In .NET Core, you can use the RabbitMQ.Client library to realize the interaction with RabbitMQ. I will demonstrate how to implement RabbitMQ's dead letter queue using the RabbitMQ.Client library.

using RabbitMQ.Client;
using RabbitMQ.Client.Events;
using System;
using System.Collections.Generic;
using System.Text;

class Program
{
    static void Main(string[] args)
    {
        var factory = new ConnectionFactory() { HostName = "localhost" };
        using (var connection = factory.CreateConnection())
        {
            using (var channel = connection.CreateModel())
            {
                // Define a dead letter exchange
                channel.ExchangeDeclare("dead-letter-exchange", ExchangeType.Direct);

                // Define a dead letter queue
                var deadLetterQueueArgs = new Dictionary<string, object>
                {
                    { "x-dead-letter-exchange", "dead-letter-exchange" },
                    { "x-message-ttl", 60000 } // The message timeout is set to 60 seconds
                };
                channel.QueueDeclare("dead-letter-queue", true, false, false, deadLetterQueueArgs);

                // define queue
                var queueName = "my-queue";
                channel.QueueDeclare(queueName, true, false, false, null);

                // Bind the queue to a dead letter exchange
                channel.QueueBind(queueName, "dead-letter-exchange", "my-routing-key");

                // Define a message consumer
                var consumer = new EventingBasicConsumer(channel);
                consumer.Received += (model, ea) =>
                {
                    var body = ea.Body;
                    var message = Encoding.UTF8.GetString(body.ToArray());
                    Console.WriteLine($"Received message:{message}");
                };
                channel.BasicConsume(queueName, true, consumer);

                // Send a message
                var message = "Hello RabbitMQ!";
                var body = Encoding.UTF8.GetBytes(message);
                var properties = channel.CreateBasicProperties();
                properties.Persistent = true;
                properties.Expiration = "5000"; // The message expiration time is set to 5 seconds
                channel.BasicPublish("", queueName, properties, body);

                Console.WriteLine("Press any key to exit.");
                Console.ReadKey();
            }
        }
    }
}

In this example, a connection factory object is first created and the host name of the RabbitMQ server is set to "localhost". I then use that connection factory to create a connection object and use that connection object to create a channel object.

Then define a dead letter exchange called "dead-letter-exchange" and set its type to "direct". Then, I defined a dead letter queue named "dead-letter-queue", and set two parameters, one is "x-dead-letter-exchange", and the name of the dead letter exchange is specified as "dead- letter-exchange", and the other is "x-message-ttl", which specifies a message timeout of 60 seconds.

Define a queue named "my-queue" and bind it to the dead letter exchange, using "my-routing-key" as the routing key. Next, I define a message consumer and register an event handler to handle incoming messages. Finally, I sent a message with "Hello RabbitMQ!" as the message content, and posted it to the queue, using a persistent message property with an expiration time of 5 seconds.

Running will see that a message is sent to the queue, received by the consumer and output to the console. Also, if you don't press any key within 5 seconds, this message will expire, because I set its expiration time to 5 seconds.

Note that in this example, I used a Dictionary<string, object> to define the parameters of the dead letter queue. This is because RabbitMQ's C# client uses a generic "AMQP protocol frame" to send and receive messages, and this protocol frame allows any type of value to be used as a parameter. Therefore, I can use a Dictionary to define parameters of any type, not just simple types like strings or integers.

In addition, it should be noted that in actual use, more factors need to be considered, such as message confirmation mechanism, message serialization method, and so on.