The paper explores the relationship between entanglement purification protocols (EPPs) and quantum error-correcting codes (QECCs) in protecting quantum states from environmental noise. It proves that an EPP involving one-way classical communication on a mixed state $\hat{M}$ (obtained by sharing halves of EPR pairs through a noisy channel $\chi$) yields a QECC on $\chi$ with rate $Q = D$, and vice versa. The paper compares the entanglement $E(M)$ required to prepare a mixed state $M$ with the amounts $D_1(M)$ and $D_2(M)$ that can be locally distilled from it using one- and two-way classical communication, respectively, and provides an exact expression for $E(M)$ when $M$ is Bell-diagonal. It shows that while EPPs require classical communication, QECCs do not, and adding one-way classical communication does not increase $Q$. However, both $D$ and $Q$ can be increased by adding two-way communication. The paper also demonstrates that certain noisy quantum channels, such as a 50% depolarizing channel, can be used for reliable transmission of quantum states if two-way communication is available, but not if only one-way communication is available. Additionally, it presents a family of codes based on universal hashing that can achieve an asymptotic $Q$ (or $D$) of $1 - S$ for simple noise models, where $S$ is the error entropy. Finally, it provides a specific, simple 5-bit single-error-correcting quantum block code and proves that if a QECC results in high fidelity for the case of no error, it can be recast into a form where the encoder is the matrix inverse of the decoder.The paper explores the relationship between entanglement purification protocols (EPPs) and quantum error-correcting codes (QECCs) in protecting quantum states from environmental noise. It proves that an EPP involving one-way classical communication on a mixed state $\hat{M}$ (obtained by sharing halves of EPR pairs through a noisy channel $\chi$) yields a QECC on $\chi$ with rate $Q = D$, and vice versa. The paper compares the entanglement $E(M)$ required to prepare a mixed state $M$ with the amounts $D_1(M)$ and $D_2(M)$ that can be locally distilled from it using one- and two-way classical communication, respectively, and provides an exact expression for $E(M)$ when $M$ is Bell-diagonal. It shows that while EPPs require classical communication, QECCs do not, and adding one-way classical communication does not increase $Q$. However, both $D$ and $Q$ can be increased by adding two-way communication. The paper also demonstrates that certain noisy quantum channels, such as a 50% depolarizing channel, can be used for reliable transmission of quantum states if two-way communication is available, but not if only one-way communication is available. Additionally, it presents a family of codes based on universal hashing that can achieve an asymptotic $Q$ (or $D$) of $1 - S$ for simple noise models, where $S$ is the error entropy. Finally, it provides a specific, simple 5-bit single-error-correcting quantum block code and proves that if a QECC results in high fidelity for the case of no error, it can be recast into a form where the encoder is the matrix inverse of the decoder.