The recently proposed unary error correction (UEC) and Elias gamma error correction (EGEC) codes facilitate the near-capacity joint source and channel coding (JSCC) of symbol values selected from large alphabets at a low complexity. Despite their large alphabet, these codes were only designed for a limited range of symbol value probability distributions. In this paper, we generalize the family of UEC and EGEC codes to the class of rice and exponential Golomb error correction codes, which have a much wider applicability, including the symbols produced by the H.265 video codec, the letters of the English alphabet, and in fact any arbitrary monotonic unbounded source distributions. Furthermore, the practicality of the proposed codes is enhanced to allow a continuous stream of symbol values to be encoded and decoded using only fixed-length system components. We explore the parameter space to offer beneficial tradeoffs between error correction capability, decoding complexity, as well as transmission-energy, -duration, and -bandwidth over a wide range of operating conditions. In each case, we show that our codes offer significant performance improvements over the best of several state-of-the-art benchmarkers. In particular, our codes achieve the same error correction capability, as well as transmission energy, transmission duration, and transmission bandwidth as a variable length error-correction code benchmarker, while reducing the decoding complexity by an order of magnitude. In comparison with the best of the other JSCC and separate source and channel coding benchmarkers, our codes consistently offer Eb/N0 gains of between 0.5 and 1.0 dB which only appear to be the modest, because the system operates close to capacity. These improvements are achieved for free, since they are not achieved at the cost of increasing transmission energy, transmission duration, transmission bandwidth, or decoding complexity.