Iterative decoding of Gold sequences

International audienceGold sequences are widely used in communications and positioning systems for synchronization purposes or spread spectrum transmissions. This paper addresses the decoding of the initial state of a Gold sequence. This can be used to detect a harmful interferer closed to a 3G femtocell base station and implement interference mitigation techniques. The decoder implements an iterative message-passing algorithm which is built upon a parity check matrix. Thus, it depends on the coding properties of Gold codes. In this paper, we synthesize the coding properties of Gold codes and use them to compute the number of parity check equations of weight t = 3, 4 or 5. Eventually, the impact of the parity check equations used for decoding is highlighted

On a Class of Optimal Nonbinary Linear Unequal-Error-Protection Codes for Two Sets of Messages

Several authors have addressed the problem of designing good linear unequal error protection (LUEP) codes. However, very little is known about good nonbinary LUEP codes. We present a class of optimal nonbinary LUEP codes for two different sets of messages. By combining t-error-correcting ReedSolomon (RS) codes and shortened nonbinary Hamming codes, we obtain nonbinary LUEP codes that protect one set of messages against any t or fewer symbol errors and the remaining set of messages against any single symbol error. For t ≥ 2, we show that these codes are optimal in the sense of achieving the Hamming lower bound on the number of redundant symbols of a nonbinary LUEP code with the same parameters