A Distribution Matcher for Asymmetric Probabilistic Amplitude Shaping
Zihan Qu
Abstract:
A communication system, which consists of a transmitter and a receiver, models the process by which the information is sent and received. The transmitted symbols that are generated by a transmitter go through a noisy channel and reach the receiver end. The receiver needs to estimate the transmitted symbols by their noisy version. Claude Shannon developed a theory that determines the maximum rate at which the receiver can reliably estimate the transmitted symbols based on the noise’s statistics. To achieve the maximum rate, the transmitted signals need to approximately follow an optimal probability distribution, which can be done through probabilistic shaping. One method for probabilistic shaping is using a distribution matcher that takes a sequence of bits equally likely to be ones and zeros and maps it bijectively to a new sequence of symbols with the desired probability distribution. There are two types of distribution matchers denoted as constant and multi-composition distribution matchers or CCDMs and MCDMs. We coded a CCDM and an MCDM, which is a union of CCDMs. Two different versions of the MCDM based on a high probability and typical set rule were constructed. We found that MCDMs outperformed CCDMs in both Kullback–Leibler (KL) divergence, a measure of how well the desired distribution was met, and matching rate, meaning we can send more information using fewer bits. By applying MCDMs to channels, we can achieve higher transmission rates and better noise correction to increase the efficiency and speed of the internet and other communication systems.