique has been described under next two sub sections information encoding and information decoding. Performance analysis, limitations and assumptions are discussed in section III followed by conclusion. Theoretical and software level implementation are discussed. Figure 1 : Organization of first and second order check digits by Elias 2. PROPOSED TECHNIQUE 2.1 Information Encoding Data bits are encoded into fixed size matrix. This size should be agreed upon and known to both sender as well as receiver. Matrix structure outlines figure1 and is shown in figure 2. A