Applied Advanced Error Control Coding for General Purpose Representation and Association Machine Systems

General-Purpose Representation and Association Machine (GPRAM) is proposed to be focusing on computations in terms of variation and flexibility, rather than precision and speed. GPRAM system has a vague representation and has no predefined tasks. With several important lessons learned from error control coding, neuroscience and human visual system, we investigate several types of error control codes, including Hamming code and Low-Density Parity Check (LDPC) codes, and extend them to different directions. While in error control codes, solely XOR logic gate is used to connect different nodes. Inspired by bio-systems and Turbo codes, we suggest and study non-linear codes with expanded operations, such as codes including AND and OR gates which raises the problem of prior-probabilities mismatching. Prior discussions about critical challenges in designing codes and iterative decoding for non-equiprobable symbols may pave the way for a more comprehensive understanding of bio-signal processing. The limitation of XOR operation in iterative decoding with non-equiprobable symbols is described and can be potentially resolved by applying quasi-XOR operation and intermediate transformation layer. Constructing codes for non-equiprobable symbols with the former approach cannot satisfyingly perform with regarding to error correction capability. Probabilistic messages for sum-product algorithm using XOR, AND, and OR operations with non-equiprobable symbols are further computed. The primary motivation for the constructing codes is to establish the GPRAM system rather than to conduct error control coding per se. The GPRAM system is fundamentally developed by applying various operations with substantial over-complete basis. This system is capable of continuously achieving better and simpler approximations for complex tasks. The approaches of decoding LDPC codes with non-equiprobable binary symbols are discussed due to the aforementioned prior-probabilities mismatching problem. The traditional Tanner graph should be modified because of the distinction of message passing to information bits and to parity check bits from check nodes. In other words, the message passing along two directions are identical in conventional Tanner graph, while the message along the forward direction and backward direction are different in our case. A method of optimizing signal constellation is described, which is able to maximize the channel mutual information. A simple Image Processing Unit (IPU) structure is proposed for GPRAM system, to which images are inputted. The IPU consists of a randomly constructed LDPC code, an iterative decoder, a switch, and scaling and decision device. The quality of input images has been severely deteriorated for the purpose of mimicking visual information variability (VIV) experienced in human visual systems. The IPU is capable of (a) reliably recognizing digits from images of which quality is extremely inadequate; (b) achieving similar hyper-acuity performance comparing to human visual system; and (c) significantly improving the recognition rate with applying randomly constructed LDPC code, which is not specifically optimized for the tasks

Low Density Parity Check Codes With Non-Equiprobable Symbols

In this letter, we analyze how to decode LDPC codes with non-equiprobable binary symbols. For such symbols, we need to modify the conventional Tanner graph, because the message passing from check nodes to information bits and to parity check bits are diverse. In other words, in conventional Tanner graph, the message passing along two directions are identical, while in our case, the message along the forward direction and backward direction are different. A method to optimize signaling constellation which maximizes the channel mutual information is presented as well. In the numerical section, symbols with prior probabilities (0.3,0.7) could gain 0.72 dB in performance if we replace equal space constellation with optimal constellation. Several cases of short LDPC codes (N, K =1024, 512) are explored and gain almost 0.4 dB. The simulation shows that additional gain of only 0.2 dB could be attainable, if optimal source coding is achievable. © 1997-2012 IEEE

Low Density Parity Check Codes with Non-Equiprobable Symbols

In this letter, we analyze how to decode LDPC codes with non-equiprobable binary symbols. For such symbols, we need to modify the conventional Tanner graph, because the message passing from check nodes to information bits and to parity check bits are diverse. In other words, in conventional Tanner graph, the message passing along two directions are identical, while in our case, the message along the forward direction and backward direction are different. A method to optimize signaling constellation which maximizes the channel mutual information is presented as well. In the numerical section, symbols with prior probabilities (0.3, 0.7) could gain 0.72 dB in performance if we replace equal space constellation with optimal constellation. Several cases of short LDPC codes (N, K = 1024, 512) are explored and gain almost 0.4 dB. The simulation shows that additional gain of only 0.2 dB could be attainable, if optimal source coding is achievable