We present a novel time-multiplexed codec for a class of low-density parity-check codes, which switches between analog decode and digital encode modes. In order to achieve this behaviour from a single circuit we have developed mode-switching gates. These logic gates are able to switch between analog (soft) and digital (hard) computation. Only a small overhead in circuit area is required to transform the analog decoder into a full codec. The encode operation can be performed two orders of magnitude faster than the decode operation, making the circuit suitable for full-duplex applications. Throughput of the codec scales linearly with block size, for both encode and decode operations. The low power and small area requirements of the circuit make it an attractive option for small portable devices.