CIRC Encoding vs Decoding: Understanding the Differences and Advantages

This page compares CIRC Encoding vs CIRC Decoding and mentions the difference between CIRC Encoding and CIRC Decoding, including the advantages of the CIRC encoder.

Introduction: CIRC stands for Cross-Interleaved Reed-Solomon Code. It is used in Compact Disc (CD) systems to provide error detection and correction. The CD digital audio system was defined for digital storage and reproduction by Philips Corp. There are several sources of channel errors, such as small unwanted particles or air bubbles in plastic material and scratches during handling.

CIRC Encoder and CIRC Decoder

CIRC encoding adds one redundant parity byte to every three data bytes. CIRC is a concatenated error control scheme that contributes to high fidelity performance, in which data are rearranged in time. Due to this arrangement, error bursts are made to appear as single random events. The figure depicts the CIRC encoder and CIRC decoder block diagram.

CIRC Encoding using CIRC Encoder

CIRC Encoding

Let’s understand CIRC encoding step by step on a system frame consisting of 24 symbols and a frame size of 6 sampling periods.

• Step-1: Even-numbered samples are separated from odd-numbered samples by two frames in time to detect byte errors.
• Step-2: Four R-S parity bytes are added to the interleaved 24-byte frame. (28,24) code is the outer code.
• Step-3: Each byte is delayed by different lengths, which spread errors over several codewords. C2 encoding and D* interleaving correct the burst errors and error patterns.
• Step-4: Four R-S parity bytes are added to the Δ interleaved 28-byte frame. (32, 28) is the inner code.
• Step-5: The purpose is to cross-interleave even bytes of the frame with odd bytes of the next frame. D interleaving and C1 decoding correct most random single errors and detect longer burst errors.

CIRC Decoding using CIRC Decoder

The inner and outer R-S codes with (n,k) -> (32,28) and (28,24) each use four parity bytes. The code rate of CIRC is (k1/n1)(k2/n2) = 24/32 = 3/4. C1 and C2 decoders can correct a maximum of 2 symbol errors or 4 symbol erasures per codeword.

CIRC Decoding Equations

Let’s understand the CIRC decoding process step by step.

CIRC Decoding

• Step-1: D Deinterleaver: Alternate delay lines, and each delay is equal to 1 byte.
• Step-2: C1 Decoder: If multiple errors occur, the C1 decoder attaches an erasure flag.
• Step-3: D* Deinterleaver: Errors at the output of C1 are spread over a number of words at the input of the C2 decoder. Reducing the number of errors enables the C2 decoder to correct these errors.
• Step-4: C2 Decoder: Corrects the burst errors that C1 could not correct. If the C2 decoder cannot correct the 24-byte codeword, it’s passed on unchanged to the deinterleaver and given an erasure flag.
• Δ Deinterleaver: Detects the byte errors using interpolation.

Advantages of CIRC Encoder

From the above, we can summarize the benefits or advantages of the CIRC Encoder as follows:

• It is useful to correct combinations of both random error and burst error. It offers higher random error correctability.
• It can correct error bursts with about 3500 bits in sequence. This corresponds to about 2.5 mm in length on the CD surface.
• It can compensate for long error bursts with 12 Kbits (i.e., 8.5 mm) that occurred due to minor scratches.
• It offers very high efficiency.

The only disadvantage of the CIRC technique is its addition of redundant bytes. The samples which cannot be corrected by the C2 decoder could cause disturbances. To avoid this condition, the interpolation process inserts new samples in place of unreliable ones.

References:

• Presentation by Diana B. Llacza Sosaya on Digital Communications at Chosun University, available at the following link: https://slideplayer.com/slide/10560809/