Universal Product Code

Abstract: A product channel code is proposed to protect progressively compressed and packetized image data that is transmitted across noisy channels. Across packets, the product code is composed of Reed-Solomon codes. Within packets, the product code uses the concatenation of a rate compatible punctured convolutional code and an error detecting parity check code. The benefits include flexibility in terms of delay, the ability to easily adapt the level of protection based on importance (i.e., unequal error protection), and scalable decoding complexity. The system outperforms the best known image coders for memoryless channels and performs well on fading channels.

Abstract: List-based algorithms for. decoding block turbo Codes (BTC) have gained popularity due to their low computational complexity. The normal way to calculate the soft outputs involves searching for a decision code word D and a competing codeword B. In addition, a scaling factor /spl alpha/ and an estimated reliability value /spl beta/ are used. In this letter, we present a new approach that does not require /spl alpha/ and /spl beta/. Soft outputs are generated based on the Euclidean distance property of decision code words. By using the new algorithm, we achieve better error performance with even less complexity-for certain BTCs.

Abstract: A method to verify a product produced by a manufacturer, the method comprising the steps of attaching a unique product code to a product prior to delivery to a retailer, storing the product code with product information in a first database linked to a verification system associated with the manufacturer, distributing the product to the retailer and selling the product from the retailer to a customer, the step of selling including the steps of using a first computer to obtain the unique product code from the product, providing the obtained product code to the verification system, comparing the obtained product code with the stored product code and when the obtained product code and the stored product code match, preparing a receipt including a verification code and providing the receipt to the customer.

Abstract: Summary form only given. This work introduces a multiple-description product code which aims at optimally generating multiple, equally-important wavelet image descriptions from an image encoded by the popular SPIHT image coder. Because the SPIHT image coder is highly sensitive to errors, forward error correction is used to protect the image against bit errors occurring in the channel. The error-correction code is a concatenated channel code including a row (outer) code based on RCPC codes with CRC error detection and a source-channel column (inner) code consisting of the scalable SPIHT image coder and an optimized array of unequal protection Reed-Solomon erasure-correction codes. By matching the unequal protection codes to the embedded source bitstream using our simple, fast optimizer, we maximize expected image quality and provide for graceful degradation of the received image during fades. To achieve unequal protection, each packet is split into many Reed-Solomon symbols. The i/sup th/ symbol in each packet forms an (n,k) Reed-Solomon code or "column". A fast, nearly-optimal optimizer, based on Lagrange multipliers and optimal to within convex hull and discretization approximations, chooses k for each Reed-Solomon "column" to minimize the expected mean-square error at the receiver. We validated our use of this structure by evaluating its performance in the context of transmitting images over a wireless fading channel. The performance of this scheme was evaluated by simulating the transmission of the Lena image over a Clarke flat-fading channel with an average SNR of 10 dB and a normalized Doppler frequency of 10/sup -5/ Hz.